A feedback linearization approach to spacecraft control using momentum exchange devices. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Dzielski, John Edward

1988-01-01

Recent developments in the area of nonlinear control theory have shown how coordiante changes in the state and input spaces can be used with nonlinear feedback to transform certain nonlinear ordinary differential equations into equivalent linear equations. These feedback linearization techniques are applied to resolve two problems arising in the control of spacecraft equipped with control moment gyroscopes (CMGs). The first application involves the computation of rate commands for the gimbals that rotate the individual gyroscopes to produce commanded torques on the spacecraft. The second application is to the long-term management of stored momentum in the system of control moment gyroscopes using environmental torques acting on the vehicle. An approach to distributing control effort among a group of redundant actuators is described that uses feedback linearization techniques to parameterize sets of controls which influence a specified subsystem in a desired way. The approach is adapted for use in spacecraft control with double-gimballed gyroscopes to produce an algorithm that avoids problematic gimbal configurations by approximating sets of gimbal rates that drive CMG rotors into desirable configurations. The momentum management problem is stated as a trajectory optimization problem with a nonlinear dynamical constraint. Feedback linearization and collocation are used to transform this problem into an unconstrainted nonlinear program. The approach to trajectory optimization is fast and robust. A number of examples are presented showing applications to the proposed NASA space station.

Non-linear feedback control of the p53 protein-mdm2 inhibitor system using the derivative-free non-linear Kalman filter.

PubMed

Rigatos, Gerasimos G

2016-06-01

It is proven that the model of the p53-mdm2 protein synthesis loop is a differentially flat one and using a diffeomorphism (change of state variables) that is proposed by differential flatness theory it is shown that the protein synthesis model can be transformed into the canonical (Brunovsky) form. This enables the design of a feedback control law that maintains the concentration of the p53 protein at the desirable levels. To estimate the non-measurable elements of the state vector describing the p53-mdm2 system dynamics, the derivative-free non-linear Kalman filter is used. Moreover, to compensate for modelling uncertainties and external disturbances that affect the p53-mdm2 system, the derivative-free non-linear Kalman filter is re-designed as a disturbance observer. The derivative-free non-linear Kalman filter consists of the Kalman filter recursion applied on the linearised equivalent of the protein synthesis model together with an inverse transformation based on differential flatness theory that enables to retrieve estimates for the state variables of the initial non-linear model. The proposed non-linear feedback control and perturbations compensation method for the p53-mdm2 system can result in more efficient chemotherapy schemes where the infusion of medication will be better administered.

Adaptive neural network decentralized backstepping output-feedback control for nonlinear large-scale systems with time delays.

PubMed

Tong, Shao Cheng; Li, Yong Ming; Zhang, Hua-Guang

2011-07-01

In this paper, two adaptive neural network (NN) decentralized output feedback control approaches are proposed for a class of uncertain nonlinear large-scale systems with immeasurable states and unknown time delays. Using NNs to approximate the unknown nonlinear functions, an NN state observer is designed to estimate the immeasurable states. By combining the adaptive backstepping technique with decentralized control design principle, an adaptive NN decentralized output feedback control approach is developed. In order to overcome the problem of "explosion of complexity" inherent in the proposed control approach, the dynamic surface control (DSC) technique is introduced into the first adaptive NN decentralized control scheme, and a simplified adaptive NN decentralized output feedback DSC approach is developed. It is proved that the two proposed control approaches can guarantee that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded, and the observer errors and the tracking errors converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approaches.

Adaptive Neural Output-Feedback Control for a Class of Nonlower Triangular Nonlinear Systems With Unmodeled Dynamics.

PubMed

Wang, Huanqing; Liu, Peter Xiaoping; Li, Shuai; Wang, Ding

2017-08-29

This paper presents the development of an adaptive neural controller for a class of nonlinear systems with unmodeled dynamics and immeasurable states. An observer is designed to estimate system states. The structure consistency of virtual control signals and the variable partition technique are combined to overcome the difficulties appearing in a nonlower triangular form. An adaptive neural output-feedback controller is developed based on the backstepping technique and the universal approximation property of the radial basis function (RBF) neural networks. By using the Lyapunov stability analysis, the semiglobally and uniformly ultimate boundedness of all signals within the closed-loop system is guaranteed. The simulation results show that the controlled system converges quickly, and all the signals are bounded. This paper is novel at least in the two aspects: 1) an output-feedback control strategy is developed for a class of nonlower triangular nonlinear systems with unmodeled dynamics and 2) the nonlinear disturbances and their bounds are the functions of all states, which is in a more general form than existing results.

Fuzzy Adaptive Decentralized Optimal Control for Strict Feedback Nonlinear Large-Scale Systems.

PubMed

Sun, Kangkang; Sui, Shuai; Tong, Shaocheng

2018-04-01

This paper considers the optimal decentralized fuzzy adaptive control design problem for a class of interconnected large-scale nonlinear systems in strict feedback form and with unknown nonlinear functions. The fuzzy logic systems are introduced to learn the unknown dynamics and cost functions, respectively, and a state estimator is developed. By applying the state estimator and the backstepping recursive design algorithm, a decentralized feedforward controller is established. By using the backstepping decentralized feedforward control scheme, the considered interconnected large-scale nonlinear system in strict feedback form is changed into an equivalent affine large-scale nonlinear system. Subsequently, an optimal decentralized fuzzy adaptive control scheme is constructed. The whole optimal decentralized fuzzy adaptive controller is composed of a decentralized feedforward control and an optimal decentralized control. It is proved that the developed optimal decentralized controller can ensure that all the variables of the control system are uniformly ultimately bounded, and the cost functions are the smallest. Two simulation examples are provided to illustrate the validity of the developed optimal decentralized fuzzy adaptive control scheme.

Data-driven model reference control of MIMO vertical tank systems with model-free VRFT and Q-Learning.

PubMed

Radac, Mircea-Bogdan; Precup, Radu-Emil; Roman, Raul-Cristian

2018-02-01

This paper proposes a combined Virtual Reference Feedback Tuning-Q-learning model-free control approach, which tunes nonlinear static state feedback controllers to achieve output model reference tracking in an optimal control framework. The novel iterative Batch Fitted Q-learning strategy uses two neural networks to represent the value function (critic) and the controller (actor), and it is referred to as a mixed Virtual Reference Feedback Tuning-Batch Fitted Q-learning approach. Learning convergence of the Q-learning schemes generally depends, among other settings, on the efficient exploration of the state-action space. Handcrafting test signals for efficient exploration is difficult even for input-output stable unknown processes. Virtual Reference Feedback Tuning can ensure an initial stabilizing controller to be learned from few input-output data and it can be next used to collect substantially more input-state data in a controlled mode, in a constrained environment, by compensating the process dynamics. This data is used to learn significantly superior nonlinear state feedback neural networks controllers for model reference tracking, using the proposed Batch Fitted Q-learning iterative tuning strategy, motivating the original combination of the two techniques. The mixed Virtual Reference Feedback Tuning-Batch Fitted Q-learning approach is experimentally validated for water level control of a multi input-multi output nonlinear constrained coupled two-tank system. Discussions on the observed control behavior are offered. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

A nonlinear Kalman filtering approach to embedded control of turbocharged diesel engines

NASA Astrophysics Data System (ADS)

Rigatos, Gerasimos; Siano, Pierluigi; Arsie, Ivan

2014-10-01

The development of efficient embedded control for turbocharged Diesel engines, requires the programming of elaborated nonlinear control and filtering methods. To this end, in this paper nonlinear control for turbocharged Diesel engines is developed with the use of Differential flatness theory and the Derivative-free nonlinear Kalman Filter. It is shown that the dynamic model of the turbocharged Diesel engine is differentially flat and admits dynamic feedback linearization. It is also shown that the dynamic model can be written in the linear Brunovsky canonical form for which a state feedback controller can be easily designed. To compensate for modeling errors and external disturbances the Derivative-free nonlinear Kalman Filter is used and redesigned as a disturbance observer. The filter consists of the Kalman Filter recursion on the linearized equivalent of the Diesel engine model and of an inverse transformation based on differential flatness theory which enables to obtain estimates for the state variables of the initial nonlinear model. Once the disturbances variables are identified it is possible to compensate them by including an additional control term in the feedback loop. The efficiency of the proposed control method is tested through simulation experiments.

Regional robust stabilisation and domain-of-attraction estimation for MIMO uncertain nonlinear systems with input saturation

NASA Astrophysics Data System (ADS)

Azizi, S.; Torres, L. A. B.; Palhares, R. M.

2018-01-01

The regional robust stabilisation by means of linear time-invariant state feedback control for a class of uncertain MIMO nonlinear systems with parametric uncertainties and control input saturation is investigated. The nonlinear systems are described in a differential algebraic representation and the regional stability is handled considering the largest ellipsoidal domain-of-attraction (DOA) inside a given polytopic region in the state space. A novel set of sufficient Linear Matrix Inequality (LMI) conditions with new auxiliary decision variables are developed aiming to design less conservative linear state feedback controllers with corresponding larger DOAs, by considering the polytopic description of the saturated inputs. A few examples are presented showing favourable comparisons with recently published similar control design methodologies.

Reinforcement-learning-based dual-control methodology for complex nonlinear discrete-time systems with application to spark engine EGR operation.

PubMed

Shih, Peter; Kaul, Brian C; Jagannathan, S; Drallmeier, James A

2008-08-01

A novel reinforcement-learning-based dual-control methodology adaptive neural network (NN) controller is developed to deliver a desired tracking performance for a class of complex feedback nonlinear discrete-time systems, which consists of a second-order nonlinear discrete-time system in nonstrict feedback form and an affine nonlinear discrete-time system, in the presence of bounded and unknown disturbances. For example, the exhaust gas recirculation (EGR) operation of a spark ignition (SI) engine is modeled by using such a complex nonlinear discrete-time system. A dual-controller approach is undertaken where primary adaptive critic NN controller is designed for the nonstrict feedback nonlinear discrete-time system whereas the secondary one for the affine nonlinear discrete-time system but the controllers together offer the desired performance. The primary adaptive critic NN controller includes an NN observer for estimating the states and output, an NN critic, and two action NNs for generating virtual control and actual control inputs for the nonstrict feedback nonlinear discrete-time system, whereas an additional critic NN and an action NN are included for the affine nonlinear discrete-time system by assuming the state availability. All NN weights adapt online towards minimization of a certain performance index, utilizing gradient-descent-based rule. Using Lyapunov theory, the uniformly ultimate boundedness (UUB) of the closed-loop tracking error, weight estimates, and observer estimates are shown. The adaptive critic NN controller performance is evaluated on an SI engine operating with high EGR levels where the controller objective is to reduce cyclic dispersion in heat release while minimizing fuel intake. Simulation and experimental results indicate that engine out emissions drop significantly at 20% EGR due to reduction in dispersion in heat release thus verifying the dual-control approach.

Steady-State Solutions Originating from an Enhanced Nonlinear Feedback in a Hybrid Opto-mechanical System

NASA Astrophysics Data System (ADS)

Fan, Qiu-Bo; Wang, Yi-Ru; Chen, Jin; Pan, Yue-Wu; Han, Bai-Ping; Fu, Chang-Bao; Sun, Yan

2017-06-01

The steady-state properties of a hybrid system are investigated in this paper. Many cold atoms in the four-level tripod configuration are confined in an optical cavity with a movable end mirror. The confined cold atoms are driven with two external classical fields and an internal cavity field. The internal cavity field is excited by an external driving field and shows a radiation pressure upon the movable end mirror. The coupling of atom-light and opto-mechanical interactions is enhanced by embedding a four-level atomic system in a typical opto-mechanical cavity. And an enhanced nonlinear feedback mechanism is offered by the enhanced coupling, which permits the observation of five and three steady-state solutions for relevant variables near two-photon resonance. The enhanced nonlinear feedback mechanism also allows us to observe the obvious difference in the double-EIT phenomenon between the atom-assisted opto-mechanical system and usual atom-field system.

Cooperative learning neural network output feedback control of uncertain nonlinear multi-agent systems under directed topologies

NASA Astrophysics Data System (ADS)

Wang, W.; Wang, D.; Peng, Z. H.

2017-09-01

Without assuming that the communication topologies among the neural network (NN) weights are to be undirected and the states of each agent are measurable, the cooperative learning NN output feedback control is addressed for uncertain nonlinear multi-agent systems with identical structures in strict-feedback form. By establishing directed communication topologies among NN weights to share their learned knowledge, NNs with cooperative learning laws are employed to identify the uncertainties. By designing NN-based κ-filter observers to estimate the unmeasurable states, a new cooperative learning output feedback control scheme is proposed to guarantee that the system outputs can track nonidentical reference signals with bounded tracking errors. A simulation example is given to demonstrate the effectiveness of the theoretical results.

Dynamics of nonlinear feedback control.

PubMed

Snippe, H P; van Hateren, J H

2007-05-01

Feedback control in neural systems is ubiquitous. Here we study the mathematics of nonlinear feedback control. We compare models in which the input is multiplied by a dynamic gain (multiplicative control) with models in which the input is divided by a dynamic attenuation (divisive control). The gain signal (resp. the attenuation signal) is obtained through a concatenation of an instantaneous nonlinearity and a linear low-pass filter operating on the output of the feedback loop. For input steps, the dynamics of gain and attenuation can be very different, depending on the mathematical form of the nonlinearity and the ordering of the nonlinearity and the filtering in the feedback loop. Further, the dynamics of feedback control can be strongly asymmetrical for increment versus decrement steps of the input. Nevertheless, for each of the models studied, the nonlinearity in the feedback loop can be chosen such that immediately after an input step, the dynamics of feedback control is symmetric with respect to increments versus decrements. Finally, we study the dynamics of the output of the control loops and find conditions under which overshoots and undershoots of the output relative to the steady-state output occur when the models are stimulated with low-pass filtered steps. For small steps at the input, overshoots and undershoots of the output do not occur when the filtering in the control path is faster than the low-pass filtering at the input. For large steps at the input, however, results depend on the model, and for some of the models, multiple overshoots and undershoots can occur even with a fast control path.

Event-Triggered Distributed Approximate Optimal State and Output Control of Affine Nonlinear Interconnected Systems.

PubMed

Narayanan, Vignesh; Jagannathan, Sarangapani

2017-06-08

This paper presents an approximate optimal distributed control scheme for a known interconnected system composed of input affine nonlinear subsystems using event-triggered state and output feedback via a novel hybrid learning scheme. First, the cost function for the overall system is redefined as the sum of cost functions of individual subsystems. A distributed optimal control policy for the interconnected system is developed using the optimal value function of each subsystem. To generate the optimal control policy, forward-in-time, neural networks are employed to reconstruct the unknown optimal value function at each subsystem online. In order to retain the advantages of event-triggered feedback for an adaptive optimal controller, a novel hybrid learning scheme is proposed to reduce the convergence time for the learning algorithm. The development is based on the observation that, in the event-triggered feedback, the sampling instants are dynamic and results in variable interevent time. To relax the requirement of entire state measurements, an extended nonlinear observer is designed at each subsystem to recover the system internal states from the measurable feedback. Using a Lyapunov-based analysis, it is demonstrated that the system states and the observer errors remain locally uniformly ultimately bounded and the control policy converges to a neighborhood of the optimal policy. Simulation results are presented to demonstrate the performance of the developed controller.

Shock and Vibration Control of a Golf-Swing Robot at Impacting the Ball

NASA Astrophysics Data System (ADS)

Hoshino, Yohei; Kobayashi, Yukinori

A golf swing robot is a kind of fast motion manipulator with a flexible link. A robot manipulator is greatly affected by Corioli's and centrifugal forces during fast motion. Nonlinearity due to these forces can have an adverse effect on the performance of feedback control. In the same way, ordinary state observers of a linear system cannot accurately estimate the states of nonlinear systems. This paper uses a state observer that considers disturbances to improve the performance of state estimation and feedback control. A mathematical model of the golf robot is derived by Hamilton's principle. A linear quadratic regulator (LQR) that considers the vibration of the club shaft is used to stop the robot during the follow-through action. The state observer that considers disturbances estimates accurate state variables when the disturbances due to Corioli's and centrifugal forces, and impact forces work on the robot. As a result, the performance of the state feedback control is improved. The study compares the results of the numerical simulations with experimental results.

Adaptive Neural Networks Prescribed Performance Control Design for Switched Interconnected Uncertain Nonlinear Systems.

PubMed

Li, Yongming; Tong, Shaocheng

2017-06-28

In this paper, an adaptive neural networks (NNs)-based decentralized control scheme with the prescribed performance is proposed for uncertain switched nonstrict-feedback interconnected nonlinear systems. It is assumed that nonlinear interconnected terms and nonlinear functions of the concerned systems are unknown, and also the switching signals are unknown and arbitrary. A linear state estimator is constructed to solve the problem of unmeasured states. The NNs are employed to approximate unknown interconnected terms and nonlinear functions. A new output feedback decentralized control scheme is developed by using the adaptive backstepping design technique. The control design problem of nonlinear interconnected switched systems with unknown switching signals can be solved by the proposed scheme, and only a tuning parameter is needed for each subsystem. The proposed scheme can ensure that all variables of the control systems are semi-globally uniformly ultimately bounded and the tracking errors converge to a small residual set with the prescribed performance bound. The effectiveness of the proposed control approach is verified by some simulation results.

Flatness-based control and Kalman filtering for a continuous-time macroeconomic model

NASA Astrophysics Data System (ADS)

Rigatos, G.; Siano, P.; Ghosh, T.; Busawon, K.; Binns, R.

2017-11-01

The article proposes flatness-based control for a nonlinear macro-economic model of the UK economy. The differential flatness properties of the model are proven. This enables to introduce a transformation (diffeomorphism) of the system's state variables and to express the state-space description of the model in the linear canonical (Brunowsky) form in which both the feedback control and the state estimation problem can be solved. For the linearized equivalent model of the macroeconomic system, stabilizing feedback control can be achieved using pole placement methods. Moreover, to implement stabilizing feedback control of the system by measuring only a subset of its state vector elements the Derivative-free nonlinear Kalman Filter is used. This consists of the Kalman Filter recursion applied on the linearized equivalent model of the financial system and of an inverse transformation that is based again on differential flatness theory. The asymptotic stability properties of the control scheme are confirmed.

Adaptive output-feedback control for switched stochastic uncertain nonlinear systems with time-varying delay.

PubMed

Song, Zhibao; Zhai, Junyong

2018-04-01

This paper addresses the problem of adaptive output-feedback control for a class of switched stochastic time-delay nonlinear systems with uncertain output function, where both the control coefficients and time-varying delay are unknown. The drift and diffusion terms are subject to unknown homogeneous growth condition. By virtue of adding a power integrator technique, an adaptive output-feedback controller is designed to render that the closed-loop system is bounded in probability, and the state of switched stochastic nonlinear system can be globally regulated to the origin almost surely. A numerical example is provided to demonstrate the validity of the proposed control method. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Adaptive Fuzzy Tracking Control for a Class of MIMO Nonlinear Systems in Nonstrict-Feedback Form.

PubMed

Chen, Bing; Lin, Chong; Liu, Xiaoping; Liu, Kefu

2015-12-01

This paper focuses on the problem of fuzzy adaptive control for a class of multiinput and multioutput (MIMO) nonlinear systems in nonstrict-feedback form, which contains the strict-feedback form as a special case. By the condition of variable partition, a new fuzzy adaptive backstepping is proposed for such a class of nonlinear MIMO systems. The suggested fuzzy adaptive controller guarantees that the proposed control scheme can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking errors eventually converge to a small neighborhood around the origin. The main advantage of this paper is that a control approach is systematically derived for nonlinear systems with strong interconnected terms which are the functions of all states of the whole system. Simulation results further illustrate the effectiveness of the suggested approach.

Fuzzy Adaptive Output Feedback Control of Uncertain Nonlinear Systems With Prescribed Performance.

PubMed

Zhang, Jin-Xi; Yang, Guang-Hong

2018-05-01

This paper investigates the tracking control problem for a family of strict-feedback systems in the presence of unknown nonlinearities and immeasurable system states. A low-complexity adaptive fuzzy output feedback control scheme is proposed, based on a backstepping method. In the control design, a fuzzy adaptive state observer is first employed to estimate the unmeasured states. Then, a novel error transformation approach together with a new modification mechanism is introduced to guarantee the finite-time convergence of the output error to a predefined region and ensure the closed-loop stability. Compared with the existing methods, the main advantages of our approach are that: 1) without using extra command filters or auxiliary dynamic surface control techniques, the problem of explosion of complexity can still be addressed and 2) the design procedures are independent of the initial conditions. Finally, two practical examples are performed to further illustrate the above theoretic findings.

Estimation of regions of attraction and ultimate boundedness for multiloop LQ regulators. [Linear Quadratic

NASA Technical Reports Server (NTRS)

Joshi, S. M.

1984-01-01

Closed-loop stability is investigated for multivariable linear time-invariant systems controlled by optimal full state feedback linear quadratic (LQ) regulators, with nonlinear gains present in the feedback channels. Estimates are obtained for the region of attraction when the nonlinearities escape the (0.5, infinity) sector in regions away from the origin and for the region of ultimate boundedness when the nonlinearities escape the sector near the origin. The expressions for these regions also provide methods for selecting the performance function parameters in order to obtain LQ designs with better tolerance for nonlinearities. The analytical results are illustrated by applying them to the problem of controlling the rigid-body pitch angle and elastic motion of a large, flexible space antenna.

Global tracking for a class of uncertain nonlinear systems with unknown sign-switching control direction by output feedback

NASA Astrophysics Data System (ADS)

Roux Oliveira, Tiago; Jacoud Peixoto, Alessandro; Hsu, Liu

2015-09-01

This paper addresses the design of a sliding mode controller for a class of high-order uncertain nonlinear plants with unmatched state-dependent nonlinearities and unknown sign of the high frequency gain, i.e., the control direction is assumed unknown. Differently from most previous studies, the control direction is allowed to switch its sign. We show that it is possible to obtain global exact tracking using only output-feedback by coupling a relay periodic switching function with a norm state observer. One significant advantage of the new scheme is its robustness and improved transient response under arbitrary changes of the control direction which have been theoretically demonstrated for jump variations and successfully tested by simulations. The proposed controller is also evaluated with a DC motor control experiment.

Sensorless Estimation and Nonlinear Control of a Rotational Energy Harvester

NASA Astrophysics Data System (ADS)

Nunna, Kameswarie; Toh, Tzern T.; Mitcheson, Paul D.; Astolfi, Alessandro

2013-12-01

It is important to perform sensorless monitoring of parameters in energy harvesting devices in order to determine the operating states of the system. However, physical measurements of these parameters is often a challenging task due to the unavailability of access points. This paper presents, as an example application, the design of a nonlinear observer and a nonlinear feedback controller for a rotational energy harvester. A dynamic model of a rotational energy harvester with its power electronic interface is derived and validated. This model is then used to design a nonlinear observer and a nonlinear feedback controller which yield a sensorless closed-loop system. The observer estimates the mechancial quantities from the measured electrical quantities while the control law sustains power generation across a range of source rotation speeds. The proposed scheme is assessed through simulations and experiments.

Model-Based Adaptive Event-Triggered Control of Strict-Feedback Nonlinear Systems.

PubMed

Li, Yuan-Xin; Yang, Guang-Hong

2018-04-01

This paper is concerned with the adaptive event-triggered control problem of nonlinear continuous-time systems in strict-feedback form. By using the event-sampled neural network (NN) to approximate the unknown nonlinear function, an adaptive model and an associated event-triggered controller are designed by exploiting the backstepping method. In the proposed method, the feedback signals and the NN weights are aperiodically updated only when the event-triggered condition is violated. A positive lower bound on the minimum intersample time is guaranteed to avoid accumulation point. The closed-loop stability of the resulting nonlinear impulsive dynamical system is rigorously proved via Lyapunov analysis under an adaptive event sampling condition. In comparing with the traditional adaptive backstepping design with a fixed sample period, the event-triggered method samples the state and updates the NN weights only when it is necessary. Therefore, the number of transmissions can be significantly reduced. Finally, two simulation examples are presented to show the effectiveness of the proposed control method.

Intelligent robust tracking control for a class of uncertain strict-feedback nonlinear systems.

PubMed

Chang, Yeong-Chan

2009-02-01

This paper addresses the problem of designing robust tracking controls for a large class of strict-feedback nonlinear systems involving plant uncertainties and external disturbances. The input and virtual input weighting matrices are perturbed by bounded time-varying uncertainties. An adaptive fuzzy-based (or neural-network-based) dynamic feedback tracking controller will be developed such that all the states and signals of the closed-loop system are bounded and the trajectory tracking error should be as small as possible. First, the adaptive approximators with linearly parameterized models are designed, and a partitioned procedure with respect to the developed adaptive approximators is proposed such that the implementation of the fuzzy (or neural network) basis functions depends only on the state variables but does not depend on the tuning approximation parameters. Furthermore, we extend to design the nonlinearly parameterized adaptive approximators. Consequently, the intelligent robust tracking control schemes developed in this paper possess the properties of computational simplicity and easy implementation. Finally, simulation examples are presented to demonstrate the effectiveness of the proposed control algorithms.

Formulation of the linear model from the nonlinear simulation for the F18 HARV

NASA Technical Reports Server (NTRS)

Hall, Charles E., Jr.

1991-01-01

The F-18 HARV is a modified F-18 Aircraft which is capable of flying in the post-stall regime in order to achieve superagility. The onset of aerodynamic stall, and continued into the post-stall region, is characterized by nonlinearities in the aerodynamic coefficients. These aerodynamic coefficients are not expressed as analytic functions, but rather in the form of tabular data. The nonlinearities in the aerodynamic coefficients yield a nonlinear model of the aircraft's dynamics. Nonlinear system theory has made many advances, but this area is not sufficiently developed to allow its application to this problem, since many of the theorems are existance theorems and that the systems are composed of analytic functions. Thus, the feedback matrices and the state estimators are obtained from linear system theory techniques. It is important, in order to obtain the correct feedback matrices and state estimators, that the linear description of the nonlinear flight dynamics be as accurate as possible. A nonlinear simulation is run under the Advanced Continuous Simulation Language (ACSL). The ACSL simulation uses FORTRAN subroutines to interface to the look-up tables for the aerodynamic data. ACSL has commands to form the linear representation for the system. Other aspects of this investigation are discussed.

Nonlinear Dynamic Models in Advanced Life Support

NASA Technical Reports Server (NTRS)

Jones, Harry

2002-01-01

To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.

A Nonlinear Physics-Based Optimal Control Method for Magnetostrictive Actuators

NASA Technical Reports Server (NTRS)

Smith, Ralph C.

1998-01-01

This paper addresses the development of a nonlinear optimal control methodology for magnetostrictive actuators. At moderate to high drive levels, the output from these actuators is highly nonlinear and contains significant magnetic and magnetomechanical hysteresis. These dynamics must be accommodated by models and control laws to utilize the full capabilities of the actuators. A characterization based upon ferromagnetic mean field theory provides a model which accurately quantifies both transient and steady state actuator dynamics under a variety of operating conditions. The control method consists of a linear perturbation feedback law used in combination with an optimal open loop nonlinear control. The nonlinear control incorporates the hysteresis and nonlinearities inherent to the transducer and can be computed offline. The feedback control is constructed through linearization of the perturbed system about the optimal system and is efficient for online implementation. As demonstrated through numerical examples, the combined hybrid control is robust and can be readily implemented in linear PDE-based structural models.

Adaptive Neural Output Feedback Control for Nonstrict-Feedback Stochastic Nonlinear Systems With Unknown Backlash-Like Hysteresis and Unknown Control Directions.

PubMed

Yu, Zhaoxu; Li, Shugang; Yu, Zhaosheng; Li, Fangfei

2018-04-01

This paper investigates the problem of output feedback adaptive stabilization for a class of nonstrict-feedback stochastic nonlinear systems with both unknown backlashlike hysteresis and unknown control directions. A new linear state transformation is applied to the original system, and then, control design for the new system becomes feasible. By combining the neural network's (NN's) parameterization, variable separation technique, and Nussbaum gain function method, an input-driven observer-based adaptive NN control scheme, which involves only one parameter to be updated, is developed for such systems. All closed-loop signals are bounded in probability and the error signals remain semiglobally bounded in the fourth moment (or mean square). Finally, the effectiveness and the applicability of the proposed control design are verified by two simulation examples.

Theory of repetitively pulsed operation of diode lasers subject to delayed feedback

DOE Office of Scientific and Technical Information (OSTI.GOV)

Napartovich, A P; Sukharev, A G

2015-03-31

Repetitively pulsed operation of a diode laser with delayed feedback has been studied theoretically at varying feedback parameters and pump power levels. A new approach has been proposed that allows one to reduce the system of Lang–Kobayashi equations for a steady-state repetitively pulsed operation mode to a first-order nonlinear differential equation. We present partial solutions that allow the pulse shape to be predicted. (lasers)

Adaptive Fuzzy Control Design for Stochastic Nonlinear Switched Systems With Arbitrary Switchings and Unmodeled Dynamics.

PubMed

Li, Yongming; Sui, Shuai; Tong, Shaocheng

2017-02-01

This paper deals with the problem of adaptive fuzzy output feedback control for a class of stochastic nonlinear switched systems. The controlled system in this paper possesses unmeasured states, completely unknown nonlinear system functions, unmodeled dynamics, and arbitrary switchings. A state observer which does not depend on the switching signal is constructed to tackle the unmeasured states. Fuzzy logic systems are employed to identify the completely unknown nonlinear system functions. Based on the common Lyapunov stability theory and stochastic small-gain theorem, a new robust adaptive fuzzy backstepping stabilization control strategy is developed. The stability of the closed-loop system on input-state-practically stable in probability is proved. The simulation results are given to verify the efficiency of the proposed fuzzy adaptive control scheme.

Nonlinear fractional order proportion-integral-derivative active disturbance rejection control method design for hypersonic vehicle attitude control

NASA Astrophysics Data System (ADS)

Song, Jia; Wang, Lun; Cai, Guobiao; Qi, Xiaoqiang

2015-06-01

Near space hypersonic vehicle model is nonlinear, multivariable and couples in the reentry process, which are challenging for the controller design. In this paper, a nonlinear fractional order proportion integral derivative (NFOPIλDμ) active disturbance rejection control (ADRC) strategy based on a natural selection particle swarm (NSPSO) algorithm is proposed for the hypersonic vehicle flight control. The NFOPIλDμ ADRC method consists of a tracking-differentiator (TD), an NFOPIλDμ controller and an extended state observer (ESO). The NFOPIλDμ controller designed by combining an FOPIλDμ method and a nonlinear states error feedback control law (NLSEF) is to overcome concussion caused by the NLSEF and conversely compensate the insufficiency for relatively simple and rough signal processing caused by the FOPIλDμ method. The TD is applied to coordinate the contradiction between rapidity and overshoot. By attributing all uncertain factors to unknown disturbances, the ESO can achieve dynamic feedback compensation for these disturbances and thus reduce their effects. Simulation results show that the NFOPIλDμ ADRC method can make the hypersonic vehicle six-degree-of-freedom nonlinear model track desired nominal signals accurately and fast, has good stability, dynamic properties and strong robustness against external environmental disturbances.

Output feedback control for a class of nonlinear systems with actuator degradation and sensor noise.

PubMed

Ai, Weiqing; Lu, Zhenli; Li, Bin; Fei, Shumin

2016-11-01

This paper investigates the output feedback control problem of a class of nonlinear systems with sensor noise and actuator degradation. Firstly, by using the descriptor observer approach, the origin system is transformed into a descriptor system. On the basis of the descriptor system, a novel Proportional Derivative (PD) observer is developed to asymptotically estimate sensor noise and system state simultaneously. Then, by designing an adaptive law to estimate the effectiveness of actuator, an adaptive observer-based controller is constructed to ensure that system state can be regulated to the origin asymptotically. Finally, the design scheme is applied to address a flexible joint robot link problem. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

L1 adaptive control of uncertain gear transmission servo systems with deadzone nonlinearity.

PubMed

Zuo, Zongyu; Li, Xiao; Shi, Zhiguang

2015-09-01

This paper deals with the adaptive control problem of Gear Transmission Servo (GTS) systems in the presence of unknown deadzone nonlinearity and viscous friction. A global differential homeomorphism based on a novel differentiable deadzone model is proposed first. Since there exist both matched and unmatched state-dependent unknown nonlinearities, a full-state feedback L1 adaptive controller is constructed to achieve uniformly bounded transient response in addition to steady-state performance. Finally, simulation results are included to show the elimination of limit cycles, in addition to demonstrating the main results in this paper. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Feedback control of nonlinear quantum systems: a rule of thumb.

PubMed

Jacobs, Kurt; Lund, Austin P

2007-07-13

We show that in the regime in which feedback control is most effective - when measurements are relatively efficient, and feedback is relatively strong - then, in the absence of any sharp inhomogeneity in the noise, it is always best to measure in a basis that does not commute with the system density matrix than one that does. That is, it is optimal to make measurements that disturb the state one is attempting to stabilize.

Control of AUVs using differential flatness theory and the derivative-free nonlinear Kalman Filter

NASA Astrophysics Data System (ADS)

Rigatos, Gerasimos; Raffo, Guilerme

2015-12-01

The paper proposes nonlinear control and filtering for Autonomous Underwater Vessels (AUVs) based on differential flatness theory and on the use of the Derivative-free nonlinear Kalman Filter. First, it is shown that the 6-DOF dynamic model of the AUV is a differentially flat one. This enables its transformation into the linear canonical (Brunovsky) form and facilitates the design of a state feedback controller. A problem that has to be dealt with is the uncertainty about the parameters of the AUV's dynamic model, as well the external perturbations which affect its motion. To cope with this, it is proposed to use a disturbance observer which is based on the Derivative-free nonlinear Kalman Filter. The considered filtering method consists of the standard Kalman Filter recursion applied on the linearized model of the vessel and of an inverse transformation based on differential flatness theory, which enables to obtain estimates of the state variables of the initial nonlinear model of the vessel. The Kalman Filter-based disturbance observer performs simultaneous estimation of the non-measurable state variables of the AUV and of the perturbation terms that affect its dynamics. By estimating such disturbances, their compensation is also succeeded through suitable modification of the feedback control input. The efficiency of the proposed AUV control and estimation scheme is confirmed through simulation experiments.

Adaptive output feedback control of uncertain nonlinear systems using single-hidden-layer neural networks.

PubMed

Hovakimyan, N; Nardi, F; Calise, A; Kim, Nakwan

2002-01-01

We consider adaptive output feedback control of uncertain nonlinear systems, in which both the dynamics and the dimension of the regulated system may be unknown. However, the relative degree of the regulated output is assumed to be known. Given a smooth reference trajectory, the problem is to design a controller that forces the system measurement to track it with bounded errors. The classical approach requires a state observer. Finding a good observer for an uncertain nonlinear system is not an obvious task. We argue that it is sufficient to build an observer for the output tracking error. Ultimate boundedness of the error signals is shown through Lyapunov's direct method. The theoretical results are illustrated in the design of a controller for a fourth-order nonlinear system of relative degree two and a high-bandwidth attitude command system for a model R-50 helicopter.

Observer-Based Adaptive Fault-Tolerant Tracking Control of Nonlinear Nonstrict-Feedback Systems.

PubMed

Wu, Chengwei; Liu, Jianxing; Xiong, Yongyang; Wu, Ligang

2017-06-28

This paper studies an output-based adaptive fault-tolerant control problem for nonlinear systems with nonstrict-feedback form. Neural networks are utilized to identify the unknown nonlinear characteristics in the system. An observer and a general fault model are constructed to estimate the unavailable states and describe the fault, respectively. Adaptive parameters are constructed to overcome the difficulties in the design process for nonstrict-feedback systems. Meanwhile, dynamic surface control technique is introduced to avoid the problem of ''explosion of complexity''. Furthermore, based on adaptive backstepping control method, an output-based adaptive neural tracking control strategy is developed for the considered system against actuator fault, which can ensure that all the signals in the resulting closed-loop system are bounded, and the system output signal can be regulated to follow the response of the given reference signal with a small error. Finally, the simulation results are provided to validate the effectiveness of the control strategy proposed in this paper.

Globally linearized control on diabatic continuous stirred tank reactor: a case study.

PubMed

Jana, Amiya Kumar; Samanta, Amar Nath; Ganguly, Saibal

2005-07-01

This paper focuses on the promise of globally linearized control (GLC) structure in the realm of strongly nonlinear reactor system control. The proposed nonlinear control strategy is comprised of: (i) an input-output linearizing state feedback law (transformer), (ii) a state observer, and (iii) an external linear controller. The synthesis of discrete-time GLC controller for single-input single-output diabatic continuous stirred tank reactor (DCSTR) has been studied first, followed by the synthesis of feedforward/feedback controller for the same reactor having dead time in process as well as in disturbance. Subsequently, the multivariable GLC structure has been designed and then applied on multi-input multi-output DCSTR system. The simulation study shows high quality performance of the derived nonlinear controllers. The better-performed GLC in conjunction with reduced-order observer has been compared with the conventional proportional integral controller on the example reactor and superior performance has been achieved by the proposed GLC control scheme.

Stability of Nonlinear Systems with Unknown Time-varying Feedback Delay

NASA Astrophysics Data System (ADS)

Chunodkar, Apurva A.; Akella, Maruthi R.

2013-12-01

This paper considers the problem of stabilizing a class of nonlinear systems with unknown bounded delayed feedback wherein the time-varying delay is 1) piecewise constant 2) continuous with a bounded rate. We also consider application of these results to the stabilization of rigid-body attitude dynamics. In the first case, the time-delay in feedback is modeled specifically as a switch among an arbitrarily large set of unknown constant values with a known strict upper bound. The feedback is a linear function of the delayed states. In the case of linear systems with switched delay feedback, a new sufficiency condition for average dwell time result is presented using a complete type Lyapunov-Krasovskii (L-K) functional approach. Further, the corresponding switched system with nonlinear perturbations is proven to be exponentially stable inside a well characterized region of attraction for an appropriately chosen average dwell time. In the second case, the concept of the complete type L-K functional is extended to a class of nonlinear time-delay systems with unknown time-varying time-delay. This extension ensures stability robustness to time-delay in the control design for all values of time-delay less than the known upper bound. Model-transformation is used in order to partition the nonlinear system into a nominal linear part that is exponentially stable with a bounded perturbation. We obtain sufficient conditions which ensure exponential stability inside a region of attraction estimate. A constructive method to evaluate the sufficient conditions is presented together with comparison with the corresponding constant and piecewise constant delay. Numerical simulations are performed to illustrate the theoretical results of this paper.

Characterizing Feedback Control Mechanisms in Nonlinear Microbial Models of Soil Organic Matter Decomposition by Stability Analysis

NASA Astrophysics Data System (ADS)

Georgiou, K.; Tang, J.; Riley, W. J.; Torn, M. S.

2014-12-01

Soil organic matter (SOM) decomposition is regulated by biotic and abiotic processes. Feedback interactions between such processes may act to dampen oscillatory responses to perturbations from equilibrium. Indeed, although biological oscillations have been observed in small-scale laboratory incubations, the overlying behavior at the plot-scale exhibits a relatively stable response to disturbances in input rates and temperature. Recent studies have demonstrated the ability of microbial models to capture nonlinear feedbacks in SOM decomposition that linear Century-type models are unable to reproduce, such as soil priming in response to increased carbon input. However, these microbial models often exhibit strong oscillatory behavior that is deemed unrealistic. The inherently nonlinear dynamics of SOM decomposition have important implications for global climate-carbon and carbon-concentration feedbacks. It is therefore imperative to represent these dynamics in Earth System Models (ESMs) by introducing sub-models that accurately represent microbial and abiotic processes. In the present study we explore, both analytically and numerically, four microbe-enabled model structures of varying levels of complexity. The most complex model combines microbial physiology, a non-linear mineral sorption isotherm, and enzyme dynamics. Based on detailed stability analysis of the nonlinear dynamics, we calculate the system modes as functions of model parameters. This dependence provides insight into the source of state oscillations. We find that feedback mechanisms that emerge from careful representation of enzyme and mineral interactions, with parameter values in a prescribed range, are critical for both maintaining system stability and capturing realistic responses to disturbances. Corroborating and expanding upon the results of recent studies, we explain the emergence of oscillatory responses and discuss the appropriate microbe-enabled model structure for inclusion in ESMs.

Time-delayed feedback control of diffusion in random walkers.

PubMed

Ando, Hiroyasu; Takehara, Kohta; Kobayashi, Miki U

2017-07-01

Time delay in general leads to instability in some systems, while specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a stochastic process, i.e., a random walk, and observe its diffusion phenomenon with time-delayed feedback. As a result, the diffusion coefficient decreases with increasing delay time. We analytically illustrate this suppression of diffusion by using stochastic delay differential equations and justify the feasibility of this suppression by applying time-delayed feedback to a molecular dynamics model.

Neuro-adaptive backstepping control of SISO non-affine systems with unknown gain sign.

PubMed

Ramezani, Zahra; Arefi, Mohammad Mehdi; Zargarzadeh, Hassan; Jahed-Motlagh, Mohammad Reza

2016-11-01

This paper presents two neuro-adaptive controllers for a class of uncertain single-input, single-output (SISO) nonlinear non-affine systems with unknown gain sign. The first approach is state feedback controller, so that a neuro-adaptive state-feedback controller is constructed based on the backstepping technique. The second approach is an observer-based controller and K-filters are designed to estimate the system states. The proposed method relaxes a priori knowledge of control gain sign and therefore by utilizing the Nussbaum-type functions this problem is addressed. In these methods, neural networks are employed to approximate the unknown nonlinear functions. The proposed adaptive control schemes guarantee that all the closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB). Finally, the theoretical results are numerically verified through simulation examples. Simulation results show the effectiveness of the proposed methods. Copyright © 2016 ISA. All rights reserved.

Adaptive Nonlinear Tracking Control of Kinematically Redundant Robot Manipulators with Sub-Task Extensions

DTIC Science & Technology

2005-01-01

C. Hughes, Spacecraft Attitude Dynamics, New York, NY: Wiley, 1994. [8] H. K. Khalil, “Adaptive Output Feedback Control of Non- linear Systems...Closed-Loop Manipulator Control Using Quaternion Feedback ”, IEEE Trans. Robotics and Automation, Vol. 4, No. 4, pp. 434-440, (1988). [23] E...full-state feedback quaternion based controller de- veloped in [5] and focuses on the design of a general sub-task controller. This sub-task controller

Adaptive Sliding Mode Control of Dynamic Systems Using Double Loop Recurrent Neural Network Structure.

PubMed

Fei, Juntao; Lu, Cheng

2018-04-01

In this paper, an adaptive sliding mode control system using a double loop recurrent neural network (DLRNN) structure is proposed for a class of nonlinear dynamic systems. A new three-layer RNN is proposed to approximate unknown dynamics with two different kinds of feedback loops where the firing weights and output signal calculated in the last step are stored and used as the feedback signals in each feedback loop. Since the new structure has combined the advantages of internal feedback NN and external feedback NN, it can acquire the internal state information while the output signal is also captured, thus the new designed DLRNN can achieve better approximation performance compared with the regular NNs without feedback loops or the regular RNNs with a single feedback loop. The new proposed DLRNN structure is employed in an equivalent controller to approximate the unknown nonlinear system dynamics, and the parameters of the DLRNN are updated online by adaptive laws to get favorable approximation performance. To investigate the effectiveness of the proposed controller, the designed adaptive sliding mode controller with the DLRNN is applied to a -axis microelectromechanical system gyroscope to control the vibrating dynamics of the proof mass. Simulation results demonstrate that the proposed methodology can achieve good tracking property, and the comparisons of the approximation performance between radial basis function NN, RNN, and DLRNN show that the DLRNN can accurately estimate the unknown dynamics with a fast speed while the internal states of DLRNN are more stable.

Finite-time stabilisation of a class of switched nonlinear systems with state constraints

NASA Astrophysics Data System (ADS)

Huang, Shipei; Xiang, Zhengrong

2018-06-01

This paper investigates the finite-time stabilisation for a class of switched nonlinear systems with state constraints. Some power orders of the system are allowed to be ratios of positive even integers over odd integers. A Barrier Lyapunov function is introduced to guarantee that the state constraint is not violated at any time. Using the convex combination method and a recursive design approach, a state-dependent switching law and state feedback controllers of individual subsystems are constructed such that the closed-loop system is finite-time stable without violation of the state constraint. Two examples are provided to show the effectiveness of the proposed method.

Tracking and disturbance rejection of MIMO nonlinear systems with PI controller

NASA Technical Reports Server (NTRS)

Desoer, C. A.; Lin, C. A.

1985-01-01

The tracking and disturbance rejection of a class of MIMO nonlinear systems with a linear proportional plus integral (PI) compensator is studied. Roughly speaking, it is shown that if the given nonlinear plant is exponentially stable and has a strictly increasing dc steady-state I/O map, then a simple PI compensator can be used to yield a stable unity-feedback closed-loop system which asymptotically tracks reference inputs that tend to constant vectors and asymptotically rejects disturbances that tend to constant vectors.

Tracking and disturbance rejection of MIMO nonlinear systems with PI controller

NASA Technical Reports Server (NTRS)

Desoer, C. A.; Lin, C.-A.

1985-01-01

The tracking and disturbance rejection of a class of MIMO nonlinear systems with linear proportional plus integral (PI) compensator is studied. Roughly speaking, it is shown that if the given nonlinear plant is exponentially stable and has a strictly increasing dc steady-state I/O map, then a simple PI compensator can be used to yield a stable unity-feedback closed-loop system which asymptotically tracks reference inputs that tend to constant vectors and asymptotically rejects disturbances that tend to constant vectors.

Robot-Arm Dynamic Control by Computer

NASA Technical Reports Server (NTRS)

Bejczy, Antal K.; Tarn, Tzyh J.; Chen, Yilong J.

1987-01-01

Feedforward and feedback schemes linearize responses to control inputs. Method for control of robot arm based on computed nonlinear feedback and state tranformations to linearize system and decouple robot end-effector motions along each of cartesian axes augmented with optimal scheme for correction of errors in workspace. Major new feature of control method is: optimal error-correction loop directly operates on task level and not on joint-servocontrol level.

Feedback loop compensates for rectifier nonlinearity

NASA Technical Reports Server (NTRS)

1966-01-01

Signal processing circuit with two negative feedback loops rectifies two sinusoidal signals which are 180 degrees out of phase and produces a single full-wave rectified output signal. Each feedback loop incorporates a feedback rectifier to compensate for the nonlinearity of the circuit.

Active Nonlinear Feedback Control for Aerospace Systems. Processor

DTIC Science & Technology

1990-12-01

relating to the role of nonlinearities in feedback control. These area include Lyapunov function theory, chaotic controllers, statistical energy analysis , phase robustness, and optimal nonlinear control theory.

Accessibility, stabilizability, and feedback control of continuous orbital transfer.

PubMed

Gurfil, Pini

2004-05-01

This paper investigates the problem of low-thrust orbital transfer using orbital element feedback from a control-theoretic standpoint, concepts of controllability, feedback stabilizability, and their interaction. The Gauss variational equations (GVEs) are used to model the state-space dynamics. First, the notion of accessibility, a weaker form of controllability, is presented. It is then shown that the GVEs are globally accessible. Based on the accessibility result, a nonlinear feedback controller is derived that asymptotically steers a vehicle from an initial elliptic Keplerian orbit to any given elliptic Keplerian orbit. The performance of the new controller is illustrated by simulating an orbital transfer between two geosynchronous Earth orbits. It is shown that the low-thrust controller requires less fuel than an impulsive maneuver for the same transfer time. Closed-form, analytic expressions for the new orbital transfer controller are given. Finally, it is proved, based on a topological nonlinear stabilizability test, that there does not exist a continuous closed-loop controller that can transfer a spacecraft to a parabolic escape trajectory.

Nonlinear time-series-based adaptive control applications

NASA Technical Reports Server (NTRS)

Mohler, R. R.; Rajkumar, V.; Zakrzewski, R. R.

1991-01-01

A control design methodology based on a nonlinear time-series reference model is presented. It is indicated by highly nonlinear simulations that such designs successfully stabilize troublesome aircraft maneuvers undergoing large changes in angle of attack as well as large electric power transients due to line faults. In both applications, the nonlinear controller was significantly better than the corresponding linear adaptive controller. For the electric power network, a flexible AC transmission system with series capacitor power feedback control is studied. A bilinear autoregressive moving average reference model is identified from system data, and the feedback control is manipulated according to a desired reference state. The control is optimized according to a predictive one-step quadratic performance index. A similar algorithm is derived for control of rapid changes in aircraft angle of attack over a normally unstable flight regime. In the latter case, however, a generalization of a bilinear time-series model reference includes quadratic and cubic terms in angle of attack.

Neural networks for feedback feedforward nonlinear control systems.

PubMed

Parisini, T; Zoppoli, R

1994-01-01

This paper deals with the problem of designing feedback feedforward control strategies to drive the state of a dynamic system (in general, nonlinear) so as to track any desired trajectory joining the points of given compact sets, while minimizing a certain cost function (in general, nonquadratic). Due to the generality of the problem, conventional methods are difficult to apply. Thus, an approximate solution is sought by constraining control strategies to take on the structure of multilayer feedforward neural networks. After discussing the approximation properties of neural control strategies, a particular neural architecture is presented, which is based on what has been called the "linear-structure preserving principle". The original functional problem is then reduced to a nonlinear programming one, and backpropagation is applied to derive the optimal values of the synaptic weights. Recursive equations to compute the gradient components are presented, which generalize the classical adjoint system equations of N-stage optimal control theory. Simulation results related to nonlinear nonquadratic problems show the effectiveness of the proposed method.

Feedback linearization for control of air breathing engines

NASA Technical Reports Server (NTRS)

Phillips, Stephen; Mattern, Duane

1991-01-01

The method of feedback linearization for control of the nonlinear nozzle and compressor components of an air breathing engine is presented. This method overcomes the need for a large number of scheduling variables and operating points to accurately model highly nonlinear plants. Feedback linearization also results in linear closed loop system performance simplifying subsequent control design. Feedback linearization is used for the nonlinear partial engine model and performance is verified through simulation.

Bifurcation and Control in a Singular Phytoplankton-Zooplankton-Fish Model with Nonlinear Fish Harvesting and Taxation

NASA Astrophysics Data System (ADS)

Meng, Xin-You; Wu, Yu-Qian

In this paper, a delayed differential algebraic phytoplankton-zooplankton-fish model with taxation and nonlinear fish harvesting is proposed. In the absence of time delay, the existence of singularity induced bifurcation is discussed by regarding economic interest as bifurcation parameter. A state feedback controller is designed to eliminate singularity induced bifurcation. Based on Liu’s criterion, Hopf bifurcation occurs at the interior equilibrium when taxation is taken as bifurcation parameter and is more than its corresponding critical value. In the presence of time delay, by analyzing the associated characteristic transcendental equation, the interior equilibrium loses local stability when time delay crosses its critical value. What’s more, the direction of Hopf bifurcation and stability of the bifurcating periodic solutions are investigated based on normal form theory and center manifold theorem, and nonlinear state feedback controller is designed to eliminate Hopf bifurcation. Furthermore, Pontryagin’s maximum principle has been used to obtain optimal tax policy to maximize the benefit as well as the conservation of the ecosystem. Finally, some numerical simulations are given to demonstrate our theoretical analysis.

The relative degree enhancement problem for MIMO nonlinear systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schoenwald, D.A.; Oezguener, Ue.

1995-07-01

The authors present a result for linearizing a nonlinear MIMO system by employing partial feedback - feedback at all but one input-output channel such that the SISO feedback linearization problem is solvable at the remaining input-output channel. The partial feedback effectively enhances the relative degree at the open input-output channel provided the feedback functions are chosen to satisfy relative degree requirements. The method is useful for nonlinear systems that are not feedback linearizable in a MIMO sense. Several examples are presented to show how these feedback functions can be computed. This strategy can be combined with decentralized observers for amore » completely decentralized feedback linearization result for at least one input-output channel.« less

Nonlinear flight control design using backstepping methodology

NASA Astrophysics Data System (ADS)

Tran, Thanh Trung

The subject of nonlinear flight control design using backstepping control methodology is investigated in the dissertation research presented here. Control design methods based on nonlinear models of the dynamic system provide higher utility and versatility because the design model more closely matches the physical system behavior. Obtaining requisite model fidelity is only half of the overall design process, however. Design of the nonlinear control loops can lessen the effects of nonlinearity, or even exploit nonlinearity, to achieve higher levels of closed-loop stability, performance, and robustness. The goal of the research is to improve control quality for a general class of strict-feedback dynamic systems and provide flight control architectures to augment the aircraft motion. The research is divided into two parts: theoretical control development for the strict-feedback form of nonlinear dynamic systems and application of the proposed theory for nonlinear flight dynamics. In the first part, the research is built on two components: transforming the nonlinear dynamic model to a canonical strict-feedback form and then applying backstepping control theory to the canonical model. The research considers a process to determine when this transformation is possible, and when it is possible, a systematic process to transfer the model is also considered when practical. When this is not the case, certain modeling assumptions are explored to facilitate the transformation. After achieving the canonical form, a systematic design procedure for formulating a backstepping control law is explored in the research. Starting with the simplest subsystem and ending with the full system, pseudo control concepts based on Lyapunov control functions are used to control each successive subsystem. Typically each pseudo control must be solved from a nonlinear algebraic equation. At the end of this process, the physical control input must be re-expressed in terms of the physical states by eliminating the pseudo control transformations. In the second part, the research focuses on nonlinear control design for flight dynamics of aircraft motion. Some assumptions on aerodynamics of the aircraft are addressed to transform full nonlinear flight dynamics into the canonical strict-feedback form. The assumptions are also analyzed, validated, and compared to show the advantages and disadvantages of the design models. With the achieved models, investigation focuses on formulating the backstepping control laws and provides an advanced control algorithm for nonlinear flight dynamics of the aircraft. Experimental and simulation studies are successfully implemented to validate the proposed control method. Advancement of nonlinear backstepping control theory and its application to nonlinear flight control are achieved in the dissertation research.

Mean state dependence of ENSO diversity resulting from an intermediate coupled model

NASA Astrophysics Data System (ADS)

Xie, Ruihuang; Jin, Fei-Fei; Mu, Mu

2016-04-01

ENSO diversity is referred to the event-to-event differences in the amplitude, longitudinal location of maximum sea surface temperature (SST) anomalies and evolutional mechanisms, as manifested in both observation data and climate model simulations. Previous studies argued that westerly wind burst (WWB) has strong influence on ENSO diversity. Here, we bring evidences, from a modified intermediate complexity Zebiak-Cane (ZC) coupled model, to illustrate that the ENSO diversity is also determined by the mean states. Stabilities of the linearized ZC model reveal that the mean state with weak (strong) wind stress and deep (shallow) thermocline prefers ENSO variation in the equitorial eastern (central) Pacific with a four-year (two-year) period. Weak wind stress and deep thermocline make the thermocline (TH) feedback the dominant contribution to the growth of ENSO SST anomalies, whereas the opposite mean state favors the zonal advective (ZA) feedback. Different leading dynamical SST-controller makes ENSO display its diversity. In a mean state that resembles the recent climate in the tropical Pacific, the four-year and two-year ENSO variations coexist with similar growth rate. Even without WWB forcing, the nonlinear integration results with adjusted parameters in this special mean state also present at least two types of El Niño, in which the maximum warming rates are contributed by either TH or ZA feedback. The consistency between linear and nonlinear model results indicates that the ENSO diversity is dependent on the mean states.

SPECIAL ISSUE ON OPTICAL PROCESSING OF INFORMATION: Multistability in an acousto-optical system with a frequency feedback

NASA Astrophysics Data System (ADS)

Balakshiĭ, V. I.; Kazar'yan, A. Y.; Lee, A. A.

1995-10-01

An investigation was made of an acousto-optical system with hybrid feedback used to control the frequency of ultrasonic waves excited in an acousto-optical cell. An amplitude transparency, placed in front of a photodetector, ensured a nonlinear dependence of the intensity of the diffracted radiation reaching the detector on the ultrasound frequency. Conditions were found under which this nonlinearity gave rise to multistable states differing in respect of the amplitude, frequency, and direction of propagation of the diffracted beam. An analysis was made of various uses of such a system as an optical channel switch and in stabilisation of the direction of propagation of a light beam.

On the Effect of Feedback Control on Benard Convection in a Boussinesq Fluid

NASA Technical Reports Server (NTRS)

Shortis, Trudi A.; Hall, Philip

1996-01-01

The effect of nonlinear feedback control strategies on the platform of convection in a Boussinesq fluid heated from below is investigated. In the absence of the control, given that non-Boussinesq effects may be neglected, it is well known that convection begins in the form of a supercritical bifurcation to rolls. Non-Boussinesq behaviour destroys the symmetry of the basic state, and through a subcritical bifurcation leads to the formation of hexagonal cells. Here we discuss the influence of regulation of the lower surface temperature by means of a control mechanism, made up of a combination of a proportional linear and nonlinear controller, on the stability of the hexagonal cell pattern.

Stabilization of exact nonlinear Timoshenko beams in space by boundary feedback

NASA Astrophysics Data System (ADS)

Do, K. D.

2018-05-01

Boundary feedback controllers are designed to stabilize Timoshenko beams with large translational and rotational motions in space under external disturbances. The exact nonlinear partial differential equations governing motion of the beams are derived and used in the control design. The designed controllers guarantee globally practically asymptotically (and locally practically exponentially) stability of the beam motions at the reference state. The control design, well-posedness and stability analysis are based on various relationships between the earth-fixed and body-fixed coordinates, Sobolev embeddings, and a Lyapunov-type theorem developed to study well-posedness and stability for a class of evolution systems in Hilbert space. Simulation results are included to illustrate the effectiveness of the proposed control design.

Lyapunov optimal feedback control of a nonlinear inverted pendulum

NASA Technical Reports Server (NTRS)

Grantham, W. J.; Anderson, M. J.

1989-01-01

Liapunov optimal feedback control is applied to a nonlinear inverted pendulum in which the control torque was constrained to be less than the nonlinear gravity torque in the model. This necessitates a control algorithm which 'rocks' the pendulum out of its potential wells, in order to stabilize it at a unique vertical position. Simulation results indicate that a preliminary Liapunov feedback controller can successfully overcome the nonlinearity and bring almost all trajectories to the target.

Adaptive Output-Feedback Neural Control of Switched Uncertain Nonlinear Systems With Average Dwell Time.

PubMed

Long, Lijun; Zhao, Jun

2015-07-01

This paper investigates the problem of adaptive neural tracking control via output-feedback for a class of switched uncertain nonlinear systems without the measurements of the system states. The unknown control signals are approximated directly by neural networks. A novel adaptive neural control technique for the problem studied is set up by exploiting the average dwell time method and backstepping. A switched filter and different update laws are designed to reduce the conservativeness caused by adoption of a common observer and a common update law for all subsystems. The proposed controllers of subsystems guarantee that all closed-loop signals remain bounded under a class of switching signals with average dwell time, while the output tracking error converges to a small neighborhood of the origin. As an application of the proposed design method, adaptive output feedback neural tracking controllers for a mass-spring-damper system are constructed.

Enhancing a slow and weak optomechanical nonlinearity with delayed quantum feedback

PubMed Central

Wang, Zhaoyou; Safavi-Naeini, Amir H.

2017-01-01

A central goal of quantum optics is to generate large interactions between single photons so that one photon can strongly modify the state of another one. In cavity optomechanics, photons interact with the motional degrees of freedom of an optical resonator, for example, by imparting radiation pressure forces on a movable mirror or sensing minute fluctuations in the position of the mirror. Here, we show that the optical nonlinearity arising from these effects, typically too small to operate on single photons, can be sufficiently enhanced with feedback to generate large interactions between single photons. We propose a protocol that allows photons propagating in a waveguide to interact with each other through multiple bounces off an optomechanical system. The protocol is analysed by evolving the full many-body quantum state of the waveguide-coupled system, illustrating that large photon–photon interactions mediated by mechanical motion may be within experimental reach. PMID:28677674

Adaptive control of Parkinson's state based on a nonlinear computational model with unknown parameters.

PubMed

Su, Fei; Wang, Jiang; Deng, Bin; Wei, Xi-Le; Chen, Ying-Yuan; Liu, Chen; Li, Hui-Yan

2015-02-01

The objective here is to explore the use of adaptive input-output feedback linearization method to achieve an improved deep brain stimulation (DBS) algorithm for closed-loop control of Parkinson's state. The control law is based on a highly nonlinear computational model of Parkinson's disease (PD) with unknown parameters. The restoration of thalamic relay reliability is formulated as the desired outcome of the adaptive control methodology, and the DBS waveform is the control input. The control input is adjusted in real time according to estimates of unknown parameters as well as the feedback signal. Simulation results show that the proposed adaptive control algorithm succeeds in restoring the relay reliability of the thalamus, and at the same time achieves accurate estimation of unknown parameters. Our findings point to the potential value of adaptive control approach that could be used to regulate DBS waveform in more effective treatment of PD.

Stabilization strategies of a general nonlinear car-following model with varying reaction-time delay of the drivers.

PubMed

Li, Shukai; Yang, Lixing; Gao, Ziyou; Li, Keping

2014-11-01

In this paper, the stabilization strategies of a general nonlinear car-following model with reaction-time delay of the drivers are investigated. The reaction-time delay of the driver is time varying and bounded. By using the Lyapunov stability theory, the sufficient condition for the existence of the state feedback control strategy for the stability of the car-following model is given in the form of linear matrix inequality, under which the traffic jam can be well suppressed with respect to the varying reaction-time delay. Moreover, by considering the external disturbance for the running cars, the robust state feedback control strategy is designed, which ensures robust stability and a smaller prescribed H∞ disturbance attenuation level for the traffic flow. Numerical examples are given to illustrate the effectiveness of the proposed methods. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Control-based continuation: Bifurcation and stability analysis for physical experiments

NASA Astrophysics Data System (ADS)

Barton, David A. W.

2017-02-01

Control-based continuation is technique for tracking the solutions and bifurcations of nonlinear experiments. The idea is to apply the method of numerical continuation to a feedback-controlled physical experiment such that the control becomes non-invasive. Since in an experiment it is not (generally) possible to set the state of the system directly, the control target becomes a proxy for the state. Control-based continuation enables the systematic investigation of the bifurcation structure of a physical system, much like if it was numerical model. However, stability information (and hence bifurcation detection and classification) is not readily available due to the presence of stabilising feedback control. This paper uses a periodic auto-regressive model with exogenous inputs (ARX) to approximate the time-varying linearisation of the experiment around a particular periodic orbit, thus providing the missing stability information. This method is demonstrated using a physical nonlinear tuned mass damper.

Controller design for a class of nonlinear MIMO coupled system using multiple models and second level adaptation.

PubMed

Pandey, Vinay Kumar; Kar, Indrani; Mahanta, Chitralekha

2017-07-01

In this paper, an adaptive control method using multiple models with second level adaptation is proposed for a class of nonlinear multi-input multi-output (MIMO) coupled systems. Multiple estimation models are used to tune the unknown parameters at the first level. The second level adaptation provides a single parameter vector for the controller. A feedback linearization technique is used to design a state feedback control. The efficacy of the designed controller is validated by conducting real time experiment on a laboratory setup of twin rotor MIMO system (TRMS). The TRMS setup is discussed in detail and the experiments were performed for regulation and tracking problem for pitch and yaw control using different reference signals. An Extended Kalman Filter (EKF) has been used to observe the unavailable states of the TRMS. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Enhancing a slow and weak optomechanical nonlinearity with delayed quantum feedback

NASA Astrophysics Data System (ADS)

Wang, Zhaoyou; Safavi-Naeini, Amir H.

2017-07-01

A central goal of quantum optics is to generate large interactions between single photons so that one photon can strongly modify the state of another one. In cavity optomechanics, photons interact with the motional degrees of freedom of an optical resonator, for example, by imparting radiation pressure forces on a movable mirror or sensing minute fluctuations in the position of the mirror. Here, we show that the optical nonlinearity arising from these effects, typically too small to operate on single photons, can be sufficiently enhanced with feedback to generate large interactions between single photons. We propose a protocol that allows photons propagating in a waveguide to interact with each other through multiple bounces off an optomechanical system. The protocol is analysed by evolving the full many-body quantum state of the waveguide-coupled system, illustrating that large photon-photon interactions mediated by mechanical motion may be within experimental reach.

Superconducting Microwave Multivibrator Produced by Coherent Feedback

NASA Astrophysics Data System (ADS)

Kerckhoff, Joseph; Lehnert, K. W.

2012-10-01

We investigate a nonlinear coherent feedback circuit constructed from preexisting superconducting microwave devices. The network exhibits emergent bistable and astable states, and we demonstrate its operation as a latch and the frequency locking of its oscillations. While the network is tedious to model by hand, our observations agree quite well with the semiclassical dynamical model produced by a new software package (N. Tezak , arXiv:1111.3081v1 [Phil. Trans. R. Soc. A (to be published)]) that systematically interpreted an idealized schematic of the system as a quantum optic feedback network.

A robust model predictive control algorithm for uncertain nonlinear systems that guarantees resolvability

NASA Technical Reports Server (NTRS)

Acikmese, Ahmet Behcet; Carson, John M., III

2006-01-01

A robustly stabilizing MPC (model predictive control) algorithm for uncertain nonlinear systems is developed that guarantees resolvability. With resolvability, initial feasibility of the finite-horizon optimal control problem implies future feasibility in a receding-horizon framework. The control consists of two components; (i) feed-forward, and (ii) feedback part. Feed-forward control is obtained by online solution of a finite-horizon optimal control problem for the nominal system dynamics. The feedback control policy is designed off-line based on a bound on the uncertainty in the system model. The entire controller is shown to be robustly stabilizing with a region of attraction composed of initial states for which the finite-horizon optimal control problem is feasible. The controller design for this algorithm is demonstrated on a class of systems with uncertain nonlinear terms that have norm-bounded derivatives and derivatives in polytopes. An illustrative numerical example is also provided.

Adaptive Fuzzy Output-Constrained Fault-Tolerant Control of Nonlinear Stochastic Large-Scale Systems With Actuator Faults.

PubMed

Li, Yongming; Ma, Zhiyao; Tong, Shaocheng

2017-09-01

The problem of adaptive fuzzy output-constrained tracking fault-tolerant control (FTC) is investigated for the large-scale stochastic nonlinear systems of pure-feedback form. The nonlinear systems considered in this paper possess the unstructured uncertainties, unknown interconnected terms and unknown nonaffine nonlinear faults. The fuzzy logic systems are employed to identify the unknown lumped nonlinear functions so that the problems of structured uncertainties can be solved. An adaptive fuzzy state observer is designed to solve the nonmeasurable state problem. By combining the barrier Lyapunov function theory, adaptive decentralized and stochastic control principles, a novel fuzzy adaptive output-constrained FTC approach is constructed. All the signals in the closed-loop system are proved to be bounded in probability and the system outputs are constrained in a given compact set. Finally, the applicability of the proposed controller is well carried out by a simulation example.

Control of nonlinear systems with applications to constrained robots and spacecraft attitude stabilization

NASA Technical Reports Server (NTRS)

Krishnan, Hariharan

1993-01-01

This thesis is organized in two parts. In Part 1, control systems described by a class of nonlinear differential and algebraic equations are introduced. A procedure for local stabilization based on a local state realization is developed. An alternative approach to local stabilization is developed based on a classical linearization of the nonlinear differential-algebraic equations. A theoretical framework is established for solving a tracking problem associated with the differential-algebraic system. First, a simple procedure is developed for the design of a feedback control law which ensures, at least locally, that the tracking error in the closed loop system lies within any given bound if the reference inputs are sufficiently slowly varying. Next, by imposing additional assumptions, a procedure is developed for the design of a feedback control law which ensures that the tracking error in the closed loop system approaches zero exponentially for reference inputs which are not necessarily slowly varying. The control design methodologies are used for simultaneous force and position control in constrained robot systems. The differential-algebraic equations are shown to characterize the slow dynamics of a certain nonlinear control system in nonstandard singularly perturbed form. In Part 2, the attitude stabilization (reorientation) of a rigid spacecraft using only two control torques is considered. First, the case of momentum wheel actuators is considered. The complete spacecraft dynamics are not controllable. However, the spacecraft dynamics are small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized using continuous feedback, but a discontinuous feedback control strategy is constructed. Next, the case of gas jet actuators is considered. If the uncontrolled principal axis is not an axis of symmetry, the complete spacecraft dynamics are small time locally controllable. However, the spacecraft attitude cannot be asymptotically stabilized using continuous feedback, but a discontinuous stabilizing feedback control strategy is constructed. If the uncontrolled principal axis is an axis of symmetry, the complete spacecraft dynamics cannot be stabilized. However, the spacecraft dynamics are small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized using continuous feedback, but again a discontinuous feedback control strategy is constructed.

Hypersonic entry vehicle state estimation using nonlinearity-based adaptive cubature Kalman filters

NASA Astrophysics Data System (ADS)

Sun, Tao; Xin, Ming

2017-05-01

Guidance, navigation, and control of a hypersonic vehicle landing on the Mars rely on precise state feedback information, which is obtained from state estimation. The high uncertainty and nonlinearity of the entry dynamics make the estimation a very challenging problem. In this paper, a new adaptive cubature Kalman filter is proposed for state trajectory estimation of a hypersonic entry vehicle. This new adaptive estimation strategy is based on the measure of nonlinearity of the stochastic system. According to the severity of nonlinearity along the trajectory, the high degree cubature rule or the conventional third degree cubature rule is adaptively used in the cubature Kalman filter. This strategy has the benefit of attaining higher estimation accuracy only when necessary without causing excessive computation load. The simulation results demonstrate that the proposed adaptive filter exhibits better performance than the conventional third-degree cubature Kalman filter while maintaining the same performance as the uniform high degree cubature Kalman filter but with lower computation complexity.

The analysis on nonlinear control of the aircraft arresting system

NASA Astrophysics Data System (ADS)

Song, Jinchun; Du, Tianrong

2005-12-01

The aircraft arresting system is a complicated nonlinear system. This paper analyzes the mechanical-hydraulic structure of aircraft arresting system composed of electro hydraulic valve and establishes the dynamic equation of the aircraft arresting system. Based on the state-feedback linearization of nonlinear system, a PD-based controller is synthesized. Simulation studies indicate, while arresting the different type aircraft, the proposed controller has fast response, good tracking performance and strong robustness. By tuning the parameters of the PD controller, a satisfactory control performance can be guaranteed.

Leader-following control of multiple nonholonomic systems over directed communication graphs

NASA Astrophysics Data System (ADS)

Dong, Wenjie; Djapic, Vladimir

2016-06-01

This paper considers the leader-following control problem of multiple nonlinear systems with directed communication topology and a leader. If the state of each system is measurable, distributed state feedback controllers are proposed using neighbours' state information with the aid of Lyapunov techniques and properties of Laplacian matrix for time-invariant communication graph and time-varying communication graph. It is shown that the state of each system exponentially converges to the state of a leader. If the state of each system is not measurable, distributed observer-based output feedback control laws are proposed. As an application of the proposed results, formation control of wheeled mobile robots is studied. The simulation results show the effectiveness of the proposed results.

Gap-metric-based robustness analysis of nonlinear systems with full and partial feedback linearisation

NASA Astrophysics Data System (ADS)

Al-Gburi, A.; Freeman, C. T.; French, M. C.

2018-06-01

This paper uses gap metric analysis to derive robustness and performance margins for feedback linearising controllers. Distinct from previous robustness analysis, it incorporates the case of output unstructured uncertainties, and is shown to yield general stability conditions which can be applied to both stable and unstable plants. It then expands on existing feedback linearising control schemes by introducing a more general robust feedback linearising control design which classifies the system nonlinearity into stable and unstable components and cancels only the unstable plant nonlinearities. This is done in order to preserve the stabilising action of the inherently stabilising nonlinearities. Robustness and performance margins are derived for this control scheme, and are expressed in terms of bounds on the plant nonlinearities and the accuracy of the cancellation of the unstable plant nonlinearity by the controller. Case studies then confirm reduced conservatism compared with standard methods.

Adaptive Importance Sampling for Control and Inference

NASA Astrophysics Data System (ADS)

Kappen, H. J.; Ruiz, H. C.

2016-03-01

Path integral (PI) control problems are a restricted class of non-linear control problems that can be solved formally as a Feynman-Kac PI and can be estimated using Monte Carlo sampling. In this contribution we review PI control theory in the finite horizon case. We subsequently focus on the problem how to compute and represent control solutions. We review the most commonly used methods in robotics and control. Within the PI theory, the question of how to compute becomes the question of importance sampling. Efficient importance samplers are state feedback controllers and the use of these requires an efficient representation. Learning and representing effective state-feedback controllers for non-linear stochastic control problems is a very challenging, and largely unsolved, problem. We show how to learn and represent such controllers using ideas from the cross entropy method. We derive a gradient descent method that allows to learn feed-back controllers using an arbitrary parametrisation. We refer to this method as the path integral cross entropy method or PICE. We illustrate this method for some simple examples. The PI control methods can be used to estimate the posterior distribution in latent state models. In neuroscience these problems arise when estimating connectivity from neural recording data using EM. We demonstrate the PI control method as an accurate alternative to particle filtering.

Differential flatness properties and multivariable adaptive control of ovarian system dynamics

NASA Astrophysics Data System (ADS)

Rigatos, Gerasimos

2016-12-01

The ovarian system exhibits nonlinear dynamics which is modeled by a set of coupled nonlinear differential equations. The paper proposes adaptive fuzzy control based on differential flatness theory for the complex dynamics of the ovarian system. It is proven that the dynamic model of the ovarian system, having as state variables the LH and the FSH hormones and their derivatives, is a differentially flat one. This means that all its state variables and its control inputs can be described as differential functions of the flat output. By exploiting differential flatness properties the system's dynamic model is written in the multivariable linear canonical (Brunovsky) form, for which the design of a state feedback controller becomes possible. After this transformation, the new control inputs of the system contain unknown nonlinear parts, which are identified with the use of neurofuzzy approximators. The learning procedure for these estimators is determined by the requirement the first derivative of the closed-loop's Lyapunov function to be a negative one. Moreover, Lyapunov stability analysis shows that H-infinity tracking performance is succeeded for the feedback control loop and this assures improved robustness to the aforementioned model uncertainty as well as to external perturbations. The efficiency of the proposed adaptive fuzzy control scheme is confirmed through simulation experiments.

Robust H(infinity) tracking control of boiler-turbine systems.

PubMed

Wu, J; Nguang, S K; Shen, J; Liu, G; Li, Y G

2010-07-01

In this paper, the problem of designing a fuzzy H(infinity) state feedback tracking control of a boiler-turbine is solved. First, the Takagi and Sugeno fuzzy model is used to model a boiler-turbine system. Next, based on the Takagi and Sugeno fuzzy model, sufficient conditions for the existence of a fuzzy H(infinity) nonlinear state feedback tracking control are derived in terms of linear matrix inequalities. The advantage of the proposed tracking control design is that it does not involve feedback linearization technique and complicated adaptive scheme. An industrial boiler-turbine system is used to illustrate the effectiveness of the proposed design as compared with a linearized approach. 2010 ISA. Published by Elsevier Ltd. All rights reserved.

Robust decentralized hybrid adaptive output feedback fuzzy control for a class of large-scale MIMO nonlinear systems and its application to AHS.

PubMed

Huang, Yi-Shao; Liu, Wel-Ping; Wu, Min; Wang, Zheng-Wu

2014-09-01

This paper presents a novel observer-based decentralized hybrid adaptive fuzzy control scheme for a class of large-scale continuous-time multiple-input multiple-output (MIMO) uncertain nonlinear systems whose state variables are unmeasurable. The scheme integrates fuzzy logic systems, state observers, and strictly positive real conditions to deal with three issues in the control of a large-scale MIMO uncertain nonlinear system: algorithm design, controller singularity, and transient response. Then, the design of the hybrid adaptive fuzzy controller is extended to address a general large-scale uncertain nonlinear system. It is shown that the resultant closed-loop large-scale system keeps asymptotically stable and the tracking error converges to zero. The better characteristics of our scheme are demonstrated by simulations. Copyright © 2014. Published by Elsevier Ltd.

Parallels between control PDE's (Partial Differential Equations) and systems of ODE's (Ordinary Differential Equations)

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Villarreal, Ramiro

1987-01-01

System theorists understand that the same mathematical objects which determine controllability for nonlinear control systems of ordinary differential equations (ODEs) also determine hypoellipticity for linear partial differentail equations (PDEs). Moreover, almost any study of ODE systems begins with linear systems. It is remarkable that Hormander's paper on hypoellipticity of second order linear p.d.e.'s starts with equations due to Kolmogorov, which are shown to be analogous to the linear PDEs. Eigenvalue placement by state feedback for a controllable linear system can be paralleled for a Kolmogorov equation if an appropriate type of feedback is introduced. Results concerning transformations of nonlinear systems to linear systems are similar to results for transforming a linear PDE to a Kolmogorov equation.

A study of the application of singular perturbation theory. [development of a real time algorithm for optimal three dimensional aircraft maneuvers

NASA Technical Reports Server (NTRS)

Mehra, R. K.; Washburn, R. B.; Sajan, S.; Carroll, J. V.

1979-01-01

A hierarchical real time algorithm for optimal three dimensional control of aircraft is described. Systematic methods are developed for real time computation of nonlinear feedback controls by means of singular perturbation theory. The results are applied to a six state, three control variable, point mass model of an F-4 aircraft. Nonlinear feedback laws are presented for computing the optimal control of throttle, bank angle, and angle of attack. Real Time capability is assessed on a TI 9900 microcomputer. The breakdown of the singular perturbation approximation near the terminal point is examined Continuation methods are examined to obtain exact optimal trajectories starting from the singular perturbation solutions.

Stabilization of nonlinear systems using sampled-data output-feedback fuzzy controller based on polynomial-fuzzy-model-based control approach.

PubMed

Lam, H K

2012-02-01

This paper investigates the stability of sampled-data output-feedback (SDOF) polynomial-fuzzy-model-based control systems. Representing the nonlinear plant using a polynomial fuzzy model, an SDOF fuzzy controller is proposed to perform the control process using the system output information. As only the system output is available for feedback compensation, it is more challenging for the controller design and system analysis compared to the full-state-feedback case. Furthermore, because of the sampling activity, the control signal is kept constant by the zero-order hold during the sampling period, which complicates the system dynamics and makes the stability analysis more difficult. In this paper, two cases of SDOF fuzzy controllers, which either share the same number of fuzzy rules or not, are considered. The system stability is investigated based on the Lyapunov stability theory using the sum-of-squares (SOS) approach. SOS-based stability conditions are obtained to guarantee the system stability and synthesize the SDOF fuzzy controller. Simulation examples are given to demonstrate the merits of the proposed SDOF fuzzy control approach.

Performance Assessment of Model-Based Optimal Feedforward and Feedback Current Profile Control in NSTX-U using the TRANSP Code

NASA Astrophysics Data System (ADS)

Ilhan, Z.; Wehner, W. P.; Schuster, E.; Boyer, M. D.; Gates, D. A.; Gerhardt, S.; Menard, J.

2015-11-01

Active control of the toroidal current density profile is crucial to achieve and maintain high-performance, MHD-stable plasma operation in NSTX-U. A first-principles-driven, control-oriented model describing the temporal evolution of the current profile has been proposed earlier by combining the magnetic diffusion equation with empirical correlations obtained at NSTX-U for the electron density, electron temperature, and non-inductive current drives. A feedforward + feedback control scheme for the requlation of the current profile is constructed by embedding the proposed nonlinear, physics-based model into the control design process. Firstly, nonlinear optimization techniques are used to design feedforward actuator trajectories that steer the plasma to a desired operating state with the objective of supporting the traditional trial-and-error experimental process of advanced scenario planning. Secondly, a feedback control algorithm to track a desired current profile evolution is developed with the goal of adding robustness to the overall control scheme. The effectiveness of the combined feedforward + feedback control algorithm for current profile regulation is tested in predictive simulations carried out in TRANSP. Supported by PPPL.

Nonlinear Time Delayed Feedback Control of Aeroelastic Systems: A Functional Approach

NASA Technical Reports Server (NTRS)

Marzocca, Piergiovanni; Librescu, Liviu; Silva, Walter A.

2003-01-01

In addition to its intrinsic practical importance, nonlinear time delayed feedback control applied to lifting surfaces can result in interesting aeroelastic behaviors. In this paper, nonlinear aeroelastic response to external time-dependent loads and stability boundary for actively controlled lifting surfaces, in an incompressible flow field, are considered. The structural model and the unsteady aerodynamics are considered linear. The implications of the presence of time delays in the linear/nonlinear feedback control and of geometrical parameters on the aeroelasticity of lifting surfaces are analyzed and conclusions on their implications are highlighted.

Parametric Stiffness Control of Flexible Structures

NASA Technical Reports Server (NTRS)

Moon, F. C.; Rand, R. H.

1985-01-01

An unconventional method for control of flexible space structures using feedback control of certain elements of the stiffness matrix is discussed. The advantage of using this method of configuration control is that it can be accomplished in practical structures by changing the initial stress state in the structure. The initial stress state can be controlled hydraulically or by cables. The method leads, however, to nonlinear control equations. In particular, a long slender truss structure under cable induced initial compression is examined. both analytical and numerical analyses are presented. Nonlinear analysis using center manifold theory and normal form theory is used to determine criteria on the nonlinear control gains for stable or unstable operation. The analysis is made possible by the use of the exact computer algebra system MACSYMA.

Differential Flatness and Cooperative Tracking in the Lorenz System

NASA Technical Reports Server (NTRS)

Crespo, Luis G.

2002-01-01

In this paper the control of the Lorenz system for both stabilization and tracking problems is studied via feedback linearization and differential flatness. By using the Rayleigh number as the control, only variable physically tunable, a barrier in the controllability of the system is incidentally imposed. This is reflected in the appearance of a singularity in the state transformation. Composite controllers that overcome this difficulty are designed and evaluated. The transition through the manifold defined by such a singularity is achieved by inducing a chaotic response within a boundary layer that contains it. Outside this region, a conventional feedback nonlinear control is applied. In this fashion, the authority of the control is enlarged to the whole. state space and the need for high control efforts is mitigated. In addition, the differential parametrization of the problem is used to track nonlinear functions of one state variable (single tracking) as well as several state variables (cooperative tracking). Control tasks that lead to integrable and non-integrable differential equations for the nominal flat output in steady-state are considered. In particular, a novel numerical strategy to deal with the non-integrable case is proposed. Numerical results validate very well the control design.

Investigation, development and application of optimal output feedback theory. Volume 2: Development of an optimal, limited state feedback outer-loop digital flight control system for 3-D terminal area operation

NASA Technical Reports Server (NTRS)

Broussard, J. R.; Halyo, N.

1984-01-01

This report contains the development of a digital outer-loop three dimensional radio navigation (3-D RNAV) flight control system for a small commercial jet transport. The outer-loop control system is designed using optimal stochastic limited state feedback techniques. Options investigated using the optimal limited state feedback approach include integrated versus hierarchical control loop designs, 20 samples per second versus 5 samples per second outer-loop operation and alternative Type 1 integration command errors. Command generator tracking techniques used in the digital control design enable the jet transport to automatically track arbitrary curved flight paths generated by waypoints. The performance of the design is demonstrated using detailed nonlinear aircraft simulations in the terminal area, frequency domain multi-input sigma plots, frequency domain single-input Bode plots and closed-loop poles. The response of the system to a severe wind shear during a landing approach is also presented.

Drag reduction in channel flow using nonlinear control

NASA Technical Reports Server (NTRS)

Keefe, Laurence R.

1993-01-01

Two nonlinear control schemes have been applied to the problem of drag reduction in channel flow. Both schemes have been tested using numerical simulations at a mass flux Reynolds numbers of 4408, utilizing 2D nonlinear neutral modes for goal dynamics. The OGY-method, which requires feedback, reduces drag to 60-80 percent of the turbulent value at the same Reynolds number, and employs forcing only within a thin region near the wall. The H-method, or model-based control, fails to achieve any drag reduction when starting from a fully turbulent initial condition, but shows potential for suppressing or retarding laminar-to-turbulent transition by imposing instead a transition to a low drag, nonlinear traveling wave solution to the Navier-Stokes equation. The drag in this state corresponds to that achieved by the OGY-method. Model-based control requires no feedback, but in experiments to date has required the forcing be imposed within a thicker layer than the OGY-method. Control energy expenditures in both methods are small, representing less than 0.1 percent of the uncontrolled flow's energy.

Modelling the influence of sensory dynamics on linear and nonlinear driver steering control

NASA Astrophysics Data System (ADS)

Nash, C. J.; Cole, D. J.

2018-05-01

A recent review of the literature has indicated that sensory dynamics play an important role in the driver-vehicle steering task, motivating the design of a new driver model incorporating human sensory systems. This paper presents a full derivation of the linear driver model developed in previous work, and extends the model to control a vehicle with nonlinear tyres. Various nonlinear controllers and state estimators are compared with different approximations of the true system dynamics. The model simulation time is found to increase significantly with the complexity of the controller and state estimator. In general the more complex controllers perform best, although with certain vehicle and tyre models linearised controllers perform as well as a full nonlinear optimisation. Various extended Kalman filters give similar results, although the driver's sensory dynamics reduce control performance compared with full state feedback. The new model could be used to design vehicle systems which interact more naturally and safely with a human driver.

Delayed-feedback chimera states: Forced multiclusters and stochastic resonance

NASA Astrophysics Data System (ADS)

Semenov, V.; Zakharova, A.; Maistrenko, Y.; Schöll, E.

2016-07-01

A nonlinear oscillator model with negative time-delayed feedback is studied numerically under external deterministic and stochastic forcing. It is found that in the unforced system complex partial synchronization patterns like chimera states as well as salt-and-pepper-like solitary states arise on the route from regular dynamics to spatio-temporal chaos. The control of the dynamics by external periodic forcing is demonstrated by numerical simulations. It is shown that one-cluster and multi-cluster chimeras can be achieved by adjusting the external forcing frequency to appropriate resonance conditions. If a stochastic component is superimposed to the deterministic external forcing, chimera states can be induced in a way similar to stochastic resonance, they appear, therefore, in regimes where they do not exist without noise.

Nonlinear compensation techniques for magnetic suspension systems. Ph.D. Thesis - MIT

NASA Technical Reports Server (NTRS)

Trumper, David L.

1991-01-01

In aerospace applications, magnetic suspension systems may be required to operate over large variations in air-gap. Thus the nonlinearities inherent in most types of suspensions have a significant effect. Specifically, large variations in operating point may make it difficult to design a linear controller which gives satisfactory stability and performance over a large range of operating points. One way to address this problem is through the use of nonlinear compensation techniques such as feedback linearization. Nonlinear compensators have received limited attention in the magnetic suspension literature. In recent years, progress has been made in the theory of nonlinear control systems, and in the sub-area of feedback linearization. The idea is demonstrated of feedback linearization using a second order suspension system. In the context of the second order suspension, sampling rate issues in the implementation of feedback linearization are examined through simulation.

Applications of nonlinear systems theory to control design

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Villarreal, Ramiro

1988-01-01

For most applications in the control area, the standard practice is to approximate a nonlinear mathematical model by a linear system. Since the feedback linearizable systems contain linear systems as a subclass, the procedure of approximating a nonlinear system by a feedback linearizable one is examined. Because many physical plants (e.g., aircraft at the NASA Ames Research Center) have mathematical models which are close to feedback linearizable systems, such approximations are certainly justified. Results and techniques are introduced for measuring the gap between the model and its truncated linearizable part. The topic of pure feedback systems is important to the study.

Non-predictor control of a class of feedforward nonlinear systems with unknown time-varying delays

NASA Astrophysics Data System (ADS)

Koo, Min-Sung; Choi, Ho-Lim

2016-08-01

This paper generalises the several recent results on the control of feedforward time-delay nonlinear systems. First, in view of system formulation, there are unknown time-varying delays in both states and main control input. Also, the considered nonlinear system has extended feedforward nonlinearities. Second, in view of control solution, our proposed controller is a non-predictor feedback controller whereas smith-predictor type controllers are used in the several existing results. Moreover, our controller does not need any information on the unknown delays except their upper bounds. Thus, our result has certain merits in both system formulation and control solution perspective. The analysis and example are given for clear illustration.

Relaxation rates of gene expression kinetics reveal the feedback signs of autoregulatory gene networks

NASA Astrophysics Data System (ADS)

Jia, Chen; Qian, Hong; Chen, Min; Zhang, Michael Q.

2018-03-01

The transient response to a stimulus and subsequent recovery to a steady state are the fundamental characteristics of a living organism. Here we study the relaxation kinetics of autoregulatory gene networks based on the chemical master equation model of single-cell stochastic gene expression with nonlinear feedback regulation. We report a novel relation between the rate of relaxation, characterized by the spectral gap of the Markov model, and the feedback sign of the underlying gene circuit. When a network has no feedback, the relaxation rate is exactly the decaying rate of the protein. We further show that positive feedback always slows down the relaxation kinetics while negative feedback always speeds it up. Numerical simulations demonstrate that this relation provides a possible method to infer the feedback topology of autoregulatory gene networks by using time-series data of gene expression.

The Stability Region for Feedback Control of the Wake Behind Twin Oscillating Cylinders

NASA Astrophysics Data System (ADS)

Borggaard, Jeff; Gugercin, Serkan; Zietsman, Lizette

2016-11-01

Linear feedback control has the ability to stabilize vortex shedding behind twin cylinders where cylinder rotation is the actuation mechanism. Complete elimination of the wake is only possible for certain Reynolds numbers and cylinder spacing. This is related to the presence of asymmetric unstable modes in the linearized system. We investigate this region of parameter space using a number of closed-loop simulations that bound this region. We then consider the practical issue of designing feedback controls based on limited state measurements by building a nonlinear compensator using linear robust control theory with and incorporating the nonlinear terms in the compensator (e.g., using the extended Kalman filter). Interpolatory model reduction methods are applied to the large discretized, linearized Navier-Stokes system and used for computing the control laws and compensators. Preliminary closed-loop simulations of a three-dimensional version of this problem will also be presented. Supported in part by the National Science Foundation.

LMI Based Robust Blood Glucose Regulation in Type-1 Diabetes Patient with Daily Multi-meal Ingestion

NASA Astrophysics Data System (ADS)

Mandal, S.; Bhattacharjee, A.; Sutradhar, A.

2014-04-01

This paper illustrates the design of a robust output feedback H ∞ controller for the nonlinear glucose-insulin (GI) process in a type-1 diabetes patient to deliver insulin through intravenous infusion device. The H ∞ design specification have been realized using the concept of linear matrix inequality (LMI) and the LMI approach has been used to quadratically stabilize the GI process via output feedback H ∞ controller. The controller has been designed on the basis of full 19th order linearized state-space model generated from the modified Sorensen's nonlinear model of GI process. The resulting controller has been tested with the nonlinear patient model (the modified Sorensen's model) in presence of patient parameter variations and other uncertainty conditions. The performance of the controller was assessed in terms of its ability to track the normoglycemic set point of 81 mg/dl with a typical multi-meal disturbance throughout a day that yields robust performance and noise rejection.

SDRE control strategy applied to a nonlinear robotic including drive motor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lima, Jeferson J. de, E-mail: jefersonjl82@gmail.com, E-mail: tusset@utfpr.edu.br, E-mail: fcjanzen@utfpr.edu.br, E-mail: piccirillo@utfpr.edu.br, E-mail: claudinor@utfpr.edu.br; Tusset, Angelo M., E-mail: jefersonjl82@gmail.com, E-mail: tusset@utfpr.edu.br, E-mail: fcjanzen@utfpr.edu.br, E-mail: piccirillo@utfpr.edu.br, E-mail: claudinor@utfpr.edu.br; Janzen, Frederic C., E-mail: jefersonjl82@gmail.com, E-mail: tusset@utfpr.edu.br, E-mail: fcjanzen@utfpr.edu.br, E-mail: piccirillo@utfpr.edu.br, E-mail: claudinor@utfpr.edu.br

A robotic control design considering all the inherent nonlinearities of the robot-engine configuration is developed. The interactions between the robot and joint motor drive mechanism are considered. The proposed control combines two strategies, one feedforward control in order to maintain the system in the desired coordinate, and feedback control system to take the system into a desired coordinate. The feedback control is obtained using State-Dependent Riccati Equation (SDRE). For link positioning two cases are considered. Case I: For control positioning, it is only used motor voltage; Case II: For control positioning, it is used both motor voltage and torque betweenmore » the links. Simulation results, including parametric uncertainties in control shows the feasibility of the proposed control for the considered system.« less

Adaptive neural output-feedback control for nonstrict-feedback time-delay fractional-order systems with output constraints and actuator nonlinearities.

PubMed

Zouari, Farouk; Ibeas, Asier; Boulkroune, Abdesselem; Cao, Jinde; Mehdi Arefi, Mohammad

2018-06-01

This study addresses the issue of the adaptive output tracking control for a category of uncertain nonstrict-feedback delayed incommensurate fractional-order systems in the presence of nonaffine structures, unmeasured pseudo-states, unknown control directions, unknown actuator nonlinearities and output constraints. Firstly, the mean value theorem and the Gaussian error function are introduced to eliminate the difficulties that arise from the nonaffine structures and the unknown actuator nonlinearities, respectively. Secondly, the immeasurable tracking error variables are suitably estimated by constructing a fractional-order linear observer. Thirdly, the neural network, the Razumikhin Lemma, the variable separation approach, and the smooth Nussbaum-type function are used to deal with the uncertain nonlinear dynamics, the unknown time-varying delays, the nonstrict feedback and the unknown control directions, respectively. Fourthly, asymmetric barrier Lyapunov functions are employed to overcome the violation of the output constraints and to tune online the parameters of the adaptive neural controller. Through rigorous analysis, it is proved that the boundedness of all variables in the closed-loop system and the semi global asymptotic tracking are ensured without transgression of the constraints. The principal contributions of this study can be summarized as follows: (1) based on Caputo's definitions and new lemmas, methods concerning the controllability, observability and stability analysis of integer-order systems are extended to fractional-order ones, (2) the output tracking objective for a relatively large class of uncertain systems is achieved with a simple controller and less tuning parameters. Finally, computer-simulation studies from the robotic field are given to demonstrate the effectiveness of the proposed controller. Copyright © 2018 Elsevier Ltd. All rights reserved.

Nonlinear laser dynamics induced by frequency shifted optical feedback: application to vibration measurements.

PubMed

Girardeau, Vadim; Goloni, Carolina; Jacquin, Olivier; Hugon, Olivier; Inglebert, Mehdi; Lacot, Eric

2016-12-01

In this article, we study the nonlinear dynamics of a laser subjected to frequency shifted optical reinjection coming back from a vibrating target. More specifically, we study the nonlinear dynamical coupling between the carrier and the vibration signal. The present work shows how the nonlinear amplification of the vibration spectrum is related to the strength of the carrier and how it must be compensated to obtain accurate (i.e., without bias) vibration measurements. The theoretical predictions, confirmed by numerical simulations, are in good agreement with the experimental data. The main motivation of this study is the understanding of the nonlinear response of a laser optical feedback imaging sensor for quantitative phase measurements of small vibrations in the case of strong optical feedback.

Quantum morphogenesis: A variation on Thom's catastrophe theory

NASA Astrophysics Data System (ADS)

Aerts, Dirk; Czachor, Marek; Gabora, Liane; Kuna, Maciej; Posiewnik, Andrzej; Pykacz, Jarosław; Syty, Monika

2003-05-01

Noncommutative propositions are characteristic of both quantum and nonquantum (sociological, biological, and psychological) situations. In a Hilbert space model, states, understood as correlations between all the possible propositions, are represented by density matrices. If systems in question interact via feedback with environment, their dynamics is nonlinear. Nonlinear evolutions of density matrices lead to the phenomenon of morphogenesis that may occur in noncommutative systems. Several explicit exactly solvable models are presented, including “birth and death of an organism” and “development of complementary properties.”

Solving a Local Boundary Value Problem for a Nonlinear Nonstationary System in the Class of Feedback Controls

NASA Astrophysics Data System (ADS)

Kvitko, A. N.

2018-01-01

An algorithm convenient for numerical implementation is proposed for constructing differentiable control functions that transfer a wide class of nonlinear nonstationary systems of ordinary differential equations from an initial state to a given point of the phase space. Constructive sufficient conditions imposed on the right-hand side of the controlled system are obtained under which this transfer is possible. The control of a robotic manipulator is considered, and its numerical simulation is performed.

Scattering Control Using Nonlinear Smart Metasurface with Internal Feedback

NASA Astrophysics Data System (ADS)

Semenikhina, D. V.; Semenikhin, A. I.

2017-05-01

The ideology of creation of a nonlinear smart metasurface with internal feedback for the adaptive control by spectral composition of scattered field is offered. The metasurface contains a lattice of strip elements with nonlinear loads-sensors. They are included in a circuit of internal feedback for the adaptive control of scattered field. Numerically it is shown that maximal levels of the second harmonic in the spectrum of scattered far field correspond to maximum of voltage rectified on metasurface. Experimentally the prototype of the plane smart covering on the basis of the metasurface in the form of strip lattice with controlled nonlinear loads-sensors is investigated for an idea confirmation.

Design of a feedback-feedforward steering controller for accurate path tracking and stability at the limits of handling

NASA Astrophysics Data System (ADS)

Kapania, Nitin R.; Gerdes, J. Christian

2015-12-01

This paper presents a feedback-feedforward steering controller that simultaneously maintains vehicle stability at the limits of handling while minimising lateral path tracking deviation. The design begins by considering the performance of a baseline controller with a lookahead feedback scheme and a feedforward algorithm based on a nonlinear vehicle handling diagram. While this initial design exhibits desirable stability properties at the limits of handling, the steady-state path deviation increases significantly at highway speeds. Results from both linear and nonlinear analyses indicate that lateral path tracking deviations are minimised when vehicle sideslip is held tangent to the desired path at all times. Analytical results show that directly incorporating this sideslip tangency condition into the steering feedback dramatically improves lateral path tracking, but at the expense of poor closed-loop stability margins. However, incorporating the desired sideslip behaviour into the feedforward loop creates a robust steering controller capable of accurate path tracking and oversteer correction at the physical limits of tyre friction. Experimental data collected from an Audi TTS test vehicle driving at the handling limits on a full length race circuit demonstrates the improved performance of the final controller design.

Neural-network-based state feedback control of a nonlinear discrete-time system in nonstrict feedback form.

PubMed

Jagannathan, Sarangapani; He, Pingan

2008-12-01

In this paper, a suite of adaptive neural network (NN) controllers is designed to deliver a desired tracking performance for the control of an unknown, second-order, nonlinear discrete-time system expressed in nonstrict feedback form. In the first approach, two feedforward NNs are employed in the controller with tracking error as the feedback variable whereas in the adaptive critic NN architecture, three feedforward NNs are used. In the adaptive critic architecture, two action NNs produce virtual and actual control inputs, respectively, whereas the third critic NN approximates certain strategic utility function and its output is employed for tuning action NN weights in order to attain the near-optimal control action. Both the NN control methods present a well-defined controller design and the noncausal problem in discrete-time backstepping design is avoided via NN approximation. A comparison between the controller methodologies is highlighted. The stability analysis of the closed-loop control schemes is demonstrated. The NN controller schemes do not require an offline learning phase and the NN weights can be initialized at zero or random. Results show that the performance of the proposed controller schemes is highly satisfactory while meeting the closed-loop stability.

Experimental feedback linearisation of a vibrating system with a non-smooth nonlinearity

NASA Astrophysics Data System (ADS)

Lisitano, D.; Jiffri, S.; Bonisoli, E.; Mottershead, J. E.

2018-03-01

Input-output partial feedback linearisation is demonstrated experimentally for the first time on a system with non-smooth nonlinearity, a laboratory three degrees of freedom lumped mass system with a piecewise-linear spring. The output degree of freedom is located away from the nonlinearity so that the partial feedback linearisation possesses nonlinear internal dynamics. The dynamic behaviour of the linearised part is specified by eigenvalue assignment and an investigation of the zero dynamics is carried out to confirm stability of the overall system. A tuned numerical model is developed for use in the controller and to produce numerical outputs for comparison with experimental closed-loop results. A new limitation of the feedback linearisation method is discovered in the case of lumped mass systems - that the input and output must share the same degrees of freedom.

Nonlinear control for a class of hydraulic servo system.

PubMed

Yu, Hong; Feng, Zheng-jin; Wang, Xu-yong

2004-11-01

The dynamics of hydraulic systems are highly nonlinear and the system may be subjected to non-smooth and discontinuous nonlinearities due to directional change of valve opening, friction, etc. Aside from the nonlinear nature of hydraulic dynamics, hydraulic servo systems also have large extent of model uncertainties. To address these challenging issues, a robust state-feedback controller is designed by employing backstepping design technique such that the system output tracks a given signal arbitrarily well, and all signals in the closed-loop system remain bounded. Moreover, a relevant disturbance attenuation inequality is satisfied by the closed-loop signals. Compared with previously proposed robust controllers, this paper's robust controller based on backstepping recursive design method is easier to design, and is more suitable for implementation.

Defense Acquisition Review Journal. Volume 16, Number 2

DTIC Science & Technology

2009-07-01

current status of the conventional munitions industry in the United States today and provides an economic theory for reviving this declining, but...Avant, 2007). United States Naval War College Professor Larry McCabe observed that an economic aspect to the emergence of private security...flows, feedback, and nonlinear relationships in managerial control. The methodology’s ability to model many diverse system components (e.g., work

Global output feedback stabilisation of stochastic high-order feedforward nonlinear systems with time-delay

NASA Astrophysics Data System (ADS)

Zhang, Kemei; Zhao, Cong-Ran; Xie, Xue-Jun

2015-12-01

This paper considers the problem of output feedback stabilisation for stochastic high-order feedforward nonlinear systems with time-varying delay. By using the homogeneous domination theory and solving several troublesome obstacles in the design and analysis, an output feedback controller is constructed to drive the closed-loop system globally asymptotically stable in probability.

Alternatives for jet engine control

NASA Technical Reports Server (NTRS)

Sain, M. K.

1984-01-01

The technical progress of researches Alternatives for Jet Engine Control is reported. A numerical study employing feedback tensors for optimal control of nonlinear systems was completed. It is believed that these studies are the first of their kind. State regulation, with a decrease in control power is demonstrated. A detailed treatment follows.

Elastic robot control - Nonlinear inversion and linear stabilization

NASA Technical Reports Server (NTRS)

Singh, S. N.; Schy, A. A.

1986-01-01

An approach to the control of elastic robot systems for space applications using inversion, servocompensation, and feedback stabilization is presented. For simplicity, a robot arm (PUMA type) with three rotational joints is considered. The third link is assumed to be elastic. Using an inversion algorithm, a nonlinear decoupling control law u(d) is derived such that in the closed-loop system independent control of joint angles by the three joint torquers is accomplished. For the stabilization of elastic oscillations, a linear feedback torquer control law u(s) is obtained applying linear quadratic optimization to the linearized arm model augmented with a servocompensator about the terminal state. Simulation results show that in spite of uncertainties in the payload and vehicle angular velocity, good joint angle control and damping of elastic oscillations are obtained with the torquer control law u = u(d) + u(s).

Model-Free control performance improvement using virtual reference feedback tuning and reinforcement Q-learning

NASA Astrophysics Data System (ADS)

Radac, Mircea-Bogdan; Precup, Radu-Emil; Roman, Raul-Cristian

2017-04-01

This paper proposes the combination of two model-free controller tuning techniques, namely linear virtual reference feedback tuning (VRFT) and nonlinear state-feedback Q-learning, referred to as a new mixed VRFT-Q learning approach. VRFT is first used to find stabilising feedback controller using input-output experimental data from the process in a model reference tracking setting. Reinforcement Q-learning is next applied in the same setting using input-state experimental data collected under perturbed VRFT to ensure good exploration. The Q-learning controller learned with a batch fitted Q iteration algorithm uses two neural networks, one for the Q-function estimator and one for the controller, respectively. The VRFT-Q learning approach is validated on position control of a two-degrees-of-motion open-loop stable multi input-multi output (MIMO) aerodynamic system (AS). Extensive simulations for the two independent control channels of the MIMO AS show that the Q-learning controllers clearly improve performance over the VRFT controllers.

Nonlinear aeroelastic analysis, flight dynamics, and control of a complete aircraft

NASA Astrophysics Data System (ADS)

Patil, Mayuresh Jayawant

The focus of this research was to analyze a high-aspect-ratio wing aircraft flying at low subsonic speeds. Such aircraft are designed for high-altitude, long-endurance missions. Due to the high flexibility and associated wing deformation, accurate prediction of aircraft response requires use of nonlinear theories. Also strong interactions between flight dynamics and aeroelasticity are expected. To analyze such aircraft one needs to have an analysis tool which includes the various couplings and interactions. A theoretical basis has been established for a consistent analysis which takes into account, (i) material anisotropy, (ii) geometrical nonlinearities of the structure, (iii) rigid-body motions, (iv) unsteady flow behavior, and (v) dynamic stall. The airplane structure is modeled as a set of rigidly attached beams. Each of the beams is modeled using the geometrically exact mixed variational formulation, thus taking into account geometrical nonlinearities arising due to large displacements and rotations. The cross-sectional stiffnesses are obtained using an asymptotically exact analysis, which can model arbitrary cross sections and material properties. An aerodynamic model, consisting of a unified lift model, a consistent combination of finite-state inflow model and a modified ONERA dynamic stall model, is coupled to the structural system to determine the equations of motion. The results obtained indicate the necessity of including nonlinear effects in aeroelastic analysis. Structural geometric nonlinearities result in drastic changes in aeroelastic characteristics, especially in case of high-aspect-ratio wings. The nonlinear stall effect is the dominant factor in limiting the amplitude of oscillation for most wings. The limit cycle oscillation (LCO) phenomenon is also investigated. Post-flutter and pre-flutter LCOs are possible depending on the disturbance mode and amplitude. Finally, static output feedback (SOF) controllers are designed for flutter suppression and gust alleviation. SOF controllers are very simple and thus easy to implement. For the case considered, SOF controllers with proper choice of sensors give results comparable to full state feedback (linear quadratic regulator) designs.

Optimal control of nonlinear continuous-time systems in strict-feedback form.

PubMed

Zargarzadeh, Hassan; Dierks, Travis; Jagannathan, Sarangapani

2015-10-01

This paper proposes a novel optimal tracking control scheme for nonlinear continuous-time systems in strict-feedback form with uncertain dynamics. The optimal tracking problem is transformed into an equivalent optimal regulation problem through a feedforward adaptive control input that is generated by modifying the standard backstepping technique. Subsequently, a neural network-based optimal control scheme is introduced to estimate the cost, or value function, over an infinite horizon for the resulting nonlinear continuous-time systems in affine form when the internal dynamics are unknown. The estimated cost function is then used to obtain the optimal feedback control input; therefore, the overall optimal control input for the nonlinear continuous-time system in strict-feedback form includes the feedforward plus the optimal feedback terms. It is shown that the estimated cost function minimizes the Hamilton-Jacobi-Bellman estimation error in a forward-in-time manner without using any value or policy iterations. Finally, optimal output feedback control is introduced through the design of a suitable observer. Lyapunov theory is utilized to show the overall stability of the proposed schemes without requiring an initial admissible controller. Simulation examples are provided to validate the theoretical results.

A nonlinear controller design for permanent magnet motors using a synchronization-based technique inspired from the Lorenz system.

PubMed

Zaher, Ashraf A

2008-03-01

The dynamic behavior of a permanent magnet synchronous machine (PMSM) is analyzed. Nominal and special operating conditions are explored to show that the PMSM can experience chaos. A nonlinear controller is introduced to control these unwanted chaotic oscillations and to bring the PMSM to a stable steady state. The designed controller uses a pole-placement approach to force the closed-loop system to follow the performance of a simple first-order linear system with zero steady-state error to a desired set point. The similarity between the mathematical model of the PMSM and the famous chaotic Lorenz system is utilized to design a synchronization-based state observer using only the angular speed for feedback. Simulation results verify the effectiveness of the proposed controller in eliminating the chaotic oscillations while using a single feedback signal. The superiority of the proposed controller is further demonstrated by comparing it with a conventional PID controller. Finally, a laboratory-based experiment was conducted using the MCK2812 C Pro-MS(BL) motion control kit to confirm the theoretical results and to verify both the causality and versatility of the proposed controller.

Hierarchical cluster-based partial least squares regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models.

PubMed

Tøndel, Kristin; Indahl, Ulf G; Gjuvsland, Arne B; Vik, Jon Olav; Hunter, Peter; Omholt, Stig W; Martens, Harald

2011-06-01

Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. HC-PLSR is a promising approach for metamodelling in systems biology, especially for highly nonlinear or non-monotone parameter to phenotype maps. The algorithm can be flexibly adjusted to suit the complexity of the dynamic model behaviour, inviting automation in the metamodelling of complex systems.

Hierarchical Cluster-based Partial Least Squares Regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models

PubMed Central

2011-01-01

Background Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Results Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. Conclusions HC-PLSR is a promising approach for metamodelling in systems biology, especially for highly nonlinear or non-monotone parameter to phenotype maps. The algorithm can be flexibly adjusted to suit the complexity of the dynamic model behaviour, inviting automation in the metamodelling of complex systems. PMID:21627852

Fuzzy Model-based Pitch Stabilization and Wing Vibration Suppression of Flexible Wing Aircraft.

NASA Technical Reports Server (NTRS)

Ayoubi, Mohammad A.; Swei, Sean Shan-Min; Nguyen, Nhan T.

2014-01-01

This paper presents a fuzzy nonlinear controller to regulate the longitudinal dynamics of an aircraft and suppress the bending and torsional vibrations of its flexible wings. The fuzzy controller utilizes full-state feedback with input constraint. First, the Takagi-Sugeno fuzzy linear model is developed which approximates the coupled aeroelastic aircraft model. Then, based on the fuzzy linear model, a fuzzy controller is developed to utilize a full-state feedback and stabilize the system while it satisfies the control input constraint. Linear matrix inequality (LMI) techniques are employed to solve the fuzzy control problem. Finally, the performance of the proposed controller is demonstrated on the NASA Generic Transport Model (GTM).

All-Union Conference on Laser Optics, 4th, Leningrad, USSR, January 13-18, 1984, Proceedings

NASA Astrophysics Data System (ADS)

Bukhenskii, M. F.

1984-08-01

The papers presented in this volume provide an overview of current theoretical and experimental research in laser optics. Topics discussed include electronically controlled tunable lasers, nonlinear phenomena in fiber-optic waveguides, holographic distributed-feedback dye lasers, and new developments in solid-state lasers. Papers are also presented on the generation of picosecond pulses through self-Q-switching in a distributed-feedback laser, temporal compression of light pulses during stimulated backscattering, and optimization of second harmonic generation in a multimode Nd:glass laser.

Rotorcraft pursuit-evasion in nap-of-the-earth flight

NASA Technical Reports Server (NTRS)

Menon, P. K. A.; Cheng, V. H. L.; Kim, E.

1990-01-01

Two approaches for studying the pursuit-evasion problem between rotorcraft executing nap-of-the-earth flight are presented. The first of these employs a constant speed kinematic helicopter model, while the second approach uses a three degree of freedom point-mass model. The candidate solutions to the first differential game are generated by integrating the state-costate equations backward in time. The second problem employs feedback linearization to obtain guidance laws in nonlinear feedback form. Both approaches explicitly use the terrain profile data. Sample extremals are presented.

A genuine nonlinear approach for controller design of a boiler-turbine system.

PubMed

Yang, Shizhong; Qian, Chunjiang; Du, Haibo

2012-05-01

This paper proposes a genuine nonlinear approach for controller design of a drum-type boiler-turbine system. Based on a second order nonlinear model, a finite-time convergent controller is first designed to drive the states to their setpoints in a finite time. In the case when the state variables are unmeasurable, the system will be regulated using a constant controller or an output feedback controller. An adaptive controller is also designed to stabilize the system since the model parameters may vary under different operating points. The novelty of the proposed controller design approach lies in fully utilizing the system nonlinearities instead of linearizing or canceling them. In addition, the newly developed techniques for finite-time convergent controller are used to guarantee fast convergence of the system. Simulations are conducted under different cases and the results are presented to illustrate the performance of the proposed controllers. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.

EKF-Based Enhanced Performance Controller Design for Nonlinear Stochastic Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Yuyang; Zhang, Qichun; Wang, Hong

In this paper, a novel control algorithm is presented to enhance the performance of tracking property for a class of non-linear dynamic stochastic systems with unmeasurable variables. To minimize the entropy of tracking errors without changing the existing closed loop with PI controller, the enhanced performance loop is constructed based on the state estimation by extended Kalman Filter and the new controller is designed by full state feedback following this presented control algorithm. Besides, the conditions are obtained for the stability analysis in the mean square sense. In the end, the comparative simulation results are given to illustrate the effectivenessmore » of proposed control algorithm.« less

SOS based robust H(∞) fuzzy dynamic output feedback control of nonlinear networked control systems.

PubMed

Chae, Seunghwan; Nguang, Sing Kiong

2014-07-01

In this paper, a methodology for designing a fuzzy dynamic output feedback controller for discrete-time nonlinear networked control systems is presented where the nonlinear plant is modelled by a Takagi-Sugeno fuzzy model and the network-induced delays by a finite state Markov process. The transition probability matrix for the Markov process is allowed to be partially known, providing a more practical consideration of the real world. Furthermore, the fuzzy controller's membership functions and premise variables are not assumed to be the same as the plant's membership functions and premise variables, that is, the proposed approach can handle the case, when the premise of the plant are not measurable or delayed. The membership functions of the plant and the controller are approximated as polynomial functions, then incorporated into the controller design. Sufficient conditions for the existence of the controller are derived in terms of sum of square inequalities, which are then solved by YALMIP. Finally, a numerical example is used to demonstrate the validity of the proposed methodology.

Self-sustained micro mechanical oscillator with linear feedback

DOE PAGES

Chen, Changyao; Zanette, Damian H.; Guest, Jeffrey R.; ...

2016-07-01

Autonomous oscillators, such as clocks and lasers, produce periodic signals without any external frequency reference. In order to sustain stable periodic motions, there needs to be external energy supply as well as nonlinearity built into the oscillator to regulate the amplitude. Usually, nonlinearity is provided by the sustaining feedback mechanism, which also supplies energy, whereas the constituent resonator that determines the output frequency stays linear. Here we propose a new self-sustaining scheme that relies on the nonlinearity originating from the resonator itself to limit the oscillation amplitude, while the feedback remains linear. We introduce a model to describe the workingmore » principle of the self-sustained oscillations and validate it with experiments performed on a nonlinear microelectromechanical (MEMS) based oscillator.« less

Inverse optimal design of input-to-state stabilisation for affine nonlinear systems with input delays

NASA Astrophysics Data System (ADS)

Cai, Xiushan; Meng, Lingxin; Zhang, Wei; Liu, Leipo

2018-03-01

We establish robustness of the predictor feedback control law to perturbations appearing at the system input for affine nonlinear systems with time-varying input delay and additive disturbances. Furthermore, it is shown that it is inverse optimal with respect to a differential game problem. All of the stability and inverse optimality proofs are based on the infinite-dimensional backstepping transformation and an appropriate Lyapunov functional. A single-link manipulator subject to input delays and disturbances is given to illustrate the validity of the proposed method.

Application of a passivity based control methodology for flexible joint robots to a simplified Space Shuttle RMS

NASA Technical Reports Server (NTRS)

Sicard, Pierre; Wen, John T.

1992-01-01

A passivity approach for the control design of flexible joint robots is applied to the rate control of a three-link arm modeled after the shoulder yaw joint of the Space Shuttle Remote Manipulator System (RMS). The system model includes friction and elastic joint couplings modeled as nonlinear springs. The basic structure of the proposed controller is the sum of a model-based feedforward and a model-independent feedback. A regulator approach with link state feedback is employed to define the desired motor state. Passivity theory is used to design a motor state-based controller to stabilize the error system formed by the feedforward. Simulation results show that greatly improved performance was obtained by using the proposed controller over the existing RMS controller.

H∞ output tracking control of discrete-time nonlinear systems via standard neural network models.

PubMed

Liu, Meiqin; Zhang, Senlin; Chen, Haiyang; Sheng, Weihua

2014-10-01

This brief proposes an output tracking control for a class of discrete-time nonlinear systems with disturbances. A standard neural network model is used to represent discrete-time nonlinear systems whose nonlinearity satisfies the sector conditions. H∞ control performance for the closed-loop system including the standard neural network model, the reference model, and state feedback controller is analyzed using Lyapunov-Krasovskii stability theorem and linear matrix inequality (LMI) approach. The H∞ controller, of which the parameters are obtained by solving LMIs, guarantees that the output of the closed-loop system closely tracks the output of a given reference model well, and reduces the influence of disturbances on the tracking error. Three numerical examples are provided to show the effectiveness of the proposed H∞ output tracking design approach.

A computational algorithm for spacecraft control and momentum management

NASA Technical Reports Server (NTRS)

Dzielski, John; Bergmann, Edward; Paradiso, Joseph

1990-01-01

Developments in the area of nonlinear control theory have shown how coordinate changes in the state and input spaces of a dynamical system can be used to transform certain nonlinear differential equations into equivalent linear equations. These techniques are applied to the control of a spacecraft equipped with momentum exchange devices. An optimal control problem is formulated that incorporates a nonlinear spacecraft model. An algorithm is developed for solving the optimization problem using feedback linearization to transform to an equivalent problem involving a linear dynamical constraint and a functional approximation technique to solve for the linear dynamics in terms of the control. The original problem is transformed into an unconstrained nonlinear quadratic program that yields an approximate solution to the original problem. Two examples are presented to illustrate the results.

Small Body GN&C Research Report: A Robust Model Predictive Control Algorithm with Guaranteed Resolvability

NASA Technical Reports Server (NTRS)

Acikmese, Behcet A.; Carson, John M., III

2005-01-01

A robustly stabilizing MPC (model predictive control) algorithm for uncertain nonlinear systems is developed that guarantees the resolvability of the associated finite-horizon optimal control problem in a receding-horizon implementation. The control consists of two components; (i) feedforward, and (ii) feedback part. Feed-forward control is obtained by online solution of a finite-horizon optimal control problem for the nominal system dynamics. The feedback control policy is designed off-line based on a bound on the uncertainty in the system model. The entire controller is shown to be robustly stabilizing with a region of attraction composed of initial states for which the finite-horizon optimal control problem is feasible. The controller design for this algorithm is demonstrated on a class of systems with uncertain nonlinear terms that have norm-bounded derivatives, and derivatives in polytopes. An illustrative numerical example is also provided.

Adaptive output feedback NN control of a class of discrete-time MIMO nonlinear systems with unknown control directions.

PubMed

Li, Yanan; Yang, Chenguang; Ge, Shuzhi Sam; Lee, Tong Heng

2011-04-01

In this paper, adaptive neural network (NN) control is investigated for a class of block triangular multiinput-multioutput nonlinear discrete-time systems with each subsystem in pure-feedback form with unknown control directions. These systems are of couplings in every equation of each subsystem, and different subsystems may have different orders. To avoid the noncausal problem in the control design, the system is transformed into a predictor form by rigorous derivation. By exploring the properties of the block triangular form, implicit controls are developed for each subsystem such that the couplings of inputs and states among subsystems have been completely decoupled. The radial basis function NN is employed to approximate the unknown control. Each subsystem achieves a semiglobal uniformly ultimately bounded stability with the proposed control, and simulation results are presented to demonstrate its efficiency.

Learning from ISS-modular adaptive NN control of nonlinear strict-feedback systems.

PubMed

Wang, Cong; Wang, Min; Liu, Tengfei; Hill, David J

2012-10-01

This paper studies learning from adaptive neural control (ANC) for a class of nonlinear strict-feedback systems with unknown affine terms. To achieve the purpose of learning, a simple input-to-state stability (ISS) modular ANC method is first presented to ensure the boundedness of all the signals in the closed-loop system and the convergence of tracking errors in finite time. Subsequently, it is proven that learning with the proposed stable ISS-modular ANC can be achieved. The cascade structure and unknown affine terms of the considered systems make it very difficult to achieve learning using existing methods. To overcome these difficulties, the stable closed-loop system in the control process is decomposed into a series of linear time-varying (LTV) perturbed subsystems with the appropriate state transformation. Using a recursive design, the partial persistent excitation condition for the radial basis function neural network (NN) is established, which guarantees exponential stability of LTV perturbed subsystems. Consequently, accurate approximation of the closed-loop system dynamics is achieved in a local region along recurrent orbits of closed-loop signals, and learning is implemented during a closed-loop feedback control process. The learned knowledge is reused to achieve stability and an improved performance, thereby avoiding the tremendous repeated training process of NNs. Simulation studies are given to demonstrate the effectiveness of the proposed method.

Adaptive Control via Neural Output Feedback for a Class of Nonlinear Discrete-Time Systems in a Nested Interconnected Form.

PubMed

Li, Dong-Juan; Li, Da-Peng

2017-09-14

In this paper, an adaptive output feedback control is framed for uncertain nonlinear discrete-time systems. The considered systems are a class of multi-input multioutput nonaffine nonlinear systems, and they are in the nested lower triangular form. Furthermore, the unknown dead-zone inputs are nonlinearly embedded into the systems. These properties of the systems will make it very difficult and challenging to construct a stable controller. By introducing a new diffeomorphism coordinate transformation, the controlled system is first transformed into a state-output model. By introducing a group of new variables, an input-output model is finally obtained. Based on the transformed model, the implicit function theorem is used to determine the existence of the ideal controllers and the approximators are employed to approximate the ideal controllers. By using the mean value theorem, the nonaffine functions of systems can become an affine structure but nonaffine terms still exist. The adaptation auxiliary terms are skillfully designed to cancel the effect of the dead-zone input. Based on the Lyapunov difference theorem, the boundedness of all the signals in the closed-loop system can be ensured and the tracking errors are kept in a bounded compact set. The effectiveness of the proposed technique is checked by a simulation study.

Delay-range-dependent chaos synchronization approach under varying time-lags and delayed nonlinear coupling.

PubMed

Zaheer, Muhammad Hamad; Rehan, Muhammad; Mustafa, Ghulam; Ashraf, Muhammad

2014-11-01

This paper proposes a novel state feedback delay-range-dependent control approach for chaos synchronization in coupled nonlinear time-delay systems. The coupling between two systems is esteemed to be nonlinear subject to time-lags. Time-varying nature of both the intrinsic and the coupling delays is incorporated to broad scope of the present study for a better-quality synchronization controller synthesis. Lyapunov-Krasovskii (LK) functional is employed to derive delay-range-dependent conditions that can be solved by means of the conventional linear matrix inequality (LMI)-tools. The resultant control approach for chaos synchronization of the master-slave time-delay systems considers non-zero lower bound of the intrinsic as well as the coupling time-delays. Further, the delay-dependent synchronization condition has been established as a special case of the proposed LK functional treatment. Furthermore, a delay-range-dependent condition, independent of the delay-rate, has been provided to address the situation when upper bound of the delay-derivative is unknown. A robust state feedback control methodology is formulated for synchronization of the time-delay chaotic networks against the L2 norm bounded perturbations by minimizing the L2 gain from the disturbance to the synchronization error. Numerical simulation results are provided for the time-delay chaotic networks to show effectiveness of the proposed delay-range-dependent chaos synchronization methodologies. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Nonlinear Control Systems

DTIC Science & Technology

2007-03-01

Finite -dimensional regulators for a class of infinite dimensional systems ,” Systems and Control Letters, 3 (1983), 7-12. [11] B...semiglobal stabilizability by encoded state feedback,” to appear in Systems and Control Letters. 22 29. C. De Persis, A. Isidori, “Global stabilization of...nonequilibrium setting, for both finite and infinite dimensional control systems . Our objectives for distributed parameter systems included

Electro-optic chaotic system based on the reverse-time chaos theory and a nonlinear hybrid feedback loop.

PubMed

Jiang, Xingxing; Cheng, Mengfan; Luo, Fengguang; Deng, Lei; Fu, Songnian; Ke, Changjian; Zhang, Minming; Tang, Ming; Shum, Ping; Liu, Deming

2016-12-12

A novel electro-optic chaos source is proposed on the basis of the reverse-time chaos theory and an analog-digital hybrid feedback loop. The analog output of the system can be determined by the numeric states of shift registers, which makes the system robust and easy to control. The dynamical properties as well as the complexity dependence on the feedback parameters are investigated in detail. The correlation characteristics of the system are also studied. Two improving strategies which were established in digital field and analog field are proposed to conceal the time-delay signature. The proposed scheme has the potential to be used in radar and optical secure communication systems.

Nonlinear filter based decision feedback equalizer for optical communication systems.

PubMed

Han, Xiaoqi; Cheng, Chi-Hao

2014-04-07

Nonlinear impairments in optical communication system have become a major concern of optical engineers. In this paper, we demonstrate that utilizing a nonlinear filter based Decision Feedback Equalizer (DFE) with error detection capability can deliver a better performance compared with the conventional linear filter based DFE. The proposed algorithms are tested in simulation using a coherent 100 Gb/sec 16-QAM optical communication system in a legacy optical network setting.

New numerical methods for open-loop and feedback solutions to dynamic optimization problems

NASA Astrophysics Data System (ADS)

Ghosh, Pradipto

The topic of the first part of this research is trajectory optimization of dynamical systems via computational swarm intelligence. Particle swarm optimization is a nature-inspired heuristic search method that relies on a group of potential solutions to explore the fitness landscape. Conceptually, each particle in the swarm uses its own memory as well as the knowledge accumulated by the entire swarm to iteratively converge on an optimal or near-optimal solution. It is relatively straightforward to implement and unlike gradient-based solvers, does not require an initial guess or continuity in the problem definition. Although particle swarm optimization has been successfully employed in solving static optimization problems, its application in dynamic optimization, as posed in optimal control theory, is still relatively new. In the first half of this thesis particle swarm optimization is used to generate near-optimal solutions to several nontrivial trajectory optimization problems including thrust programming for minimum fuel, multi-burn spacecraft orbit transfer, and computing minimum-time rest-to-rest trajectories for a robotic manipulator. A distinct feature of the particle swarm optimization implementation in this work is the runtime selection of the optimal solution structure. Optimal trajectories are generated by solving instances of constrained nonlinear mixed-integer programming problems with the swarming technique. For each solved optimal programming problem, the particle swarm optimization result is compared with a nearly exact solution found via a direct method using nonlinear programming. Numerical experiments indicate that swarm search can locate solutions to very great accuracy. The second half of this research develops a new extremal-field approach for synthesizing nearly optimal feedback controllers for optimal control and two-player pursuit-evasion games described by general nonlinear differential equations. A notable revelation from this development is that the resulting control law has an algebraic closed-form structure. The proposed method uses an optimal spatial statistical predictor called universal kriging to construct the surrogate model of a feedback controller, which is capable of quickly predicting an optimal control estimate based on current state (and time) information. With universal kriging, an approximation to the optimal feedback map is computed by conceptualizing a set of state-control samples from pre-computed extremals to be a particular realization of a jointly Gaussian spatial process. Feedback policies are computed for a variety of example dynamic optimization problems in order to evaluate the effectiveness of this methodology. This feedback synthesis approach is found to combine good numerical accuracy with low computational overhead, making it a suitable candidate for real-time applications. Particle swarm and universal kriging are combined for a capstone example, a near optimal, near-admissible, full-state feedback control law is computed and tested for the heat-load-limited atmospheric-turn guidance of an aeroassisted transfer vehicle. The performance of this explicit guidance scheme is found to be very promising; initial errors in atmospheric entry due to simulated thruster misfirings are found to be accurately corrected while closely respecting the algebraic state-inequality constraint.

Adaptive Neural Network-Based Event-Triggered Control of Single-Input Single-Output Nonlinear Discrete-Time Systems.

PubMed

Sahoo, Avimanyu; Xu, Hao; Jagannathan, Sarangapani

2016-01-01

This paper presents a novel adaptive neural network (NN) control of single-input and single-output uncertain nonlinear discrete-time systems under event sampled NN inputs. In this control scheme, the feedback signals are transmitted, and the NN weights are tuned in an aperiodic manner at the event sampled instants. After reviewing the NN approximation property with event sampled inputs, an adaptive state estimator (SE), consisting of linearly parameterized NNs, is utilized to approximate the unknown system dynamics in an event sampled context. The SE is viewed as a model and its approximated dynamics and the state vector, during any two events, are utilized for the event-triggered controller design. An adaptive event-trigger condition is derived by using both the estimated NN weights and a dead-zone operator to determine the event sampling instants. This condition both facilitates the NN approximation and reduces the transmission of feedback signals. The ultimate boundedness of both the NN weight estimation error and the system state vector is demonstrated through the Lyapunov approach. As expected, during an initial online learning phase, events are observed more frequently. Over time with the convergence of the NN weights, the inter-event times increase, thereby lowering the number of triggered events. These claims are illustrated through the simulation results.

An analysis of a nonlinear instability in the implementation of a VTOL control system

NASA Technical Reports Server (NTRS)

Weber, J. M.

1982-01-01

The contributions to nonlinear behavior and unstable response of the model following yaw control system of a VTOL aircraft during hover were determined. The system was designed as a state rate feedback implicit model follower that provided yaw rate command/heading hold capability and used combined full authority parallel and limited authority series servo actuators to generate an input to the yaw reaction control system of the aircraft. Both linear and nonlinear system models, as well as describing function linearization techniques were used to determine the influence on the control system instability of input magnitude and bandwidth, series servo authority, and system bandwidth. Results of the analysis describe stability boundaries as a function of these system design characteristics.

Model reference tracking control of an aircraft: a robust adaptive approach

NASA Astrophysics Data System (ADS)

Tanyer, Ilker; Tatlicioglu, Enver; Zergeroglu, Erkan

2017-05-01

This work presents the design and the corresponding analysis of a nonlinear robust adaptive controller for model reference tracking of an aircraft that has parametric uncertainties in its system matrices and additive state- and/or time-dependent nonlinear disturbance-like terms in its dynamics. Specifically, robust integral of the sign of the error feedback term and an adaptive term is fused with a proportional integral controller. Lyapunov-based stability analysis techniques are utilised to prove global asymptotic convergence of the output tracking error. Extensive numerical simulations are presented to illustrate the performance of the proposed robust adaptive controller.

Inferring Instantaneous, Multivariate and Nonlinear Sensitivities for the Analysis of Feedback Processes in a Dynamical System: Lorenz Model Case Study

NASA Technical Reports Server (NTRS)

Aires, Filipe; Rossow, William B.; Hansen, James E. (Technical Monitor)

2001-01-01

A new approach is presented for the analysis of feedback processes in a nonlinear dynamical system by observing its variations. The new methodology consists of statistical estimates of the sensitivities between all pairs of variables in the system based on a neural network modeling of the dynamical system. The model can then be used to estimate the instantaneous, multivariate and nonlinear sensitivities, which are shown to be essential for the analysis of the feedbacks processes involved in the dynamical system. The method is described and tested on synthetic data from the low-order Lorenz circulation model where the correct sensitivities can be evaluated analytically.

Nonlinear feedback method of robot control - A preliminary experimental study

NASA Technical Reports Server (NTRS)

Tarn, T. J.; Ganguly, S.; Li, Z.; Bejczy, A. K.

1990-01-01

The nonlinear feedback method of robot control has been experimentally implemented on two PUMA 560 robot arms. The feasibility of the proposed controller, which was shown viable through simulation results earlier, is stressed. The servomechanism operates in task space, and the nonlinear feedback takes care of the necessary transformations to compute the necessary joint currents. A discussion is presented of the implementation with details of the experiments performed. The performance of the controller is encouraging but was limited to 100-Hz sampling frequency and to derived velocity information at the time of the experimentation. The setup of the lab, the software aspects, results, and the control hardware architecture that has recently been implemented are discussed.

Soft tissue deformation modelling through neural dynamics-based reaction-diffusion mechanics.

PubMed

Zhang, Jinao; Zhong, Yongmin; Gu, Chengfan

2018-05-30

Soft tissue deformation modelling forms the basis of development of surgical simulation, surgical planning and robotic-assisted minimally invasive surgery. This paper presents a new methodology for modelling of soft tissue deformation based on reaction-diffusion mechanics via neural dynamics. The potential energy stored in soft tissues due to a mechanical load to deform tissues away from their rest state is treated as the equivalent transmembrane potential energy, and it is distributed in the tissue masses in the manner of reaction-diffusion propagation of nonlinear electrical waves. The reaction-diffusion propagation of mechanical potential energy and nonrigid mechanics of motion are combined to model soft tissue deformation and its dynamics, both of which are further formulated as the dynamics of cellular neural networks to achieve real-time computational performance. The proposed methodology is implemented with a haptic device for interactive soft tissue deformation with force feedback. Experimental results demonstrate that the proposed methodology exhibits nonlinear force-displacement relationship for nonlinear soft tissue deformation. Homogeneous, anisotropic and heterogeneous soft tissue material properties can be modelled through the inherent physical properties of mass points. Graphical abstract Soft tissue deformation modelling with haptic feedback via neural dynamics-based reaction-diffusion mechanics.

Optical feedback technique extends frequency response of photoconductors

NASA Technical Reports Server (NTRS)

Katzberg, S. J.

1975-01-01

Feedback circuit consists of high-gain light-to-voltage converter with frequency-limited nonlinear photoconductor inside feedback loop. Feedback element is visible light-emitting diode with light-out versus current-in characteristic that is linear over several decades.

Reinforcement learning controller design for affine nonlinear discrete-time systems using online approximators.

PubMed

Yang, Qinmin; Jagannathan, Sarangapani

2012-04-01

In this paper, reinforcement learning state- and output-feedback-based adaptive critic controller designs are proposed by using the online approximators (OLAs) for a general multi-input and multioutput affine unknown nonlinear discretetime systems in the presence of bounded disturbances. The proposed controller design has two entities, an action network that is designed to produce optimal signal and a critic network that evaluates the performance of the action network. The critic estimates the cost-to-go function which is tuned online using recursive equations derived from heuristic dynamic programming. Here, neural networks (NNs) are used both for the action and critic whereas any OLAs, such as radial basis functions, splines, fuzzy logic, etc., can be utilized. For the output-feedback counterpart, an additional NN is designated as the observer to estimate the unavailable system states, and thus, separation principle is not required. The NN weight tuning laws for the controller schemes are also derived while ensuring uniform ultimate boundedness of the closed-loop system using Lyapunov theory. Finally, the effectiveness of the two controllers is tested in simulation on a pendulum balancing system and a two-link robotic arm system.

Decentralized Adaptive Neural Output-Feedback DSC for Switched Large-Scale Nonlinear Systems.

PubMed

Lijun Long; Jun Zhao

2017-04-01

In this paper, for a class of switched large-scale uncertain nonlinear systems with unknown control coefficients and unmeasurable states, a switched-dynamic-surface-based decentralized adaptive neural output-feedback control approach is developed. The approach proposed extends the classical dynamic surface control (DSC) technique for nonswitched version to switched version by designing switched first-order filters, which overcomes the problem of multiple "explosion of complexity." Also, a dual common coordinates transformation of all subsystems is exploited to avoid individual coordinate transformations for subsystems that are required when applying the backstepping recursive design scheme. Nussbaum-type functions are utilized to handle the unknown control coefficients, and a switched neural network observer is constructed to estimate the unmeasurable states. Combining with the average dwell time method and backstepping and the DSC technique, decentralized adaptive neural controllers of subsystems are explicitly designed. It is proved that the approach provided can guarantee the semiglobal uniformly ultimately boundedness for all the signals in the closed-loop system under a class of switching signals with average dwell time, and the tracking errors to a small neighborhood of the origin. A two inverted pendulums system is provided to demonstrate the effectiveness of the method proposed.

Feedback Control of Unsteady Flow and Vortex-Induced Vibration

NASA Astrophysics Data System (ADS)

Jaiman, Rajeev; Yao, Weigang

2017-11-01

We present an active feedback blowing and suction (AFBS) procedure via model reduction for unsteady wake flow and the vortex-induced vibration (VIV) of circular cylinders. The reduced-order model (ROM) for the AFBS procedure is developed by the eigensystem realization (ERA) algorithm, which provides a low-order representation of the unsteady flow dynamics in the neighbourhood of the equilibrium steady state. The actuation is considered via vertical suction and blowing jet at the porous surface of a circular cylinder with a body mounted force sensor. The resulting controller designed by linear low-order approximation is able to suppress the nonlinear saturated state. A systematic linear ROM-based stability analysis is performed to understand the eigenvalue distributions of elastically mounted circular cylinders. The results from the ROM analysis are consistent with those obtained from full nonlinear fluid-structure interaction simulations. A sensitivity study on the number of suction/blowing actuators, the angular arrangement of actuators, and the combined versus independent control architectures has been performed. Overall, the proposed control is found to be effective in suppressing the vortex street and the VIV for a range of reduced velocities and mass ratios.

New nonlinear control algorithms for multiple robot arms

NASA Technical Reports Server (NTRS)

Tarn, T. J.; Bejczy, A. K.; Yun, X.

1988-01-01

Multiple coordinated robot arms are modeled by considering the arms as closed kinematic chains and as a force-constrained mechanical system working on the same object simultaneously. In both formulations, a novel dynamic control method is discussed. It is based on feedback linearization and simultaneous output decoupling technique. By applying a nonlinear feedback and a nonlinear coordinate transformation, the complicated model of the multiple robot arms in either formulation is converted into a linear and output decoupled system. The linear system control theory and optimal control theory are used to design robust controllers in the task space. The first formulation has the advantage of automatically handling the coordination and load distribution among the robot arms. In the second formulation, it was found that by choosing a general output equation it became possible simultaneously to superimpose the position and velocity error feedback with the force-torque error feedback in the task space.

Control of constraint forces and trajectories in a rich sensory and actuation environment.

PubMed

Hemami, Hooshang; Dariush, Behzad

2010-12-01

A simple control strategy is proposed and applied to a class of non-linear systems that have abundant sensory and actuation channels as in living systems. The main objective is the independent control of constrained trajectories of motion, and control of the corresponding constraint forces. The peripheral controller is a proportional, derivative and integral (PID) controller. A central controller produces, via pattern generators, reference signals that are the desired constrained position and velocity trajectories, and the desired constraint forces. The basic tenet of the this hybrid control strategy is the use of two mechanisms: 1. linear state and force feedback, and 2. non-linear constraint velocity feedback - sliding mode feedback. The first mechanism can be envisioned as a high gain feedback systems. The high gain attribute imitates the agonist-antagonist co-activation in natural systems. The strategy is applied to the control of the force and trajectory of a two-segment thigh-leg planar biped leg with a mass-less foot cranking a pedal that is analogous to a bicycle pedal. Five computational experiments are presented to show the effectiveness of the strategy and the performance of the controller. The findings of this paper are applicable to the design of orthoses and prostheses to supplement functional electrical stimulation for support purposes in the spinally injured cases. Copyright © 2010 Elsevier Inc. All rights reserved.

Implementing Nonlinear Feedback Controllers Using DNA Strand Displacement Reactions.

PubMed

Sawlekar, Rucha; Montefusco, Francesco; Kulkarni, Vishwesh V; Bates, Declan G

2016-07-01

We show how an important class of nonlinear feedback controllers can be designed using idealized abstract chemical reactions and implemented via DNA strand displacement (DSD) reactions. Exploiting chemical reaction networks (CRNs) as a programming language for the design of complex circuits and networks, we show how a set of unimolecular and bimolecular reactions can be used to realize input-output dynamics that produce a nonlinear quasi sliding mode (QSM) feedback controller. The kinetics of the required chemical reactions can then be implemented as enzyme-free, enthalpy/entropy driven DNA reactions using a toehold mediated strand displacement mechanism via Watson-Crick base pairing and branch migration. We demonstrate that the closed loop response of the nonlinear QSM controller outperforms a traditional linear controller by facilitating much faster tracking response dynamics without introducing overshoots in the transient response. The resulting controller is highly modular and is less affected by retroactivity effects than standard linear designs.

Chaos synchronization of uncertain chaotic systems using composite nonlinear feedback based integral sliding mode control.

PubMed

Mobayen, Saleh

2018-06-01

This paper proposes a combination of composite nonlinear feedback and integral sliding mode techniques for fast and accurate chaos synchronization of uncertain chaotic systems with Lipschitz nonlinear functions, time-varying delays and disturbances. The composite nonlinear feedback method allows accurate following of the master chaotic system and the integral sliding mode control provides invariance property which rejects the perturbations and preserves the stability of the closed-loop system. Based on the Lyapunov- Krasovskii stability theory and linear matrix inequalities, a novel sufficient condition is offered for the chaos synchronization of uncertain chaotic systems. This method not only guarantees the robustness against perturbations and time-delays, but also eliminates reaching phase and avoids chattering problem. Simulation results demonstrate that the suggested procedure leads to a great control performance. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Nonlinear force feedback control of piezoelectric-hydraulic pump actuator for automotive transmission shift control

NASA Astrophysics Data System (ADS)

Kim, Gi-Woo; Wang, K. W.

2008-03-01

In recent years, researchers have investigated the feasibility of utilizing piezoelectric-hydraulic pump based actuation systems for automotive transmission controls. This new concept could eventually reduce the complexity, weight, and fuel consumption of the current transmissions. In this research, we focus on how to utilize this new approach on the shift control of automatic transmissions (AT), which generally requires pressure profiling for friction elements during the operation. To illustrate the concept, we will consider the 1--> 2 up shift control using band brake friction elements. In order to perform the actuation force tracking for AT shift control, nonlinear force feedback control laws are designed based on the sliding mode theory for the given nonlinear system. This paper will describe the modeling of the band brake actuation system, the design of the nonlinear force feedback controller, and simulation and experimental results for demonstration of the new concept.

Neural dynamic programming and its application to control systems

NASA Astrophysics Data System (ADS)

Seong, Chang-Yun

There are few general practical feedback control methods for nonlinear MIMO (multi-input-multi-output) systems, although such methods exist for their linear counterparts. Neural Dynamic Programming (NDP) is proposed as a practical design method of optimal feedback controllers for nonlinear MIMO systems. NDP is an offspring of both neural networks and optimal control theory. In optimal control theory, the optimal solution to any nonlinear MIMO control problem may be obtained from the Hamilton-Jacobi-Bellman equation (HJB) or the Euler-Lagrange equations (EL). The two sets of equations provide the same solution in different forms: EL leads to a sequence of optimal control vectors, called Feedforward Optimal Control (FOC); HJB yields a nonlinear optimal feedback controller, called Dynamic Programming (DP). DP produces an optimal solution that can reject disturbances and uncertainties as a result of feedback. Unfortunately, computation and storage requirements associated with DP solutions can be problematic, especially for high-order nonlinear systems. This dissertation presents an approximate technique for solving the DP problem based on neural network techniques that provides many of the performance benefits (e.g., optimality and feedback) of DP and benefits from the numerical properties of neural networks. We formulate neural networks to approximate optimal feedback solutions whose existence DP justifies. We show the conditions under which NDP closely approximates the optimal solution. Finally, we introduce the learning operator characterizing the learning process of the neural network in searching the optimal solution. The analysis of the learning operator provides not only a fundamental understanding of the learning process in neural networks but also useful guidelines for selecting the number of weights of the neural network. As a result, NDP finds---with a reasonable amount of computation and storage---the optimal feedback solutions to nonlinear MIMO control problems that would be very difficult to solve with DP. NDP was demonstrated on several applications such as the lateral autopilot logic for a Boeing 747, the minimum fuel control of a double-integrator plant with bounded control, the backward steering of a two-trailer truck, and the set-point control of a two-link robot arm.

A direct method for synthesizing low-order optimal feedback control laws with application to flutter suppression

NASA Technical Reports Server (NTRS)

Mukhopadhyay, V.; Newsom, J. R.; Abel, I.

1980-01-01

A direct method of synthesizing a low-order optimal feedback control law for a high order system is presented. A nonlinear programming algorithm is employed to search for the control law design variables that minimize a performance index defined by a weighted sum of mean square steady state responses and control inputs. The controller is shown to be equivalent to a partial state estimator. The method is applied to the problem of active flutter suppression. Numerical results are presented for a 20th order system representing an aeroelastic wind-tunnel wing model. Low-order controllers (fourth and sixth order) are compared with a full order (20th order) optimal controller and found to provide near optimal performance with adequate stability margins.

Some Properties and Stability Results for Sector-Bounded LTI Systems

NASA Technical Reports Server (NTRS)

Gupta, Sandeep; Joshi, Suresh M.

1994-01-01

This paper presents necessary and sufficient conditions for a linear, time-invariant (LTI) system to be inside sector (n, b) in terms of linear matrix inequalities in its state-space realization matrices, which represents a generalization of similar conditions for bounded H(sub infinity)-norm systems. Further, a weaker definition of LTI systems strictly inside closed sector (a, b) is proposed, and state-space characterization of such systems is presented. Sector conditions for stability of the negative feedback interconnection of two LTI systems and for stability of LTI systems with feedback nonlinearities are investigated using the Lyapunov function approach. It is shown that the proposed weaker conditions for an LTI system to be strictly inside a sector are sufficient to establish closed-loop stability of these systems.

Ontology of Earth's nonlinear dynamic complex systems

NASA Astrophysics Data System (ADS)

Babaie, Hassan; Davarpanah, Armita

2017-04-01

As a complex system, Earth and its major integrated and dynamically interacting subsystems (e.g., hydrosphere, atmosphere) display nonlinear behavior in response to internal and external influences. The Earth Nonlinear Dynamic Complex Systems (ENDCS) ontology formally represents the semantics of the knowledge about the nonlinear system element (agent) behavior, function, and structure, inter-agent and agent-environment feedback loops, and the emergent collective properties of the whole complex system as the result of interaction of the agents with other agents and their environment. It also models nonlinear concepts such as aperiodic, random chaotic behavior, sensitivity to initial conditions, bifurcation of dynamic processes, levels of organization, self-organization, aggregated and isolated functionality, and emergence of collective complex behavior at the system level. By incorporating several existing ontologies, the ENDCS ontology represents the dynamic system variables and the rules of transformation of their state, emergent state, and other features of complex systems such as the trajectories in state (phase) space (attractor and strange attractor), basins of attractions, basin divide (separatrix), fractal dimension, and system's interface to its environment. The ontology also defines different object properties that change the system behavior, function, and structure and trigger instability. ENDCS will help to integrate the data and knowledge related to the five complex subsystems of Earth by annotating common data types, unifying the semantics of shared terminology, and facilitating interoperability among different fields of Earth science.

Walking dynamics of the passive compass-gait model under OGY-based control: Emergence of bifurcations and chaos

NASA Astrophysics Data System (ADS)

Gritli, Hassène; Belghith, Safya

2017-06-01

An analysis of the passive dynamic walking of a compass-gait biped model under the OGY-based control approach using the impulsive hybrid nonlinear dynamics is presented in this paper. We describe our strategy for the development of a simplified analytical expression of a controlled hybrid Poincaré map and then for the design of a state-feedback control. Our control methodology is based mainly on the linearization of the impulsive hybrid nonlinear dynamics around a desired nominal one-periodic hybrid limit cycle. Our analysis of the controlled walking dynamics is achieved by means of bifurcation diagrams. Some interesting nonlinear phenomena are displayed, such as the period-doubling bifurcation, the cyclic-fold bifurcation, the period remerging, the period bubbling and chaos. A comparison between the raised phenomena in the impulsive hybrid nonlinear dynamics and the hybrid Poincaré map under control was also presented.

Two-dimensional dissipative rogue waves due to time-delayed feedback in cavity nonlinear optics.

PubMed

Tlidi, Mustapha; Panajotov, Krassimir

2017-01-01

We demonstrate a way to generate two-dimensional rogue waves in two types of broad area nonlinear optical systems subject to time-delayed feedback: in the generic Lugiato-Lefever model and in the model of a broad-area surface-emitting laser with saturable absorber. The delayed feedback is found to induce a spontaneous formation of rogue waves. In the absence of delayed feedback, spatial pulses are stationary. The rogue waves are exited and controlled by the delay feedback. We characterize their formation by computing the probability distribution of the pulse height. The long-tailed statistical contribution, which is often considered as a signature of the presence of rogue waves, appears for sufficiently strong feedback. The generality of our analysis suggests that the feedback induced instability leading to the spontaneous formation of two-dimensional rogue waves is a universal phenomenon.

Long-lived fluctuations driven by shear flows

NASA Astrophysics Data System (ADS)

Kim, J.-H.; Horton, W.; Morrison, P.; Chagelishvili, G. D.; Gogoberidze, G.; Dahlburg, R.

2004-11-01

In flows that are stable in accordance to the Rayleigh criterion there are long lived transient fluctuations that can lead to the onset of turbulence. We show examples of transitions to turbulence due to the positive nonlinear feedback from the transients. Simulations show that the intensity of the nonlinear decay processes depends on the angle between wave vectors of the interacting spatial Fourier harmonics. Positive nonlinear feedback occurs when vorticities of the perturbation are the same direction. Above some amplitude the cyclonic perturbation is self-sustained due to the feedback loop. Generalization and applications of the simulations for atmospheric and plasma flows are discussed. This work was supported in part by the Department of Energy Grant No. DE-FG03-96ER-54346 and ISTC Grant G-5333.

Global robust output regulation control for cascaded nonlinear systems using the internal model principle

NASA Astrophysics Data System (ADS)

Yu, Jiang-Bo; Zhao, Yan; Wu, Yu-Qiang

2014-04-01

This article considers the global robust output regulation problem via output feedback for a class of cascaded nonlinear systems with input-to-state stable inverse dynamics. The system uncertainties depend not only on the measured output but also all the unmeasurable states. By introducing an internal model, the output regulation problem is converted into a stabilisation problem for an appropriately augmented system. The designed dynamic controller could achieve the global asymptotic tracking control for a class of time-varying reference signals for the system output while keeping all other closed-loop signals bounded. It is of interest to note that the developed control approach can be applied to the speed tracking control of the fan speed control system. The simulation results demonstrate its effectiveness.

Theoretical transient analysis of a hearing aid feedback canceller with a saturation type nonlinearity in the direct path.

PubMed

Costa, Márcio Holsbach

2017-12-01

Feedback cancellation in a hearing aid is essential for achieving high maximum stable gain to compensate for the losses in severe to profound hearing impaired people. The performance of adaptive feedback cancellers has been studied by assuming that the feedback path can be modeled as a linear system. However, limited dynamic range, low-cost loudspeakers, and nonlinear power amplifiers may distort the hearing aid output signal. In this way, linear-based predictions of the canceller performance may lead to significant deviations from its actual behavior. This work presents a theoretical performance analysis of a Least Mean Square based shadow filter that is applied to set up the coefficients of a feedback canceller, which is subject to a static saturation type nonlinearity at the output of the direct path. Deterministic recursive equations are derived to predict the mean square feedback error and the mean coefficient vector evolution between updates of the feedback canceller. These models are defined as functions of the canceller parameters and input signal statistics. Comparisons with Monte Carlo simulations show the provided models are highly accurate under the considered assumptions. The developed models allow inferences about the potential impact of an overdriven loudspeaker over the transient performance of the direct method feedback canceller, serving as insightful tools for understanding the involved mechanisms. Copyright © 2017 Elsevier Ltd. All rights reserved.

A combined stochastic feedforward and feedback control design methodology with application to autoland design

NASA Technical Reports Server (NTRS)

Halyo, Nesim

1987-01-01

A combined stochastic feedforward and feedback control design methodology was developed. The objective of the feedforward control law is to track the commanded trajectory, whereas the feedback control law tries to maintain the plant state near the desired trajectory in the presence of disturbances and uncertainties about the plant. The feedforward control law design is formulated as a stochastic optimization problem and is embedded into the stochastic output feedback problem where the plant contains unstable and uncontrollable modes. An algorithm to compute the optimal feedforward is developed. In this approach, the use of error integral feedback, dynamic compensation, control rate command structures are an integral part of the methodology. An incremental implementation is recommended. Results on the eigenvalues of the implemented versus designed control laws are presented. The stochastic feedforward/feedback control methodology is used to design a digital automatic landing system for the ATOPS Research Vehicle, a Boeing 737-100 aircraft. The system control modes include localizer and glideslope capture and track, and flare to touchdown. Results of a detailed nonlinear simulation of the digital control laws, actuator systems, and aircraft aerodynamics are presented.

Failure detection and correction for turbofan engines

NASA Technical Reports Server (NTRS)

Corley, R. C.; Spang, H. A., III

1977-01-01

In this paper, a failure detection and correction strategy for turbofan engines is discussed. This strategy allows continuing control of the engines in the event of a sensor failure. An extended Kalman filter is used to provide the best estimate of the state of the engine based on currently available sensor outputs. Should a sensor failure occur the control is based on the best estimate rather than the sensor output. The extended Kalman filter consists of essentially two parts, a nonlinear model of the engine and up-date logic which causes the model to track the actual engine. Details on the model and up-date logic are presented. To allow implementation, approximations are made to the feedback gain matrix which result in a single feedback matrix which is suitable for use over the entire flight envelope. The effect of these approximations on stability and response is discussed. Results from a detailed nonlinear simulation indicate that good control can be maintained even under multiple failures.

Nonlinear dynamics of attractive magnetic bearings

NASA Technical Reports Server (NTRS)

Hebbale, K. V.; Taylor, D. L.

1987-01-01

The nonlinear dynamics of a ferromagnetic shaft suspended by the force of attraction of 1, 2, or 4 independent electromagnets is presented. Each model includes a state variable feedback controller which has been designed using the pole placement method. The constitutive relationships for the magnets are derived analytically from magnetic circuit theory, and the effects of induced eddy currents due to the rotation of the journal are included using Maxwell's field relations. A rotor suspended by four electro-magnets with closed loop feedback is shown to have nine equilibrium points within the bearing clearance space. As the rotor spin speed increases, the system is shown to pass through a Hopf bifurcation (a flutter instability). Using center manifold theory, this bifurcation can be shown to be of the subcritical type, indicating an unstable limit cycle below the critical speed. The bearing is very sensitive to initial conditions, and the equilibrium position is easily upset by transient excitation. The results are confirmed by numerical simulation.

Adaptive Neural Tracking Control for Switched High-Order Stochastic Nonlinear Systems.

PubMed

Zhao, Xudong; Wang, Xinyong; Zong, Guangdeng; Zheng, Xiaolong

2017-10-01

This paper deals with adaptive neural tracking control design for a class of switched high-order stochastic nonlinear systems with unknown uncertainties and arbitrary deterministic switching. The considered issues are: 1) completely unknown uncertainties; 2) stochastic disturbances; and 3) high-order nonstrict-feedback system structure. The considered mathematical models can represent many practical systems in the actual engineering. By adopting the approximation ability of neural networks, common stochastic Lyapunov function method together with adding an improved power integrator technique, an adaptive state feedback controller with multiple adaptive laws is systematically designed for the systems. Subsequently, a controller with only two adaptive laws is proposed to solve the problem of over parameterization. Under the designed controllers, all the signals in the closed-loop system are bounded-input bounded-output stable in probability, and the system output can almost surely track the target trajectory within a specified bounded error. Finally, simulation results are presented to show the effectiveness of the proposed approaches.

Decision-feedback detection strategy for nonlinear frequency-division multiplexing

NASA Astrophysics Data System (ADS)

Civelli, Stella; Forestieri, Enrico; Secondini, Marco

2018-04-01

By exploiting a causality property of the nonlinear Fourier transform, a novel decision-feedback detection strategy for nonlinear frequency-division multiplexing (NFDM) systems is introduced. The performance of the proposed strategy is investigated both by simulations and by theoretical bounds and approximations, showing that it achieves a considerable performance improvement compared to previously adopted techniques in terms of Q-factor. The obtained improvement demonstrates that, by tailoring the detection strategy to the peculiar properties of the nonlinear Fourier transform, it is possible to boost the performance of NFDM systems and overcome current limitations imposed by the use of more conventional detection techniques suitable for the linear regime.

Modeling, Control and Simulation of Three-Dimensional Robotic Systems with Applications to Biped Locomotion.

NASA Astrophysics Data System (ADS)

Zheng, Yuan-Fang

A three-dimensional, five link biped system is established. Newton-Euler state space formulation is employed to derive the equations of the system. The constraint forces involved in the equations can be eliminated by projection onto a smaller state space system for deriving advanced control laws. A model-referenced adaptive control scheme is developed to control the system. Digital computer simulations of point to point movement are carried out to show that the model-referenced adaptive control increases the dynamic range and speeds up the response of the system in comparison with linear and nonlinear feedback control. Further, the implementation of the controller is simpler. Impact effects of biped contact with the environment are modeled and studied. The instant velocity change at the moment of impact is derived as a function of the biped state and contact speed. The effects of impact on the state, as well as constraints are studied in biped landing on heels and toes simultaneously or on toes first. Rate and nonlinear position feedback are employed for stability of the biped after the impact. The complex structure of the foot is properly modeled. A spring and dashpot pair is suggested to represent the action of plantar fascia during the impact. This action prevents the arch of the foot from collapsing. A mathematical model of the skeletal muscle is discussed. A direct relationship between the stimulus rate and the active state is established. A piecewise linear relation between the length of the contractile element and the isometric force is considered. Hill's characteristic equation is maintained for determining the actual output force during different shortening velocities. A physical threshold model is proposed for recruitment which encompasses the size principle, its manifestations and exceptions to the size principle. Finally the role of spindle feedback in stability of the model is demonstrated by study of a pair of muscles.

A unified perspective on robot control - The energy Lyapunov function approach

NASA Technical Reports Server (NTRS)

Wen, John T.

1990-01-01

A unified framework for the stability analysis of robot tracking control is presented. By using an energy-motivated Lyapunov function candidate, the closed-loop stability is shown for a large family of control laws sharing a common structure of proportional and derivative feedback and a model-based feedforward. The feedforward can be zero, partial or complete linearized dynamics, partial or complete nonlinear dynamics, or linearized or nonlinear dynamics with parameter adaptation. As result, the dichotomous approaches to the robot control problem based on the open-loop linearization and nonlinear Lyapunov analysis are both included in this treatment. Furthermore, quantitative estimates of the trade-offs between different schemes in terms of the tracking performance, steady state error, domain of convergence, realtime computation load and required a prior model information are derived.

Improvement of time-delayed feedback control by periodic modulation: analytical theory of Floquet mode control scheme.

PubMed

Just, Wolfram; Popovich, Svitlana; Amann, Andreas; Baba, Nilüfer; Schöll, Eckehard

2003-02-01

We investigate time-delayed feedback control schemes which are based on the unstable modes of the target state, to stabilize unstable periodic orbits. The periodic time dependence of these modes introduces an external time scale in the control process. Phase shifts that develop between these modes and the controlled periodic orbit may lead to a huge increase of the control performance. We illustrate such a feature on a nonlinear reaction diffusion system with global coupling and give a detailed investigation for the Rössler model. In addition we provide the analytical explanation for the observed control features.

Nonlinear cellular dynamics of keratinocytes in normal and psoriatic epidermis under action of UV radiation

NASA Astrophysics Data System (ADS)

Stolnitz, Mikhail M.; Medvedev, Boris A.; Gribko, Tatyana V.

2004-05-01

The semi-phenomenological model of epidermal cell dynamics is submitted. The model takes into account three types of basal layer keratinocytes (stem, transient amplifying, terminally differentiated), distribution of first two types cells on mitotic cycle stages and resting states, keratinocytes-lymphocytes interactions that provide a positive feedback loop, influence of more differentiated cells on their progenitors that provide a negative feedback loop. Simplified model are developed and its stationary solutions are received. The opportunity of interpretation of some received modes as corresponding to various stages of psoriasis is discussed. Influence of UV-radiation on transitions between various modes of epidermis functioning is qualitatively analyzed.

Fast cooling for a system of stochastic oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Yongxin, E-mail: chen2468@umn.edu; Georgiou, Tryphon T., E-mail: tryphon@umn.edu; Pavon, Michele, E-mail: pavon@math.unipd.it

2015-11-15

We study feedback control of coupled nonlinear stochastic oscillators in a force field. We first consider the problem of asymptotically driving the system to a desired steady state corresponding to reduced thermal noise. Among the feedback controls achieving the desired asymptotic transfer, we find that the most efficient one from an energy point of view is characterized by time-reversibility. We also extend the theory of Schrödinger bridges to this model, thereby steering the system in finite time and with minimum effort to a target steady-state distribution. The system can then be maintained in this state through the optimal steady-state feedbackmore » control. The solution, in the finite-horizon case, involves a space-time harmonic function φ, and −logφ plays the role of an artificial, time-varying potential in which the desired evolution occurs. This framework appears extremely general and flexible and can be viewed as a considerable generalization of existing active control strategies such as macromolecular cooling. In the case of a quadratic potential, the results assume a form particularly attractive from the algorithmic viewpoint as the optimal control can be computed via deterministic matricial differential equations. An example involving inertial particles illustrates both transient and steady state optimal feedback control.« less

Approximation-based adaptive tracking control of pure-feedback nonlinear systems with multiple unknown time-varying delays.

PubMed

Wang, Min; Ge, Shuzhi Sam; Hong, Keum-Shik

2010-11-01

This paper presents adaptive neural tracking control for a class of non-affine pure-feedback systems with multiple unknown state time-varying delays. To overcome the design difficulty from non-affine structure of pure-feedback system, mean value theorem is exploited to deduce affine appearance of state variables x(i) as virtual controls α(i), and of the actual control u. The separation technique is introduced to decompose unknown functions of all time-varying delayed states into a series of continuous functions of each delayed state. The novel Lyapunov-Krasovskii functionals are employed to compensate for the unknown functions of current delayed state, which is effectively free from any restriction on unknown time-delay functions and overcomes the circular construction of controller caused by the neural approximation of a function of u and [Formula: see text] . Novel continuous functions are introduced to overcome the design difficulty deduced from the use of one adaptive parameter. To achieve uniformly ultimate boundedness of all the signals in the closed-loop system and tracking performance, control gains are effectively modified as a dynamic form with a class of even function, which makes stability analysis be carried out at the present of multiple time-varying delays. Simulation studies are provided to demonstrate the effectiveness of the proposed scheme.

Homodyne versus photon-counting quantum trajectories for dissipative Kerr resonators with two-photon driving

NASA Astrophysics Data System (ADS)

Bartolo, Nicola; Minganti, Fabrizio; Lolli, Jared; Ciuti, Cristiano

2017-07-01

We investigate two different kinds of quantum trajectories for a nonlinear photon resonator subject to two-photon pumping, a configuration recently studied for the generation of photonic Schrödinger cat states. In the absence of feedback control and in the strong-driving limit, the steady-state density matrix is a statistical mixture of two states with equal weight. While along a single photon-counting trajectory the systems intermittently switches between an odd and an even cat state, we show that upon homodyne detection the situation is different. Indeed, homodyne quantum trajectories reveal switches between coherent states of opposite phase.

Stabilization and robustness of non-linear unity-feedback system - Factorization approach

NASA Technical Reports Server (NTRS)

Desoer, C. A.; Kabuli, M. G.

1988-01-01

The paper is a self-contained discussion of a right factorization approach in the stability analysis of the nonlinear continuous-time or discrete-time, time-invariant or time-varying, well-posed unity-feedback system S1(P, C). It is shown that a well-posed stable feedback system S1(P, C) implies that P and C have right factorizations. In the case where C is stable, P has a normalized right-coprime factorization. The factorization approach is used in stabilization and simultaneous stabilization results.

High alpha feedback control for agile half-loop maneuvers of the F-18 airplane

NASA Technical Reports Server (NTRS)

Stalford, Harold

1988-01-01

A nonlinear feedback control law for the F/A-18 airplane that provides time-optimal or agile maneuvering of the half-loop maneuver at high angles of attack is given. The feedback control law was developed using the mathematical approach of singular perturbations, in which the control devices considered were conventional aerodynamic control surfaces and thrusting. The derived nonlinear control law was used to simulate F/A-18 half-loop maneuvers. The simulated results at Mach 0.6 and 0.9 compared well with pilot simulations conducted at NASA.

Short-term depression and transient memory in sensory cortex.

PubMed

Gillary, Grant; Heydt, Rüdiger von der; Niebur, Ernst

2017-12-01

Persistent neuronal activity is usually studied in the context of short-term memory localized in central cortical areas. Recent studies show that early sensory areas also can have persistent representations of stimuli which emerge quickly (over tens of milliseconds) and decay slowly (over seconds). Traditional positive feedback models cannot explain sensory persistence for at least two reasons: (i) They show attractor dynamics, with transient perturbations resulting in a quasi-permanent change of system state, whereas sensory systems return to the original state after a transient. (ii) As we show, those positive feedback models which decay to baseline lose their persistence when their recurrent connections are subject to short-term depression, a common property of excitatory connections in early sensory areas. Dual time constant network behavior has also been implemented by nonlinear afferents producing a large transient input followed by much smaller steady state input. We show that such networks require unphysiologically large onset transients to produce the rise and decay observed in sensory areas. Our study explores how memory and persistence can be implemented in another model class, derivative feedback networks. We show that these networks can operate with two vastly different time courses, changing their state quickly when new information is coming in but retaining it for a long time, and that these capabilities are robust to short-term depression. Specifically, derivative feedback networks with short-term depression that acts differentially on positive and negative feedback projections are capable of dynamically changing their time constant, thus allowing fast onset and slow decay of responses without requiring unrealistically large input transients.

On a Model of a Nonlinear Feedback System for River Flow Prediction

NASA Astrophysics Data System (ADS)

Ozaki, T.

1980-02-01

A nonlinear system with feedback is proposed as a dynamic model for the hydrological system, whose input is the rainfall and whose output is the discharge of river flow. Parameters and orders of the model are estimated using Akaike's information criterion. Its application to the prediction of daily discharges of Kanna River and Bird Creek is discussed.

Non-linear quenching of current fluctuations in a self-exciting homopolar dynamo, proved by feedback system theory

NASA Astrophysics Data System (ADS)

de Paor, A. M.

Hide (Nonlinear Processes in Geophysics, 1998) has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ɛ has the value 1 is proved via the Popov theorem from feedback system stability theory.

Delay-controlled primary and stochastic resonances of the SD oscillator with stiffness nonlinearities

NASA Astrophysics Data System (ADS)

Yang, Tao; Cao, Qingjie

2018-03-01

This work presents analytical studies of the stiffness nonlinearities SD (smooth and discontinuous) oscillator under displacement and velocity feedback control with a time delay. The SD oscillator can capture the qualitative characteristics of quasi-zero-stiffness and negative-stiffness. We focus mainly on the primary resonance of the quasi-zero-stiffness SD oscillator and the stochastic resonance (SR) of the negative-stiffness SD oscillator. Using the averaging method, we have been analyzed the amplitude response of the quasi-zero-stiffness SD oscillator. In this regard, the optimum time delay for changing the control intensity according to the optimization standard proposed can be obtained. For the optimum time delay, increasing the displacement feedback intensity is advantageous to suppress the vibrations in resonant regime where vibration isolation is needed, however, increasing the velocity feedback intensity is advantageous to strengthen the vibrations. Moreover, the effects of time-delayed feedback on the SR of the negative-stiffness SD oscillator are investigated under harmonic forcing and Gaussian white noise, based on the Langevin and Fokker-Planck approaches. The time-delayed feedback can enhance the SR phenomenon where vibrational energy harvesting is needed. This paper established the relationship between the parameters and vibration properties of a stiffness nonlinearities SD which provides the guidance for optimizing time-delayed control for vibration isolation and vibrational energy harvesting of the nonlinear systems.

Time series analyses of breathing patterns of lung cancer patients using nonlinear dynamical system theory.

PubMed

Tewatia, D K; Tolakanahalli, R P; Paliwal, B R; Tomé, W A

2011-04-07

The underlying requirements for successful implementation of any efficient tumour motion management strategy are regularity and reproducibility of a patient's breathing pattern. The physiological act of breathing is controlled by multiple nonlinear feedback and feed-forward couplings. It would therefore be appropriate to analyse the breathing pattern of lung cancer patients in the light of nonlinear dynamical system theory. The purpose of this paper is to analyse the one-dimensional respiratory time series of lung cancer patients based on nonlinear dynamics and delay coordinate state space embedding. It is very important to select a suitable pair of embedding dimension 'm' and time delay 'τ' when performing a state space reconstruction. Appropriate time delay and embedding dimension were obtained using well-established methods, namely mutual information and the false nearest neighbour method, respectively. Establishing stationarity and determinism in a given scalar time series is a prerequisite to demonstrating that the nonlinear dynamical system that gave rise to the scalar time series exhibits a sensitive dependence on initial conditions, i.e. is chaotic. Hence, once an appropriate state space embedding of the dynamical system has been reconstructed, we show that the time series of the nonlinear dynamical systems under study are both stationary and deterministic in nature. Once both criteria are established, we proceed to calculate the largest Lyapunov exponent (LLE), which is an invariant quantity under time delay embedding. The LLE for all 16 patients is positive, which along with stationarity and determinism establishes the fact that the time series of a lung cancer patient's breathing pattern is not random or irregular, but rather it is deterministic in nature albeit chaotic. These results indicate that chaotic characteristics exist in the respiratory waveform and techniques based on state space dynamics should be employed for tumour motion management.

Nonlinear feedback guidance law for aero-assisted orbit transfer maneuvers

NASA Technical Reports Server (NTRS)

Menon, P. K. A.

1992-01-01

Aero-assisted orbit transfer vehicles have the potential for significantly reducing the fuel requirements in certain classes of orbit transfer operations. Development of a nonlinear feedback guidance law for performing aero-assisted maneuvers that accomplish simultaneous change of all the orbital elements with least vehicle acceleration magnitude is discussed. The analysis is based on a sixth order nonlinear point-mass vehicle model with lift, bank angle, thrust and drag modulation as the control variables. The guidance law uses detailed vehicle aerodynamic and the atmosphere models in the feedback loop. Higher-order gravitational harmonics, planetary atmosphere rotation and ambient winds are included in the formulation. Due to modest computational requirements, the guidance law is implementable on-board an orbit transfer vehicle. The guidance performance is illustrated for three sets of boundary conditions.

Linear stable unity-feedback system - Necessary and sufficient conditions for stability under nonlinear plant perturbations

NASA Technical Reports Server (NTRS)

Desoer, C. A.; Kabuli, M. G.

1989-01-01

The authors consider a linear (not necessarily time-invariant) stable unity-feedback system, where the plant and the compensator have normalized right-coprime factorizations. They study two cases of nonlinear plant perturbations (additive and feedback), with four subcases resulting from: (1) allowing exogenous input to Delta P or not; 2) allowing the observation of the output of Delta P or not. The plant perturbation Delta P is not required to be stable. Using the factorization approach, the authors obtain necessary and sufficient conditions for all cases in terms of two pairs of nonlinear pseudostate maps. Simple physical considerations explain the form of these necessary and sufficient conditions. Finally, the authors obtain the characterization of all perturbations Delta P for which the perturbed system remains stable.

Robust model predictive control for constrained continuous-time nonlinear systems

NASA Astrophysics Data System (ADS)

Sun, Tairen; Pan, Yongping; Zhang, Jun; Yu, Haoyong

2018-02-01

In this paper, a robust model predictive control (MPC) is designed for a class of constrained continuous-time nonlinear systems with bounded additive disturbances. The robust MPC consists of a nonlinear feedback control and a continuous-time model-based dual-mode MPC. The nonlinear feedback control guarantees the actual trajectory being contained in a tube centred at the nominal trajectory. The dual-mode MPC is designed to ensure asymptotic convergence of the nominal trajectory to zero. This paper extends current results on discrete-time model-based tube MPC and linear system model-based tube MPC to continuous-time nonlinear model-based tube MPC. The feasibility and robustness of the proposed robust MPC have been demonstrated by theoretical analysis and applications to a cart-damper springer system and a one-link robot manipulator.

Feedback control of an interacting Bose-Einstein condensate using phase-contrast imaging

NASA Astrophysics Data System (ADS)

Szigeti, S. S.; Hush, M. R.; Carvalho, A. R. R.; Hope, J. J.

2010-10-01

The linewidth of an atom laser is limited by density fluctuations in the Bose-Einstein condensate (BEC) from which the atom laser beam is outcoupled. In this paper we show that a stable spatial mode for an interacting BEC can be generated using a realistic control scheme that includes the effects of the measurement backaction. This model extends the feedback theory, based on a phase-contrast imaging setup, presented by Szigeti, Hush, Carvalho, and Hope [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.80.013614 80, 013614 (2009)]. In particular, it is applicable to a BEC with large interatomic interactions and solves the problem of inadequacy of the mean-field (coherent state) approximation by utilizing a fixed number state approximation. Our numerical analysis shows the control to be more effective for a condensate with a large nonlinearity.

Feedback control of an interacting Bose-Einstein condensate using phase-contrast imaging

DOE Office of Scientific and Technical Information (OSTI.GOV)

Szigeti, S. S.; Hush, M. R.; Carvalho, A. R. R.

2010-10-15

The linewidth of an atom laser is limited by density fluctuations in the Bose-Einstein condensate (BEC) from which the atom laser beam is outcoupled. In this paper we show that a stable spatial mode for an interacting BEC can be generated using a realistic control scheme that includes the effects of the measurement backaction. This model extends the feedback theory, based on a phase-contrast imaging setup, presented by Szigeti, Hush, Carvalho, and Hope [Phys. Rev. A 80, 013614 (2009)]. In particular, it is applicable to a BEC with large interatomic interactions and solves the problem of inadequacy of the mean-fieldmore » (coherent state) approximation by utilizing a fixed number state approximation. Our numerical analysis shows the control to be more effective for a condensate with a large nonlinearity.« less

Robustness of linear quadratic state feedback designs in the presence of system uncertainty. [application to Augmentor Wing Jet STOL Research Aircraft flare control autopilot design

NASA Technical Reports Server (NTRS)

Patel, R. V.; Toda, M.; Sridhar, B.

1977-01-01

The paper deals with the problem of expressing the robustness (stability) property of a linear quadratic state feedback (LQSF) design quantitatively in terms of bounds on the perturbations (modeling errors or parameter variations) in the system matrices so that the closed-loop system remains stable. Nonlinear time-varying and linear time-invariant perturbations are considered. The only computation required in obtaining a measure of the robustness of an LQSF design is to determine the eigenvalues of two symmetric matrices determined when solving the algebraic Riccati equation corresponding to the LQSF design problem. Results are applied to a complex dynamic system consisting of the flare control of a STOL aircraft. The design of the flare control is formulated as an LQSF tracking problem.

Stabilization of business cycles of finance agents using nonlinear optimal control

NASA Astrophysics Data System (ADS)

Rigatos, G.; Siano, P.; Ghosh, T.; Sarno, D.

2017-11-01

Stabilization of the business cycles of interconnected finance agents is performed with the use of a new nonlinear optimal control method. First, the dynamics of the interacting finance agents and of the associated business cycles is described by a modeled of coupled nonlinear oscillators. Next, this dynamic model undergoes approximate linearization round a temporary operating point which is defined by the present value of the system's state vector and the last value of the control inputs vector that was exerted on it. The linearization procedure is based on Taylor series expansion of the dynamic model and on the computation of Jacobian matrices. The modelling error, which is due to the truncation of higher-order terms in the Taylor series expansion is considered as a disturbance which is compensated by the robustness of the control loop. Next, for the linearized model of the interacting finance agents, an H-infinity feedback controller is designed. The computation of the feedback control gain requires the solution of an algebraic Riccati equation at each iteration of the control algorithm. Through Lyapunov stability analysis it is proven that the control scheme satisfies an H-infinity tracking performance criterion, which signifies elevated robustness against modelling uncertainty and external perturbations. Moreover, under moderate conditions the global asymptotic stability features of the control loop are proven.

Composite Robust $$H_\\infty$$ Control for Uncertain Stochastic Nonlinear Systems with State Delay via Disturbance Observer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Yunlong; Wang, Hong; Guo, Lei

Here in this note, the robust stochastic stabilization and robust H_infinity control problems are investigated for uncertain stochastic time-delay systems with nonlinearity and multiple disturbances. By estimating the disturbance, which can be described by an exogenous model, a composite hierarchical control scheme is proposed that integrates the output of the disturbance observer with state feedback control law. Sufficient conditions for the existence of the disturbance observer and composite hierarchical controller are established in terms of linear matrix inequalities, which ensure the mean-square asymptotic stability of the resulting closed-loop system and the disturbance attenuation. It has been shown that the disturbancemore » rejection performance can also be achieved. A numerical example is provided to show the potential of the proposed techniques and encouraging results have been obtained.« less

Application of dynamical systems theory to the high angle of attack dynamics of the F-14

NASA Technical Reports Server (NTRS)

Jahnke, Craig C.; Culick, Fred E. C.

1990-01-01

Dynamical systems theory has been used to study the nonlinear dynamics of the F-14. An eight degree of freedom model that does not include the control system present in operational F-14s has been analyzed. The aerodynamic model, supplied by NASA, includes nonlinearities as functions of the angles of attack and sideslip, the rotation rate, and the elevator deflection. A continuation method has been used to calculate the steady states of the F-14 as continuous functions of the control surface deflections. Bifurcations of these steady states have been used to predict the onset of wing rock, spiral divergence, and jump phenomena which cause the aircraft to enter a spin. A simple feedback control system was designed to eliminate the wing rock and spiral divergence instabilities. The predictions were verified with numerical simulations.

Composite Robust $$H_\\infty$$ Control for Uncertain Stochastic Nonlinear Systems with State Delay via Disturbance Observer

DOE PAGES

Liu, Yunlong; Wang, Hong; Guo, Lei

2018-03-26

Here in this note, the robust stochastic stabilization and robust H_infinity control problems are investigated for uncertain stochastic time-delay systems with nonlinearity and multiple disturbances. By estimating the disturbance, which can be described by an exogenous model, a composite hierarchical control scheme is proposed that integrates the output of the disturbance observer with state feedback control law. Sufficient conditions for the existence of the disturbance observer and composite hierarchical controller are established in terms of linear matrix inequalities, which ensure the mean-square asymptotic stability of the resulting closed-loop system and the disturbance attenuation. It has been shown that the disturbancemore » rejection performance can also be achieved. A numerical example is provided to show the potential of the proposed techniques and encouraging results have been obtained.« less

Spacecraft Formation Flying near Sun-Earth L2 Lagrange Point: Trajectory Generation and Adaptive Full-State Feedback Control

NASA Technical Reports Server (NTRS)

Wong, Hong; Kapila, Vikram

2004-01-01

In this paper, we present a method for trajectory generation and adaptive full-state feedback control to facilitate spacecraft formation flying near the Sun-Earth L2 Lagrange point. Specifically, the dynamics of a spacecraft in the neighborhood of a Halo orbit reveals that there exist quasi-periodic orbits surrounding the Halo orbit. Thus, a spacecraft formation is created by placing a leader spacecraft on a desired Halo orbit and placing follower spacecraft on desired quasi-periodic orbits. To produce a formation maintenance controller, we first develop the nonlinear dynamics of a follower spacecraft relative to the leader spacecraft. We assume that the leader spacecraft is on a desired Halo orbit trajectory and the follower spacecraft is to track a desired quasi-periodic orbit surrounding the Halo orbit. Then, we design an adaptive, full-state feedback position tracking controller for the follower spacecraft providing an adaptive compensation for the unknown mass of the follower spacecraft. The proposed control law is simulated for the case of the leader and follower spacecraft pair and is shown to yield global, asymptotic convergence of the relative position tracking errors.

Application of dynamic recurrent neural networks in nonlinear system identification

NASA Astrophysics Data System (ADS)

Du, Yun; Wu, Xueli; Sun, Huiqin; Zhang, Suying; Tian, Qiang

2006-11-01

An adaptive identification method of simple dynamic recurrent neural network (SRNN) for nonlinear dynamic systems is presented in this paper. This method based on the theory that by using the inner-states feed-back of dynamic network to describe the nonlinear kinetic characteristics of system can reflect the dynamic characteristics more directly, deduces the recursive prediction error (RPE) learning algorithm of SRNN, and improves the algorithm by studying topological structure on recursion layer without the weight values. The simulation results indicate that this kind of neural network can be used in real-time control, due to its less weight values, simpler learning algorithm, higher identification speed, and higher precision of model. It solves the problems of intricate in training algorithm and slow rate in convergence caused by the complicate topological structure in usual dynamic recurrent neural network.

A third-order class-D amplifier with and without ripple compensation

NASA Astrophysics Data System (ADS)

Cox, Stephen M.; du Toit Mouton, H.

2018-06-01

We analyse the nonlinear behaviour of a third-order class-D amplifier, and demonstrate the remarkable effectiveness of the recently introduced ripple compensation (RC) technique in reducing the audio distortion of the device. The amplifier converts an input audio signal to a high-frequency train of rectangular pulses, whose widths are modulated according to the input signal (pulse-width modulation) and employs negative feedback. After determining the steady-state operating point for constant input and calculating its stability, we derive a small-signal model (SSM), which yields in closed form the transfer function relating (infinitesimal) input and output disturbances. This SSM shows how the RC technique is able to linearise the small-signal response of the device. We extend this SSM through a fully nonlinear perturbation calculation of the dynamics of the amplifier, based on the disparity in time scales between the pulse train and the audio signal. We obtain the nonlinear response of the amplifier to a general audio signal, avoiding the linearisation inherent in the SSM; we thereby more precisely quantify the reduction in distortion achieved through RC. Finally, simulations corroborate our theoretical predictions and illustrate the dramatic deterioration in performance that occurs when the amplifier is operated in an unstable regime. The perturbation calculation is rather general, and may be adapted to quantify the way in which other nonlinear negative-feedback pulse-modulated devices track a time-varying input signal that slowly modulates the system parameters.

Discrete-Time Mapping for an Impulsive Goodwin Oscillator with Three Delays

NASA Astrophysics Data System (ADS)

Churilov, Alexander N.; Medvedev, Alexander; Zhusubaliyev, Zhanybai T.

A popular biomathematics model of the Goodwin oscillator has been previously generalized to a more biologically plausible construct by introducing three time delays to portray the transport phenomena arising due to the spatial distribution of the model states. The present paper addresses a similar conversion of an impulsive version of the Goodwin oscillator that has found application in mathematical modeling, e.g. in endocrine systems with pulsatile hormone secretion. While the cascade structure of the linear continuous part pertinent to the Goodwin oscillator is preserved in the impulsive Goodwin oscillator, the static nonlinear feedback of the former is substituted with a pulse modulation mechanism thus resulting in hybrid dynamics of the closed-loop system. To facilitate the analysis of the mathematical model under investigation, a discrete mapping propagating the continuous state variables through the firing times of the impulsive feedback is derived. Due to the presence of multiple time delays in the considered model, previously developed mapping derivation approaches are not applicable here and a novel technique is proposed and applied. The mapping captures the dynamics of the original hybrid system and is instrumental in studying complex nonlinear phenomena arising in the impulsive Goodwin oscillator. A simulation example is presented to demonstrate the utility of the proposed approach in bifurcation analysis.

Negative Feedback Mediated by Fast Inhibitory Autapse Enhances Neuronal Oscillations Near a Hopf Bifurcation Point

NASA Astrophysics Data System (ADS)

Jia, Bing

One-parameter and two-parameter bifurcations of the Morris-Lecar (ML) neuron model with and without the fast inhibitory autapse, which is a synapse from a neuron onto itself, are investigated. The ML neuron model without autapse manifests an inverse Hopf bifurcation point from firing to a depolarized resting state with high level of membrane potential, with increasing depolarization current. When a fast inhibitory autapse is introduced, a negative feedback or inhibitory current is applied to the ML model. With increasing conductance of the autapse to middle level, the depolarized resting state near the inverse Hopf bifurcation point can change to oscillation and the parameter region of the oscillation becomes wide, which can be well interpreted by the dynamic responses of the depolarized resting state to the inhibitory current stimulus mediated by the autapse. The enlargement of the parameter region of the oscillation induced by the negative feedback presents a novel viewpoint different from the traditional one that inhibitory synapse often suppresses the neuronal oscillation activities. Furthermore, complex nonlinear dynamics such as the coexisting behaviors and codimension-2 bifurcations including the Bautin and cusp bifurcations are acquired. The relationship between the bifurcations and the depolarization block, a physiological concept that indicates a neuron can enter resting state when receiving the depolarization current, is discussed.

Acceleration and torque feedback for robotic control - Experimental results

NASA Technical Reports Server (NTRS)

Mclnroy, John E.; Saridis, George N.

1990-01-01

Gross motion control of robotic manipulators typically requires significant on-line computations to compensate for nonlinear dynamics due to gravity, Coriolis, centripetal, and friction nonlinearities. One controller proposed by Luo and Saridis avoids these computations by feeding back joint acceleration and torque. This study implements the controller on a Puma 600 robotic manipulator. Joint acceleration measurement is obtained by measuring linear accelerations of each joint, and deriving a computationally efficient transformation from the linear measurements to the angular accelerations. Torque feedback is obtained by using the previous torque sent to the joints. The implementation has stability problems on the Puma 600 due to the extremely high gains inherent in the feedback structure. Since these high gains excite frequency modes in the Puma 600, the algorithm is modified to decrease the gain inherent in the feedback structure. The resulting compensator is stable and insensitive to high frequency unmodeled dynamics. Moreover, a second compensator is proposed which uses acceleration and torque feedback, but still allows nonlinear terms to be fed forward. Thus, by feeding the increment in the easily calculated gravity terms forward, improved responses are obtained. Both proposed compensators are implemented, and the real time results are compared to those obtained with the computed torque algorithm.

Finite-time output feedback stabilization of high-order uncertain nonlinear systems

NASA Astrophysics Data System (ADS)

Jiang, Meng-Meng; Xie, Xue-Jun; Zhang, Kemei

2018-06-01

This paper studies the problem of finite-time output feedback stabilization for a class of high-order nonlinear systems with the unknown output function and control coefficients. Under the weaker assumption that output function is only continuous, by using homogeneous domination method together with adding a power integrator method, introducing a new analysis method, the maximal open sector Ω of output function is given. As long as output function belongs to any closed sector included in Ω, an output feedback controller can be developed to guarantee global finite-time stability of the closed-loop system.

Chaotic operation and chaos control of travelling wave ultrasonic motor.

PubMed

Shi, Jingzhuo; Zhao, Fujie; Shen, Xiaoxi; Wang, Xiaojie

2013-08-01

The travelling wave ultrasonic motor, which is a nonlinear dynamic system, has complex chaotic phenomenon with some certain choices of system parameters and external inputs, and its chaotic characteristics have not been studied until now. In this paper, the preliminary study of the chaos phenomenon in ultrasonic motor driving system has been done. The experiment of speed closed-loop control is designed to obtain several groups of time sampling data sequence of the amplitude of driving voltage, and phase-space reconstruction is used to analyze the chaos characteristics of these time sequences. The largest Lyapunov index is calculated and the result is positive, which shows that the travelling wave ultrasonic motor has chaotic characteristics in a certain working condition Then, the nonlinear characteristics of travelling wave ultrasonic motor are analyzed which includes Lyapunov exponent map, the bifurcation diagram and the locus of voltage relative to speed based on the nonlinear chaos model of a travelling wave ultrasonic motor. After that, two kinds of adaptive delay feedback controllers are designed in this paper to control and suppress chaos in USM speed control system. Simulation results show that the method can control unstable periodic orbits, suppress chaos in USM control system. Proportion-delayed feedback controller was designed following and arithmetic of fuzzy logic was used to adaptively adjust the delay time online. Simulation results show that this method could fast and effectively change the chaos movement into periodic or fixed-point movement and make the system enter into stable state from chaos state. Finally the chaos behavior was controlled. Copyright © 2013 Elsevier B.V. All rights reserved.

Effect of motor dynamics on nonlinear feedback robot arm control

NASA Technical Reports Server (NTRS)

Tarn, Tzyh-Jong; Li, Zuofeng; Bejczy, Antal K.; Yun, Xiaoping

1991-01-01

A nonlinear feedback robot controller that incorporates the robot manipulator dynamics and the robot joint motor dynamics is proposed. The manipulator dynamics and the motor dynamics are coupled to obtain a third-order-dynamic model, and differential geometric control theory is applied to produce a linearized and decoupled robot controller. The derived robot controller operates in the robot task space, thus eliminating the need for decomposition of motion commands into robot joint space commands. Computer simulations are performed to verify the feasibility of the proposed robot controller. The controller is further experimentally evaluated on the PUMA 560 robot arm. The experiments show that the proposed controller produces good trajectory tracking performances and is robust in the presence of model inaccuracies. Compared with a nonlinear feedback robot controller based on the manipulator dynamics only, the proposed robot controller yields conspicuously improved performance.

Distributed Adaptive Neural Control for Stochastic Nonlinear Multiagent Systems.

PubMed

Wang, Fang; Chen, Bing; Lin, Chong; Li, Xuehua

2016-11-14

In this paper, a consensus tracking problem of nonlinear multiagent systems is investigated under a directed communication topology. All the followers are modeled by stochastic nonlinear systems in nonstrict feedback form, where nonlinearities and stochastic disturbance terms are totally unknown. Based on the structural characteristic of neural networks (in Lemma 4), a novel distributed adaptive neural control scheme is put forward. The raised control method not only effectively handles unknown nonlinearities in nonstrict feedback systems, but also copes with the interactions among agents and coupling terms. Based on the stochastic Lyapunov functional method, it is indicated that all the signals of the closed-loop system are bounded in probability and all followers' outputs are convergent to a neighborhood of the output of leader. At last, the efficiency of the control method is testified by a numerical example.

Nonlinear feedback model attitude control using CCD in magnetic suspension system

NASA Technical Reports Server (NTRS)

Lin, CHIN-E.; Hou, Ann-San

1994-01-01

A model attitude control system for a CCD camera magnetic suspension system is studied in this paper. In a recent work, a position and attitude sensing method was proposed. From this result, model position and attitude of a magnetic suspension system can be detected by generating digital outputs. Based on this achievement, a control system design using nonlinear feedback techniques for magnetic suspended model attitude control is proposed.

Effective Desynchronization by Nonlinear Delayed Feedback

NASA Astrophysics Data System (ADS)

Popovych, Oleksandr V.; Hauptmann, Christian; Tass, Peter A.

2005-04-01

We show that nonlinear delayed feedback opens up novel means for the control of synchronization. In particular, we propose a demand-controlled method for powerful desynchronization, which does not require any time-consuming calibration. Our technique distinguishes itself by its robustness against variations of system parameters, even in strongly coupled ensembles of oscillators. We suggest our method for mild and effective deep brain stimulation in neurological diseases characterized by pathological cerebral synchronization.

Statistics based sampling for controller and estimator design

NASA Astrophysics Data System (ADS)

Tenne, Dirk

The purpose of this research is the development of statistical design tools for robust feed-forward/feedback controllers and nonlinear estimators. This dissertation is threefold and addresses the aforementioned topics nonlinear estimation, target tracking and robust control. To develop statistically robust controllers and nonlinear estimation algorithms, research has been performed to extend existing techniques, which propagate the statistics of the state, to achieve higher order accuracy. The so-called unscented transformation has been extended to capture higher order moments. Furthermore, higher order moment update algorithms based on a truncated power series have been developed. The proposed techniques are tested on various benchmark examples. Furthermore, the unscented transformation has been utilized to develop a three dimensional geometrically constrained target tracker. The proposed planar circular prediction algorithm has been developed in a local coordinate framework, which is amenable to extension of the tracking algorithm to three dimensional space. This tracker combines the predictions of a circular prediction algorithm and a constant velocity filter by utilizing the Covariance Intersection. This combined prediction can be updated with the subsequent measurement using a linear estimator. The proposed technique is illustrated on a 3D benchmark trajectory, which includes coordinated turns and straight line maneuvers. The third part of this dissertation addresses the design of controller which include knowledge of parametric uncertainties and their distributions. The parameter distributions are approximated by a finite set of points which are calculated by the unscented transformation. This set of points is used to design robust controllers which minimize a statistical performance of the plant over the domain of uncertainty consisting of a combination of the mean and variance. The proposed technique is illustrated on three benchmark problems. The first relates to the design of prefilters for a linear and nonlinear spring-mass-dashpot system and the second applies a feedback controller to a hovering helicopter. Lastly, the statistical robust controller design is devoted to a concurrent feed-forward/feedback controller structure for a high-speed low tension tape drive.

Butterfly, Recurrence, and Predictability in Lorenz Models

NASA Astrophysics Data System (ADS)

Shen, B. W.

2017-12-01

Over the span of 50 years, the original three-dimensional Lorenz model (3DLM; Lorenz,1963) and its high-dimensional versions (e.g., Shen 2014a and references therein) have been used for improving our understanding of the predictability of weather and climate with a focus on chaotic responses. Although the Lorenz studies focus on nonlinear processes and chaotic dynamics, people often apply a "linear" conceptual model to understand the nonlinear processes in the 3DLM. In this talk, we present examples to illustrate the common misunderstandings regarding butterfly effect and discuss the importance of solutions' recurrence and boundedness in the 3DLM and high-dimensional LMs. The first example is discussed with the following folklore that has been widely used as an analogy of the butterfly effect: "For want of a nail, the shoe was lost.For want of a shoe, the horse was lost.For want of a horse, the rider was lost.For want of a rider, the battle was lost.For want of a battle, the kingdom was lost.And all for the want of a horseshoe nail."However, in 2008, Prof. Lorenz stated that he did not feel that this verse described true chaos but that it better illustrated the simpler phenomenon of instability; and that the verse implicitly suggests that subsequent small events will not reverse the outcome (Lorenz, 2008). Lorenz's comments suggest that the verse neither describes negative (nonlinear) feedback nor indicates recurrence, the latter of which is required for the appearance of a butterfly pattern. The second example is to illustrate that the divergence of two nearby trajectories should be bounded and recurrent, as shown in Figure 1. Furthermore, we will discuss how high-dimensional LMs were derived to illustrate (1) negative nonlinear feedback that stabilizes the system within the five- and seven-dimensional LMs (5D and 7D LMs; Shen 2014a; 2015a; 2016); (2) positive nonlinear feedback that destabilizes the system within the 6D and 8D LMs (Shen 2015b; 2017); and (3) recurrence (e.g., quasi-periodic solutions) within non-dissipative LMs (Faghih-Naini and Shen, 2017; Shen and Faghih-Naini, 2017). http://bwshen.sdsu.edu/shen_agu17.html

Hardware Simulations of Spacecraft Attitude Synchronization Using Lyapunov-Based Controllers

NASA Astrophysics Data System (ADS)

Jung, Juno; Park, Sang-Young; Eun, Youngho; Kim, Sung-Woo; Park, Chandeok

2018-04-01

In the near future, space missions with multiple spacecraft are expected to replace traditional missions with a single large spacecraft. These spacecraft formation flying missions generally require precise knowledge of relative position and attitude between neighboring agents. In this study, among the several challenging issues, we focus on the technique to control spacecraft attitude synchronization in formation. We develop a number of nonlinear control schemes based on the Lyapunov stability theorem and considering special situations: full-state feedback control, full-state feedback control with unknown inertia parameters, and output feedback control without angular velocity measurements. All the proposed controllers offer absolute and relative control using reaction wheel assembly for both regulator and tracking problems. In addition to the numerical simulations, an air-bearing-based hardware-in-the-loop (HIL) system is used to verify the proposed control laws in real-time hardware environments. The pointing errors converge to 0.5{°} with numerical simulations and to 2{°} using the HIL system. Consequently, both numerical and hardware simulations confirm the performance of the spacecraft attitude synchronization algorithms developed in this study.

Biomimetic Hybrid Feedback Feedforward Neural-Network Learning Control.

PubMed

Pan, Yongping; Yu, Haoyong

2017-06-01

This brief presents a biomimetic hybrid feedback feedforward neural-network learning control (NNLC) strategy inspired by the human motor learning control mechanism for a class of uncertain nonlinear systems. The control structure includes a proportional-derivative controller acting as a feedback servo machine and a radial-basis-function (RBF) NN acting as a feedforward predictive machine. Under the sufficient constraints on control parameters, the closed-loop system achieves semiglobal practical exponential stability, such that an accurate NN approximation is guaranteed in a local region along recurrent reference trajectories. Compared with the existing NNLC methods, the novelties of the proposed method include: 1) the implementation of an adaptive NN control to guarantee plant states being recurrent is not needed, since recurrent reference signals rather than plant states are utilized as NN inputs, which greatly simplifies the analysis and synthesis of the NNLC and 2) the domain of NN approximation can be determined a priori by the given reference signals, which leads to an easy construction of the RBF-NNs. Simulation results have verified the effectiveness of this approach.

Jump resonant frequency islands in nonlinear feedback control systems

NASA Technical Reports Server (NTRS)

Koenigsberg, W. D.; Dunn, J. C.

1975-01-01

A new type of jump resonance is predicted and observed in certain nonlinear feedback control systems. The new jump resonance characteristic is described as a 'frequency island' due to the fact that a portion of the input-output transfer characteristic is disjoint from the main body. The presence of such frequency islands was predicted by using a sinusoidal describing function characterization of the dynamics of an inertial gyro employing nonlinear ternary rebalance logic. While the general conditions under which such islands are possible has not been examined, a numerical approach is presented which can aid in establishing their presence. The existence of the frequency islands predicted for the ternary rebalanced gyro was confirmed by simulating the nonlinear system and measuring the transfer function.

Feedback and Control of Linear and Nonlinear Global MHD Modes in Rotating Plasmas

NASA Astrophysics Data System (ADS)

Finn, J. M.; Chacon, L.

2002-11-01

We present studies of feedback applied to resistive wall modes in the presence of plasma rotation. The main tool used is a Newton-Krylov nonlinear reduced resistive MHD code with completely implicit time stepping[1]. The effects of proportional and derivative gain and toroidal phase shift are investigated. In addition to studying the complete stabilization of the resistive wall mode, we present results on controlling the amplitude of nonlinear modes locked to the wall but propagating slowly; we also show results on reducing the hysteresis in the locking-unlocking bifurcation diagram. [1] L. Chacon, D. A. Knoll and J. M. Finn, "An implicit, nonlinear reduced resistive MHD solver", J. Comp. Phys. v. 178, pp 15-36 (2002).

Robust adaptive fuzzy tracking control for pure-feedback stochastic nonlinear systems with input constraints.

PubMed

Wang, Huanqing; Chen, Bing; Liu, Xiaoping; Liu, Kefu; Lin, Chong

2013-12-01

This paper is concerned with the problem of adaptive fuzzy tracking control for a class of pure-feedback stochastic nonlinear systems with input saturation. To overcome the design difficulty from nondifferential saturation nonlinearity, a smooth nonlinear function of the control input signal is first introduced to approximate the saturation function; then, an adaptive fuzzy tracking controller based on the mean-value theorem is constructed by using backstepping technique. The proposed adaptive fuzzy controller guarantees that all signals in the closed-loop system are bounded in probability and the system output eventually converges to a small neighborhood of the desired reference signal in the sense of mean quartic value. Simulation results further illustrate the effectiveness of the proposed control scheme.

Variable structure control of nonlinear systems through simplified uncertain models

NASA Technical Reports Server (NTRS)

Sira-Ramirez, Hebertt

1986-01-01

A variable structure control approach is presented for the robust stabilization of feedback equivalent nonlinear systems whose proposed model lies in the same structural orbit of a linear system in Brunovsky's canonical form. An attempt to linearize exactly the nonlinear plant on the basis of the feedback control law derived for the available model results in a nonlinearly perturbed canonical system for the expanded class of possible equivalent control functions. Conservatism tends to grow as modeling errors become larger. In order to preserve the internal controllability structure of the plant, it is proposed that model simplification be carried out on the open-loop-transformed system. As an example, a controller is developed for a single link manipulator with an elastic joint.

Development of control strategies for safe microburst penetration: A progress report

NASA Technical Reports Server (NTRS)

Psiaki, Mark L.

1987-01-01

A single-engine, propeller-driven, general-aviation model was incorporated into the nonlinear simulation and into the linear analysis of root loci and frequency response. Full-scale wind tunnel data provided its aerodynamic model, and the thrust model included the airspeed dependent effects of power and propeller efficiency. Also, the parameters of the Jet Transport model were changed to correspond more closely to the Boeing 727. In order to study their effects on steady-state repsonse to vertical wind inputs, altitude and total specific energy (air-relative and inertial) feedback capabilities were added to the nonlinear and linear models. Multiloop system design goals were defined. Attempts were made to develop controllers which achieved these goals.

The Anthropocene Generalized: Evolution of Exo-Civilizations and Their Planetary Feedback.

PubMed

Frank, A; Carroll-Nellenback, Jonathan; Alberti, M; Kleidon, A

2018-05-01

We present a framework for studying generic behaviors possible in the interaction between a resource-harvesting technological civilization (an exo-civilization) and the planetary environment in which it evolves. Using methods from dynamical systems theory, we introduce and analyze a suite of simple equations modeling a population which consumes resources for the purpose of running a technological civilization and the feedback those resources drive on the state of the host planet. The feedbacks can drive the planet away from the initial state the civilization originated in and into domains that are detrimental to its sustainability. Our models conceptualize the problem primarily in terms of feedbacks from the resource use onto the coupled planetary systems. In addition, we also model the population growth advantages gained via the harvesting of these resources. We present three models of increasing complexity: (1) Civilization-planetary interaction with a single resource; (2) Civilization-planetary interaction with two resources each of which has a different level of planetary system feedback; (3) Civilization-planetary interaction with two resources and nonlinear planetary feedback (i.e., runaways). All three models show distinct classes of exo-civilization trajectories. We find smooth entries into long-term, "sustainable" steady states. We also find population booms followed by various levels of "die-off." Finally, we also observe rapid "collapse" trajectories for which the population approaches n = 0. Our results are part of a program for developing an "Astrobiology of the Anthropocene" in which questions of sustainability, centered on the coupled Earth-system, can be seen in their proper astronomical/planetary context. We conclude by discussing the implications of our results for both the coupled Earth system and for the consideration of exo-civilizations across cosmic history. Key Words: Anthropocene-Astrobiology-Civilization-Dynamical system theory-Exoplanets-Population dynamics. Astrobiology 18, 503-518.

Mass Transport and Turbulence in Gravitationally Unstable Disk Galaxies. I. The Case of Pure Self-gravity

NASA Astrophysics Data System (ADS)

Goldbaum, Nathan J.; Krumholz, Mark R.; Forbes, John C.

2015-12-01

The role of gravitational instability-driven turbulence in determining the structure and evolution of disk galaxies, and the extent to which gravity rather than feedback can explain galaxy properties, remains an open question. To address it, we present high-resolution adaptive mesh refinement simulations of Milky Way-like isolated disk galaxies, including realistic heating and cooling rates and a physically motivated prescription for star formation, but no form of star formation feedback. After an initial transient, our galaxies reach a state of fully nonlinear gravitational instability. In this state, gravity drives turbulence and radial inflow. Despite the lack of feedback, the gas in our galaxy models shows substantial turbulent velocity dispersions, indicating that gravitational instability alone may be able to power the velocity dispersions observed in nearby disk galaxies on 100 pc scales. Moreover, the rate of mass transport produced by this turbulence approaches ˜ 1 {M}⊙ yr-1 for Milky Way-like conditions, sufficient to fully fuel star formation in the inner disks of galaxies. In a companion paper, we add feedback to our models, and use the comparison between the two cases to understand which galaxy properties depend sensitively on feedback and which can be understood as the product of gravity alone. All of the code, initial conditions, and simulation data for our model are publicly available.

SPHERES tethered formation flight testbed: application to NASA's SPECS mission

NASA Astrophysics Data System (ADS)

Chung, Soon-Jo; Kong, Edmund M.; Miller, David W.

2005-08-01

This paper elaborates on theory and experiment of the formation flight control for the future space-borne tethered interferometers. The nonlinear equations of multi-vehicle tethered spacecraft system are derived by Lagrange equations and decoupling method. The preliminary analysis predicts unstable dynamics depending on the direction of the tether motor. The controllability analysis indicates that both array resizing and spin-up are fully controllable only by the reaction wheels and the tether motor, thereby eliminating the need for thrusters. Linear and nonlinear decentralized control techniques have been implemented into the tethered SPHERES testbed, and tested at the NASA MSFC's flat floor facility using two and three SPHERES configurations. The nonlinear control using feedback linearization technique performed successfully in both two SPHERES in-line configuration and three triangular configuration while varying the tether length. The relative metrology system, using the ultra sound metrology system and the inertial sensors as well as the decentralized nonlinear estimator, is developed to provide necessary state information.

Spacecraft stability and control using new techniques for periodic and time-delayed systems

NASA Astrophysics Data System (ADS)

NAzari, Morad

This dissertation addresses various problems in spacecraft stability and control using specialized theoretical and numerical techniques for time-periodic and time-delayed systems. First, the effects of energy dissipation are considered in the dual-spin spacecraft, where the damper masses in the platform (?) and the rotor (?) cause energy loss in the system. Floquet theory is employed to obtain stability charts for different relative spin rates of the subsystem [special characters omitted] with respect to the subsystem [special characters omitted]. Further, the stability and bifurcation of delayed feedback spin stabilization of a rigid spacecraft is investigated. The spin is stabilized about the principal axis of the intermediate moment of inertia using a simple delayed feedback control law. In particular, linear stability is analyzed via the exponential-polynomial characteristic equations and then the method of multiple scales is used to obtain the normal form of the Hopf bifurcation. Next, the dynamics of a rigid spacecraft with nonlinear delayed multi-actuator feedback control are studied, where a nonlinear feedback controller using an inverse dynamics approach is sought for the controlled system to have the desired linear delayed closed-loop dynamics (CLD). Later, three linear state feedback control strategies based on Chebyshev spectral collocation and the Lyapunov Floquet transformation (LFT) are explored for regulation control of linear periodic time delayed systems. First , a delayed feedback control law with discrete delay is implemented and the stability of the closed-loop response is investigated in the parameter space of available control gains using infinite-dimensional Floquet theory. Second, the delay differential equation (DDE) is discretized into a large set of ordinary differential equations (ODEs) using the Chebyshev spectral continuous time approximation (CSCTA) and delayed feedback with distributed delay is applied. The third strategy involves use of both CSCTA and the reduced Lyapunov Floquet transformation (RLFT) in order to design a non-delayed feedback control law. The delayed Mathieu equation is used as an illustrative example in which the closed-loop response and control effort are compared for all three control strategies. Finally, three example applications of control of time-periodic astrodynamic systems, i.e. formation flying control for an elliptic Keplerian chief orbit, body-fixed hovering control over a tumbling asteroid, and stationkeeping in Earth-Moon L1 halo orbits, are shown using versions of the control strategies introduced above. These applications employ a mixture of feedforward and non-delayed periodic-gain state feedback for tracking control of natural and non-natural motions in these systems. A major conclusion is that control effort is minimized by employing periodic-gain (rather than constant-gain) feedback control in such systems.

Reinforcement learning state estimator.

PubMed

Morimoto, Jun; Doya, Kenji

2007-03-01

In this study, we propose a novel use of reinforcement learning for estimating hidden variables and parameters of nonlinear dynamical systems. A critical issue in hidden-state estimation is that we cannot directly observe estimation errors. However, by defining errors of observable variables as a delayed penalty, we can apply a reinforcement learning frame-work to state estimation problems. Specifically, we derive a method to construct a nonlinear state estimator by finding an appropriate feedback input gain using the policy gradient method. We tested the proposed method on single pendulum dynamics and show that the joint angle variable could be successfully estimated by observing only the angular velocity, and vice versa. In addition, we show that we could acquire a state estimator for the pendulum swing-up task in which a swing-up controller is also acquired by reinforcement learning simultaneously. Furthermore, we demonstrate that it is possible to estimate the dynamics of the pendulum itself while the hidden variables are estimated in the pendulum swing-up task. Application of the proposed method to a two-linked biped model is also presented.

Ultra-high-frequency chaos in a time-delay electronic device with band-limited feedback.

PubMed

Illing, Lucas; Gauthier, Daniel J

2006-09-01

We report an experimental study of ultra-high-frequency chaotic dynamics generated in a delay-dynamical electronic device. It consists of a transistor-based nonlinearity, commercially-available amplifiers, and a transmission-line for feedback. The feedback is band-limited, allowing tuning of the characteristic time-scales of both the periodic and high-dimensional chaotic oscillations that can be generated with the device. As an example, periodic oscillations ranging from 48 to 913 MHz are demonstrated. We develop a model and use it to compare the experimentally observed Hopf bifurcation of the steady-state to existing theory [Illing and Gauthier, Physica D 210, 180 (2005)]. We find good quantitative agreement of the predicted and the measured bifurcation threshold, bifurcation type and oscillation frequency. Numerical integration of the model yields quasiperiodic and high dimensional chaotic solutions (Lyapunov dimension approximately 13), which match qualitatively the observed device dynamics.

Strong quantum squeezing of mechanical resonator via parametric amplification and coherent feedback

NASA Astrophysics Data System (ADS)

You, Xiang; Li, Zongyang; Li, Yongmin

2017-12-01

A scheme to achieve strong quantum squeezing of a mechanical resonator in a membrane-in-the-middle optomechanical system is developed. To this end, simultaneous linear and nonlinear coupling between the mechanical resonator and the cavity modes is applied. A two-tone driving light field, comprising unequal red-detuned and blue-detuned sidebands, helps in generating a coherent feedback force through the linear coupling with the membrane resonator. Another driving light field with its amplitude modulated at twice the mechanical frequency drives the mechanical parametric amplification through a second-order coupling with the resonator. The combined effect produces strong quantum squeezing of the mechanical state. The proposed scheme is quite robust to excess second-order coupling observed in coherent feedback operations and can suppress the fluctuations in the mechanical quadrature to far below the zero point and achieve strong squeezing (greater than 10 dB) for realistic parameters.

Finite-horizon control-constrained nonlinear optimal control using single network adaptive critics.

PubMed

Heydari, Ali; Balakrishnan, Sivasubramanya N

2013-01-01

To synthesize fixed-final-time control-constrained optimal controllers for discrete-time nonlinear control-affine systems, a single neural network (NN)-based controller called the Finite-horizon Single Network Adaptive Critic is developed in this paper. Inputs to the NN are the current system states and the time-to-go, and the network outputs are the costates that are used to compute optimal feedback control. Control constraints are handled through a nonquadratic cost function. Convergence proofs of: 1) the reinforcement learning-based training method to the optimal solution; 2) the training error; and 3) the network weights are provided. The resulting controller is shown to solve the associated time-varying Hamilton-Jacobi-Bellman equation and provide the fixed-final-time optimal solution. Performance of the new synthesis technique is demonstrated through different examples including an attitude control problem wherein a rigid spacecraft performs a finite-time attitude maneuver subject to control bounds. The new formulation has great potential for implementation since it consists of only one NN with single set of weights and it provides comprehensive feedback solutions online, though it is trained offline.

Adaptive nonlinear robust relative pose control of spacecraft autonomous rendezvous and proximity operations.

PubMed

Sun, Liang; Huo, Wei; Jiao, Zongxia

2017-03-01

This paper studies relative pose control for a rigid spacecraft with parametric uncertainties approaching to an unknown tumbling target in disturbed space environment. State feedback controllers for relative translation and relative rotation are designed in an adaptive nonlinear robust control framework. The element-wise and norm-wise adaptive laws are utilized to compensate the parametric uncertainties of chaser and target spacecraft, respectively. External disturbances acting on two spacecraft are treated as a lumped and bounded perturbation input for system. To achieve the prescribed disturbance attenuation performance index, feedback gains of controllers are designed by solving linear matrix inequality problems so that lumped disturbance attenuation with respect to the controlled output is ensured in the L 2 -gain sense. Moreover, in the absence of lumped disturbance input, asymptotical convergence of relative pose are proved by using the Lyapunov method. Numerical simulations are performed to show that position tracking and attitude synchronization are accomplished in spite of the presence of couplings and uncertainties. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Reinforcement learning neural-network-based controller for nonlinear discrete-time systems with input constraints.

PubMed

He, Pingan; Jagannathan, S

2007-04-01

A novel adaptive-critic-based neural network (NN) controller in discrete time is designed to deliver a desired tracking performance for a class of nonlinear systems in the presence of actuator constraints. The constraints of the actuator are treated in the controller design as the saturation nonlinearity. The adaptive critic NN controller architecture based on state feedback includes two NNs: the critic NN is used to approximate the "strategic" utility function, whereas the action NN is employed to minimize both the strategic utility function and the unknown nonlinear dynamic estimation errors. The critic and action NN weight updates are derived by minimizing certain quadratic performance indexes. Using the Lyapunov approach and with novel weight updates, the uniformly ultimate boundedness of the closed-loop tracking error and weight estimates is shown in the presence of NN approximation errors and bounded unknown disturbances. The proposed NN controller works in the presence of multiple nonlinearities, unlike other schemes that normally approximate one nonlinearity. Moreover, the adaptive critic NN controller does not require an explicit offline training phase, and the NN weights can be initialized at zero or random. Simulation results justify the theoretical analysis.

On the Stability of Collocated Controllers in the Presence or Uncertain Nonlinearities and Other Perils

NASA Technical Reports Server (NTRS)

Joshi, S. M.

1985-01-01

Robustness properties are investigated for two types of controllers for large flexible space structures, which use collocated sensors and actuators. The first type is an attitude controller which uses negative definite feedback of measured attitude and rate, while the second type is a damping enhancement controller which uses only velocity (rate) feedback. It is proved that collocated attitude controllers preserve closed loop global asymptotic stability when linear actuator/sensor dynamics satisfying certain phase conditions are present, or monotonic increasing nonlinearities are present. For velocity feedback controllers, the global asymptotic stability is proved under much weaker conditions. In particular, they have 90 phase margin and can tolerate nonlinearities belonging to the (0,infinity) sector in the actuator/sensor characteristics. The results significantly enhance the viability of both types of collocated controllers, especially when the available information about the large space structure (LSS) parameters is inadequate or inaccurate.

Polynomial law for controlling the generation of n-scroll chaotic attractors in an optoelectronic delayed oscillator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Márquez, Bicky A., E-mail: bmarquez@ivic.gob.ve; Suárez-Vargas, José J., E-mail: jjsuarez@ivic.gob.ve; Ramírez, Javier A.

2014-09-01

Controlled transitions between a hierarchy of n-scroll attractors are investigated in a nonlinear optoelectronic oscillator. Using the system's feedback strength as a control parameter, it is shown experimentally the transition from Van der Pol-like attractors to 6-scroll, but in general, this scheme can produce an arbitrary number of scrolls. The complexity of every state is characterized by Lyapunov exponents and autocorrelation coefficients.

The local, remote, and global consequences of climate feedbacks

NASA Astrophysics Data System (ADS)

Feldl, Nicole

Climate feedbacks offer a powerful framework for revealing the energetic pathways by which the system adjusts to an imposed forcing, such as an increase in atmospheric CO2. We investigate how local atmospheric feedbacks, such as those associated with Arctic sea ice and the Walker circulation, affect both global climate sensitivity and spatial patterns of warming. Emphasis is placed on a general circulation model with idealized boundary conditions, for the clarity it provides. For this aquaplanet simulation, we account for rapid tropospheric adjustments to CO2 and explicitly diagnose feedbacks (using radiative kernels) and forcing for this precise model set-up. In particular, a detailed closure of the energy budget within a clean experimental set-up allows us to consider nonlinear interactions between feedbacks. The inclusion of a tropical Walker circulation is found to prime the Hadley Circulation for a larger deceleration under CO2 doubling, by altering subtropical stratus decks and the meridional feedback gradient. We perform targeted experiments to isolate the atmospheric processes responsible for the variability in climate sensitivity, with implications for high-sensitivity paleoclimates. The local climate response is characterized in terms of the meridional structure of feedbacks, atmospheric heat transport, nonlinearities, and forcing. Our results display a combination of positive subtropical feedbacks and polar amplified warming. These two factors imply a critical role for transport and nonlinear effects, with the latter acting to substantially reduce global climate sensitivity. At the hemispheric scale, a rich picture emerges: anomalous divergence of heat flux away from positive feedbacks in the subtropics; clear-sky nonlinearities that reinforce the pattern of tropical cooling and high-latitude warming tendencies; and strong ice-line feedbacks that drive further amplification of polar warming. These results have implications for regional climate predictability, by providing an indication of how spatial patterns in feedbacks combine to affect both the local and nonlocal climate response, and how constraining uncertainty in those feedbacks may constrain the climate response. We also consider how competing definitions of feedbacks influence interpretation of climate sensitivity. While climate feedbacks represent a convenient breakdown of the energy balance, their widespread appeal has led to a profusion of definitions, and to variations upon the traditional decomposition. We demonstrate that a locally defined feedback framework does provide several advantages from the perspective of regional climate predictability. Namely, it enables a partial temperature change analysis which quantifies contributions to spatial patterns of warming; it also ensures feedbacks are not biased at high latitudes due to polar amplification. Alternative approaches to characterizing feedbacks can also isolate and illuminate different atmospheric processes. In particular, comparison of two versions of the water vapor feedback, one focused on specific humidity and the other on relative humidity, allows for an elegant dissection of the relative importance of thermodynamical and dynamical changes in a warmer world.

A Mixed Mode Cochlear Amplifier Including Neural Feedback

NASA Astrophysics Data System (ADS)

Flax, Matthew R.; Holmes, W. Harvey

2011-11-01

The mixed mode cochlear amplifier (MMCA) model is derived from the physiology of the cochlea. It is comprised of three main elements of the peripheral hearing system: the cochlear mechanics, hair cell motility, and neurophysiology. This model expresses both active compression wave and active traveling wave modes of operation. The inclusion of a neural loop with a time delay, and a new paradigm for the mechanical response of the outer hair cells, are believed to be unique features of the MMCA. These elements combine to form an active feedback loop to constitute the cochlear amplifier, whose input is a passive traveling wave vibration. The result is a cycle-by-cycle amplifier with nonlinear response. This system can assume an infinite number of different operating states. The stable state and the first few amplitude-limited unstable (Hopf-bifurcated) states are significant in describing the operation of the peripheral hearing system. A hierarchy of models can be constructed from this concept, depending on the amount of detail included. The simplest model of the MMCA is a nonlinear delay line resonator. It was found that even this simple MMCA version can explain a large number of hearing phenomena, at least qualitatively. This paper concentrates on explaining the fractional octave shift from the living to postmortem response in terms of the new model. Other mechanical, hair cell and neurological phenomena can also be accounted for by the MMCA, including two-tone suppression behavior, distortion product responses, otoacoustic emissions and neural spontaneous rates.

Zero Power Non-Contact Suspension System with Permanent Magnet Motion Feedback

NASA Astrophysics Data System (ADS)

Sun, Feng; Oka, Koichi

This paper proposes a zero power control method for a permanent magnetic suspension system consisting mainly of a permanent magnet, an actuator, sensors, a suspended iron ball and a spring. A system using this zero power control method will consume quasi-zero power when the levitated object is suspended in an equilibrium state. To realize zero power control, a spring is installed in the magnetic suspension device to counterbalance the gravitational force on the actuator in the equilibrium position. In addition, an integral feedback loop in the controller affords zero actuator current when the device is in a balanced state. In this study, a model was set up for feasibility analysis, a prototype was manufactured for experimental confirmation, numerical simulations of zero power control with nonlinear attractive force were carried out based on the model, and experiments were completed to confirm the practicality of the prototype. The simulations and experiments were performed under varied conditions, such as without springs and without zero power control, with springs and without zero power control, with springs and with zero power control, using different springs and integral feedback gains. Some results are shown and analyzed in this paper. All results indicate that this zero power control method is feasible and effective for use in this suspension system with a permanent magnet motion feedback loop.

Robust Fuzzy Logic Stabilization with Disturbance Elimination

PubMed Central

Danapalasingam, Kumeresan A.

2014-01-01

A robust fuzzy logic controller is proposed for stabilization and disturbance rejection in nonlinear control systems of a particular type. The dynamic feedback controller is designed as a combination of a control law that compensates for nonlinear terms in a control system and a dynamic fuzzy logic controller that addresses unknown model uncertainties and an unmeasured disturbance. Since it is challenging to derive a highly accurate mathematical model, the proposed controller requires only nominal functions of a control system. In this paper, a mathematical derivation is carried out to prove that the controller is able to achieve asymptotic stability by processing state measurements. Robustness here refers to the ability of the controller to asymptotically steer the state vector towards the origin in the presence of model uncertainties and a disturbance input. Simulation results of the robust fuzzy logic controller application in a magnetic levitation system demonstrate the feasibility of the control design. PMID:25177713

Distributed neural network control for adaptive synchronization of uncertain dynamical multiagent systems.

PubMed

Peng, Zhouhua; Wang, Dan; Zhang, Hongwei; Sun, Gang

2014-08-01

This paper addresses the leader-follower synchronization problem of uncertain dynamical multiagent systems with nonlinear dynamics. Distributed adaptive synchronization controllers are proposed based on the state information of neighboring agents. The control design is developed for both undirected and directed communication topologies without requiring the accurate model of each agent. This result is further extended to the output feedback case where a neighborhood observer is proposed based on relative output information of neighboring agents. Then, distributed observer-based synchronization controllers are derived and a parameter-dependent Riccati inequality is employed to prove the stability. This design has a favorable decouple property between the observer and the controller designs for nonlinear multiagent systems. For both cases, the developed controllers guarantee that the state of each agent synchronizes to that of the leader with bounded residual errors. Two illustrative examples validate the efficacy of the proposed methods.

A comparative study of linear and nonlinear MIMO feedback configurations

NASA Technical Reports Server (NTRS)

Desoer, C. A.; Lin, C. A.

1984-01-01

In this paper, a comparison is conducted of several feedback configurations which have appeared in the literature (e.g. unity-feedback, model-reference, etc.). The linear time-invariant multi-input multi-output case is considered. For each configuration, the stability conditions are specified, the relation between achievable I/O maps and the achievable disturbance-to-output maps is examined, and the effect of various subsystem perturbations on the system performance is studied. In terms of these considerations, it is demonstrated that one of the configurations considered is better than all the others. The results are then extended to the nonlinear multi-input multi-output case.

Feedback control of plasma instabilities with charged particle beams and study of plasma turbulence

NASA Technical Reports Server (NTRS)

Tham, Philip Kin-Wah

1994-01-01

A new non-perturbing technique for feedback control of plasma instabilities has been developed in the Columbia Linear Machine (CLM). The feedback control scheme involves the injection of a feedback modulated ion beam as a remote suppressor. The ion beam was obtained from a compact ion beam source which was developed for this purpose. A Langmuir probe was used as the feedback sensor. The feedback controller consisted of a phase-shifter and amplifiers. This technique was demonstrated by stabilizing various plasma instabilities to the background noise level, like the trapped particle instability, the ExB instability and the ion-temperature-gradient (ITG) driven instability. An important feature of this scheme is that the injected ion beam is non-perturbing to the plasma equilibrium parameters. The robustness of this feedback stabilization scheme was also investigated. The principal result is that the scheme is fairly robust, tolerating about 100% variation about the nominal parameter values. Next, this scheme is extended to the unsolved general problem of controlling multimode plasma instabilities simultaneously with a single sensor-suppressor pair. A single sensor-suppressor pair of feedback probes is desirable to reduce the perturbation caused by the probes. Two plasma instabilities the ExB and the ITG modes, were simultaneously stabilized. A simple 'state' feedback type method was used where more state information was generated from the single sensor Langmuir probe by appropriate signal processing, in this case, by differentiation. This proof-of-principle experiment demonstrated for the first time that by designing a more sophisticated electronic feedback controller, many plasma instabilities may be simultaneously controlled. Simple theoretical models showed generally good agreement with the feedback experimental results. On a parallel research front, a better understanding of the saturated state of a plasma instability was sought partly with the help of feedback. A plasma instability is usually observed in its saturated state and appears as a single feature in the frequency spectrum with a single azimuthal and parallel wavenumbers. The physics of the non-zero spectral width was investigated in detail because the finite spectral width can cause "turbulent" transport. One aspect of the "turbulence" was investigated by obtaining the scaling of the linear growth rate of the instabilities with the fluctuation levels. The linear growth rates were measured with the established gated feedback technique. The research showed that the ExB instability evolves into a quasi-coherent state when the fluctuation level is high. The coherent aspects were studied with a bispectral analysis. Moreover, the single spectral feature was discovered to be actually composed of a few radial harmonics. The radial harmonics play a role in the nonlinear saturation of the instability via three-wave coupling.

Phase-selective entrainment of nonlinear oscillator ensembles

DOE PAGES

Zlotnik, Anatoly V.; Nagao, Raphael; Kiss, Istvan Z.; ...

2016-03-18

The ability to organize and finely manipulate the hierarchy and timing of dynamic processes is important for understanding and influencing brain functions, sleep and metabolic cycles, and many other natural phenomena. However, establishing spatiotemporal structures in biological oscillator ensembles is a challenging task that requires controlling large collections of complex nonlinear dynamical units. In this report, we present a method to design entrainment signals that create stable phase patterns in ensembles of heterogeneous nonlinear oscillators without using state feedback information. We demonstrate the approach using experiments with electrochemical reactions on multielectrode arrays, in which we selectively assign ensemble subgroups intomore » spatiotemporal patterns with multiple phase clusters. As a result, the experimentally confirmed mechanism elucidates the connection between the phases and natural frequencies of a collection of dynamical elements, the spatial and temporal information that is encoded within this ensemble, and how external signals can be used to retrieve this information.« less

Phase-selective entrainment of nonlinear oscillator ensembles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zlotnik, Anatoly V.; Nagao, Raphael; Kiss, Istvan Z.

The ability to organize and finely manipulate the hierarchy and timing of dynamic processes is important for understanding and influencing brain functions, sleep and metabolic cycles, and many other natural phenomena. However, establishing spatiotemporal structures in biological oscillator ensembles is a challenging task that requires controlling large collections of complex nonlinear dynamical units. In this report, we present a method to design entrainment signals that create stable phase patterns in ensembles of heterogeneous nonlinear oscillators without using state feedback information. We demonstrate the approach using experiments with electrochemical reactions on multielectrode arrays, in which we selectively assign ensemble subgroups intomore » spatiotemporal patterns with multiple phase clusters. As a result, the experimentally confirmed mechanism elucidates the connection between the phases and natural frequencies of a collection of dynamical elements, the spatial and temporal information that is encoded within this ensemble, and how external signals can be used to retrieve this information.« less

Continuous uniformly finite time exact disturbance observer based control for fixed-time stabilization of nonlinear systems with mismatched disturbances

PubMed Central

Liu, Chongxin; Liu, Hang

2017-01-01

This paper presents a continuous composite control scheme to achieve fixed-time stabilization for nonlinear systems with mismatched disturbances. The composite controller is constructed in two steps: First, uniformly finite time exact disturbance observers are proposed to estimate and compensate the disturbances. Then, based on adding a power integrator technique and fixed-time stability theory, continuous fixed-time stable state feedback controller and Lyapunov functions are constructed to achieve global fixed-time system stabilization. The proposed control method extends the existing fixed-time stable control results to high order nonlinear systems with mismatched disturbances and achieves global fixed-time system stabilization. Besides, the proposed control scheme improves the disturbance rejection performance and achieves performance recovery of nominal system. Simulation results are provided to show the effectiveness, the superiority and the applicability of the proposed control scheme. PMID:28406966

Intelligent Tracking Control for a Class of Uncertain High-Order Nonlinear Systems.

PubMed

Zhao, Xudong; Shi, Peng; Zheng, Xiaolong; Zhang, Jianhua

2016-09-01

This brief is concerned with the problem of intelligent tracking control for a class of high-order nonlinear systems with completely unknown nonlinearities. An intelligent adaptive control algorithm is presented by combining the adaptive backstepping technique with the neural networks' approximation ability. It is shown that the practical output tracking performance of the system is achieved using the proposed state-feedback controller under two mild assumptions. In particular, by introducing a parameter in the derivations, the tracking error between the time-varying target signal and the output can be reduced via tuning the controller design parameters. Moreover, in order to solve the problem of overparameterization, which is a common issue in adaptive control design, a controller with one adaptive law is also designed. Finally, simulation results are given to show the effectiveness of the theoretical approaches and the potential of the proposed new design techniques.

Phase-selective entrainment of nonlinear oscillator ensembles

NASA Astrophysics Data System (ADS)

Zlotnik, Anatoly; Nagao, Raphael; Kiss, István Z.; Li-Shin, Jr.

2016-03-01

The ability to organize and finely manipulate the hierarchy and timing of dynamic processes is important for understanding and influencing brain functions, sleep and metabolic cycles, and many other natural phenomena. However, establishing spatiotemporal structures in biological oscillator ensembles is a challenging task that requires controlling large collections of complex nonlinear dynamical units. In this report, we present a method to design entrainment signals that create stable phase patterns in ensembles of heterogeneous nonlinear oscillators without using state feedback information. We demonstrate the approach using experiments with electrochemical reactions on multielectrode arrays, in which we selectively assign ensemble subgroups into spatiotemporal patterns with multiple phase clusters. The experimentally confirmed mechanism elucidates the connection between the phases and natural frequencies of a collection of dynamical elements, the spatial and temporal information that is encoded within this ensemble, and how external signals can be used to retrieve this information.

Adaptive Fuzzy Output Constrained Control Design for Multi-Input Multioutput Stochastic Nonstrict-Feedback Nonlinear Systems.

PubMed

Li, Yongming; Tong, Shaocheng

2017-12-01

In this paper, an adaptive fuzzy output constrained control design approach is addressed for multi-input multioutput uncertain stochastic nonlinear systems in nonstrict-feedback form. The nonlinear systems addressed in this paper possess unstructured uncertainties, unknown gain functions and unknown stochastic disturbances. Fuzzy logic systems are utilized to tackle the problem of unknown nonlinear uncertainties. The barrier Lyapunov function technique is employed to solve the output constrained problem. In the framework of backstepping design, an adaptive fuzzy control design scheme is constructed. All the signals in the closed-loop system are proved to be bounded in probability and the system outputs are constrained in a given compact set. Finally, the applicability of the proposed controller is well carried out by a simulation example.

Coordinated three-dimensional motion of the head and torso by dynamic neural networks.

PubMed

Kim, J; Hemami, H

1998-01-01

The problem of trajectory tracking control of a three dimensional (3D) model of the human upper torso and head is considered. The torso and the head are modeled as two rigid bodies connected at one point, and the Newton-Euler method is used to derive the nonlinear differential equations that govern the motion of the system. The two-link system is driven by six pairs of muscle like actuators that possess physiologically inspired alpha like and gamma like inputs, and spindle like and Golgi tendon organ like outputs. These outputs are utilized as reflex feedback for stability and stiffness control, in a long loop feedback for the purpose of estimating the state of the system (somesthesis), and as part of the input to the controller. Ideal delays of different duration are included in the feedforward and feedback paths of the system to emulate such delays encountered in physiological systems. Dynamical neural networks are trained to learn effective control of the desired maneuvers of the system. The feasibility of the controller is demonstrated by computer simulation of the successful execution of the desired maneuvers. This work demonstrates the capabilities of neural circuits in controlling highly nonlinear systems with multidelays in their feedforward and feedback paths. The ultimate long range goal of this research is toward understanding the working of the central nervous system in controlling movement. It is an interdisciplinary effort relying on mechanics, biomechanics, neuroscience, system theory, physiology and anatomy, and its short range relevance to rehabilitation must be noted.

Which way will the circulation shift in a changing climate? Possible nonlinearity of extratropical cloud feedbacks

NASA Astrophysics Data System (ADS)

Tandon, Neil F.; Cane, Mark A.

2017-06-01

In a suite of idealized experiments with the Community Atmospheric Model version 3 coupled to a slab ocean, we show that the atmospheric circulation response to CO2 increase is sensitive to extratropical cloud feedback that is potentially nonlinear. Doubling CO2 produces a poleward shift of the Southern Hemisphere (SH) midlatitude jet that is driven primarily by cloud shortwave feedback and modulated by ice albedo feedback, in agreement with earlier studies. More surprisingly, for CO2 increases smaller than 25 %, the SH jet shifts equatorward. Nonlinearities are also apparent in the Northern Hemisphere, but with less zonal symmetry. Baroclinic instability theory and climate feedback analysis suggest that as the CO2 forcing amplitude is reduced, there is a transition from a regime in which cloud and circulation changes are largely decoupled to a regime in which they are highly coupled. In the dynamically coupled regime, there is an apparent cancellation between cloud feedback due to warming and cloud feedback due to the shifting jet, and this allows the ice albedo feedback to dominate in the high latitudes. The extent to which dynamical coupling effects exceed thermodynamic forcing effects is strongly influenced by cloud microphysics: an alternate model configuration with slightly increased cloud liquid (LIQ) produces poleward jet shifts regardless of the amplitude of CO2 forcing. Altering the cloud microphysics also produces substantial spread in the circulation response to CO2 doubling: the LIQ configuration produces a poleward SH jet shift approximately twice that produced under the default configuration. Analysis of large ensembles of the Canadian Earth System Model version 2 demonstrates that nonlinear, cloud-coupled jet shifts are also possible in comprehensive models. We still expect a poleward trend in SH jet latitude for timescales on which CO2 increases by more than 25 %. But on shorter timescales, our results give good reason to expect significant equatorward deviations. We also discuss the implications for understanding the circulation response to small external forcings from other sources, such as the solar cycle.

Three-axis stabilization of spacecraft using parameter-independent nonlinear quaternion feedback

NASA Technical Reports Server (NTRS)

Joshi, Suresh M.; Kelkar, Atul G.

1994-01-01

This paper considers the problem of rigid spacecraft. A nonlinear control law which uses the feedback of the unit quaternion and the measured angular velocities is proposed and is shown to provide global asymptotic stability. The control law does not require the knowledge of the system parameters, and is therefore robust to modeling errors. The significance of the control law is that it can be used for large-angle maneuvers with guaranteed stability.

Simulations of neutral wind shear effect on the equatorial ionosphere irregularities

NASA Astrophysics Data System (ADS)

Kim, J.; Chagelishvili, G.; Horton, W.

2005-12-01

We present numerical calculations of the large-scale electron density driven by the gradient drift instability in the daytime equatorial electrojet. Under two-fluid theory the linear analysis for kilometer scale waves lead to the result that all the perturbations are transformed to small scales through linear convection by shear and then damped by diffusion. The inclusion of the nonlinearity enables inverse energy cascade to provide energy to long scale. The feedback between velocity shear and nonlinearity keeps waves growing and leads to the turbulence. In strongly turbulent regime, the nonlinear states are saturated [1]. Since the convective nonlinearities are isotropic while the interactions of velocity shear with waves are anisotropic, the feedback do not necessarily enable waves to grow. The growth of waves are highly variable on k-space configuration [2]. Our simulations show that the directional relationship between vorticity of irregularities and shear are one of key factors. Thus during the transient period, the irregularities show the anisotropy of the vorticity power spectrum. We report the evolution of the power spectrum of the vorticity and density of irregularties and its anistropic nature as observed. The work was supported in part by the Department of NSF Grant ATM-0229863 and ISTC Grant G-553. C. Ronchi, R.N. Sudan, and D.T. Farley. Numerical simulations of large-scale plasma turbulece in teh day time equatorial electrojet. J. Geophys. Res., 96:21263--21279, 1991. G.D. Chagelishvili, R.G. Chanishvili, T.S. Hristov, and J.G. Lominadze. A turbulence model in unbounded smooth shear flows : The weak turbulence approach. JETP, 94(2):434--445, 2002.

Transient and asymptotic behavior in a regular network model for the ice-albedo feedback under thermal forcing

NASA Astrophysics Data System (ADS)

Mueller-Stoffels, M.; Wackerbauer, R.

2010-12-01

The Arctic ocean and sea ice form a feedback system which plays an important role in the global climate. Variations of the global ice and snow distribution have a significant effect on the planetary albedo which governs the absorption of shortwave radiation. The complexity of highly parametrized GCMs makes it very difficult to assess single feedback processes in the climate system without the concurrent use of simple models where the physics are understood [1][2][3]. We introduce a complex systems model to investigate thermodynamic feedback processes in an Arctic ice-ocean layer. The ice-ocean layer is represented as a regular network of coupled cells. The state of each cell is determined by its energy content, which also defines the phase of the cell. The energy transport between cells is described with nonlinear and heterogeneous diffusion constants. And the time-evolution of the ice-ocean is driven by shortwave, longwave and lateral oceanic and atmospheric thermal forcing. This model is designed to study the stability of an ice cover under various heat intake scenarios. The network structure of the model allows to easily introduce albedo heterogeneities due to aging ice, wind blown snow cover, and ice movement to explore the time-evolution and pattern formation (melt ponds) processes in the Arctic sea ice. The solely thermodynamic model exhibits two stable states; one in the perennially ice covered domain and one in the perennially open water domain. Their existence is due to the temperature dependence of the longwave radiative budget. Transition between these states can be forced via lateral heat fluxes. During the transition from the ice covered to the open water stable state the ice albedo feedback effects are manifested as an increased warming rate of the ice cover together with enhanced seasonal energy oscillations. In the current model realization seasonal ice cover is present as a transient state only. Furthermore, the model exhibits hysteresis between the ice covered and the open water state when varying the lateral atmospheric (or oceanic) heat intake. Once the ice-ocean layer has transitioned from the ice covered to the open water stable state significant cooling (reduction of lateral fluxes) is necessary to return to the ice covered stable state. We also find that ocean heat fluxes are more efficient than atmospheric heat fluxes to melt Arctic sea ice; only small portions of heat entering from the bottom of the ice-ocean layer induce already a transition to the stable asymptotic state with perennial open water. This indicates that ocean currents, understood as heat conveyors, can play a significant role in melting continuous ice covers. This is consistent with the findings of Shimada et al. for the Canada basin [4]. References: [1] S. Bony et al., How well do we understand and evaluate climate change feedback processes?, J of Climate 19, 3445 (2006). [2]I. Eisenman and J.S. Wettlaufer, Nonlinear threshold behavior during the loss of Arctic sea ice, PNAS 106, 28 (2009). [3]A.S. Thorndike, A Toy Model Linking Atmospheric and Thermal Radiation and Sea Ice Growth, JGR 97, 9401 (1992). [4] K. Shimada et al., Paci[|#12#|]c Ocean inflow: Influence on catastrophic reduction of sea ice cover in the Arctic Ocean, GRL 33, L08605 (2006).

Adaptive control of stochastic linear systems with unknown parameters. M.S. Thesis

NASA Technical Reports Server (NTRS)

Ku, R. T.

1972-01-01

The problem of optimal control of linear discrete-time stochastic dynamical system with unknown and, possibly, stochastically varying parameters is considered on the basis of noisy measurements. It is desired to minimize the expected value of a quadratic cost functional. Since the simultaneous estimation of the state and plant parameters is a nonlinear filtering problem, the extended Kalman filter algorithm is used. Several qualitative and asymptotic properties of the open loop feedback optimal control and the enforced separation scheme are discussed. Simulation results via Monte Carlo method show that, in terms of the performance measure, for stable systems the open loop feedback optimal control system is slightly better than the enforced separation scheme, while for unstable systems the latter scheme is far better.

Leader-Follower Formation Control of UUVs with Model Uncertainties, Current Disturbances, and Unstable Communication

PubMed Central

Yan, Zheping; Xu, Da; Chen, Tao; Zhang, Wei; Liu, Yibo

2018-01-01

Unmanned underwater vehicles (UUVs) have rapidly developed as mobile sensor networks recently in the investigation, survey, and exploration of the underwater environment. The goal of this paper is to develop a practical and efficient formation control method to improve work efficiency of multi-UUV sensor networks. Distributed leader-follower formation controllers are designed based on a state feedback and consensus algorithm. Considering that each vehicle is subject to model uncertainties and current disturbances, a second-order integral UUV model with a nonlinear function is established using the state feedback linearized method under current disturbances. For unstable communication among UUVs, communication failure and acoustic link noise interference are considered. Two-layer random switching communication topologies are proposed to solve the problem of communication failure. For acoustic link noise interference, accurate representation of valid communication information and noise stripping when designing controllers is necessary. Effective communication topology weights are designed to represent the validity of communication information interfered by noise. Utilizing state feedback and noise stripping, sufficient conditions for design formation controllers are proposed to ensure UUV formation achieves consensus under model uncertainties, current disturbances, and unstable communication. The stability of formation controllers is proven by the Lyapunov-Razumikhin theorem, and the validity is verified by simulation results. PMID:29473919

State reference design and saturated control of doubly-fed induction generators under voltage dips

NASA Astrophysics Data System (ADS)

Tilli, Andrea; Conficoni, Christian; Hashemi, Ahmad

2017-04-01

In this paper, the stator/rotor currents control problem of doubly-fed induction generator under faulty line voltage is carried out. Common grid faults cause a steep decline in the line voltage profile, commonly denoted as voltage dip. This point is critical for such kind of machines, having their stator windings directly connected to the grid. In this respect, solid methodological nonlinear control theory arguments are exploited and applied to design a novel controller, whose main goal is to improve the system behaviour during voltage dips, endowing it with low voltage ride through capability, a fundamental feature required by modern Grid Codes. The proposed solution exploits both feedforward and feedback actions. The feedforward part relies on suitable reference trajectories for the system internal dynamics, which are designed to prevent large oscillations in the rotor currents and command voltages, excited by line perturbations. The feedback part uses state measurements and is designed according to Linear Matrix Inequalities (LMI) based saturated control techniques to further reduce oscillations, while explicitly accounting for the system constraints. Numerical simulations verify the benefits of the internal dynamics trajectory planning, and the saturated state feedback action, in crucially improving the Doubly-Fed Induction Machine response under severe grid faults.

Gust alleviation of highly flexible UAVs with artificial hair sensors

NASA Astrophysics Data System (ADS)

Su, Weihua; Reich, Gregory W.

2015-04-01

Artificial hair sensors (AHS) have been recently developed in Air Force Research Laboratory (AFRL) using carbon nanotube (CNT). The deformation of CNT in air flow causes voltage and current changes in the circuit, which can be used to quantify the dynamic pressure and aerodynamic load along the wing surface. AFRL has done a lot of essential work in design, manufacturing, and measurement of AHSs. The work in this paper is to bridge the current AFRL's work on AHSs and their feasible applications in flight dynamics and control (e.g., the gust alleviation) of highly flexible aircraft. A highly flexible vehicle is modeled using a strain-based geometrically nonlinear beam formulation, coupled with finite-state inflow aerodynamics. A feedback control algorithm for the rejection of gust perturbations will be developed. A simplified Linear Quadratic Regulator (LQR) controller will be implemented based on the state-space representation of the linearized system. All AHS measurements will be used as the control input, i.e., wing sectional aerodynamic loads will be defined as the control output for designing the feedback gain. Once the controller is designed, closed-loop aeroelastic simulations will be performed to evaluate the performance of different controllers with the force feedback and be compared to traditional controller designs with the state feedback. From the study, the feasibility of AHSs in flight control will be assessed. The whole study will facilitate in building a fly-by-feel simulation environment for autonomous vehicles.

Linear control of the flywheel inverted pendulum.

PubMed

Olivares, Manuel; Albertos, Pedro

2014-09-01

The flywheel inverted pendulum is an underactuated mechanical system with a nonlinear model but admitting a linear approximation around the unstable equilibrium point in the upper position. Although underactuated systems usually require nonlinear controllers, the easy tuning and understanding of linear controllers make them more attractive for designers and final users. In a recent paper, a simple PID controller was proposed by the authors, leading to an internally unstable controlled plant. To achieve global stability, two options are developed here: first by introducing an internal stabilizing controller and second by replacing the PID controller by an observer-based state feedback control. Simulation and experimental results show the effectiveness of the design. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Cooperative Adaptive Output Regulation for Second-Order Nonlinear Multiagent Systems With Jointly Connected Switching Networks.

PubMed

Liu, Wei; Huang, Jie

2018-03-01

This paper studies the cooperative global robust output regulation problem for a class of heterogeneous second-order nonlinear uncertain multiagent systems with jointly connected switching networks. The main contributions consist of the following three aspects. First, we generalize the result of the adaptive distributed observer from undirected jointly connected switching networks to directed jointly connected switching networks. Second, by performing a new coordinate and input transformation, we convert our problem into the cooperative global robust stabilization problem of a more complex augmented system via the distributed internal model principle. Third, we solve the stabilization problem by a distributed state feedback control law. Our result is illustrated by the leader-following consensus problem for a group of Van der Pol oscillators.

Multistability and switching in oppositely-directed saturated coupler

NASA Astrophysics Data System (ADS)

Nithyanandan, K.; Shafeeque Ali, A. K.; Porsezian, K.; Nishad, M. P. M.; Tchofo Dinda, P.; Grelu, Ph.

2018-06-01

We investigate theoretically the optical multistability that takes place in a two-core oppositely-directed saturated coupler (ODSC) having negative index material (NIM) channel. The dynamics are studied using the Lagrangian variational method, and analytical solutions are constructed with Jacobi elliptic functions. The ODSC exhibits a bandgap as a consequence of the effective feedback mechanism due to the opposite directionality of the phase velocity and the Poynting vector in the NIM channel. Depending on the strength of the nonlinear saturation, the system admits multiple stable states. Considering the additional degrees of design freedom with respect to conventional nonlinear couplers, the ODSC could become an attractive choice for all-optical switching. The existence of multiple transmission resonance windows could also facilitate the realization of gap solitons.

Analysis of a dc bus system with a nonlinear constant power load and its delayed feedback control.

PubMed

Konishi, Keiji; Sugitani, Yoshiki; Hara, Naoyuki

2014-02-01

This paper tackles a destabilizing problem of a direct-current (dc) bus system with constant power loads, which can be considered a fundamental problem of dc power grid networks. The present paper clarifies scenarios of the destabilization and applies the well-known delayed-feedback control to the stabilization of the destabilized bus system on the basis of nonlinear science. Further, we propose a systematic procedure for designing the delayed feedback controller. This controller can converge the bus voltage exactly on an unstable operating point without accurate information and can track it using tiny control energy even when a system parameter, such as the power consumption of the load, is slowly varied. These features demonstrate that delayed feedback control can be considered a strong candidate for solving the destabilizing problem.

High Accuracy Attitude Control of a Spacecraft Using Feedback Linearization

DTIC Science & Technology

1992-05-01

High Accuracy Attitude Control of a Spacecraft Using Feedback Linearization A Thesis Presented by Louis Joseph PoehIman, Captain, USAF B.S., U.S. Air...High Accuracy Attitude Control of a Spacecraft Using Feedback Linearization by Louis Joseph Poehlman, Captain, USAF Submitted to the Department of...31 2-4 Attitude Determination and Control System Architecture ................. 33 3-1 Exact Linearization Using Nonlinear Feedback

An open-closed-loop iterative learning control approach for nonlinear switched systems with application to freeway traffic control

NASA Astrophysics Data System (ADS)

Sun, Shu-Ting; Li, Xiao-Dong; Zhong, Ren-Xin

2017-10-01

For nonlinear switched discrete-time systems with input constraints, this paper presents an open-closed-loop iterative learning control (ILC) approach, which includes a feedforward ILC part and a feedback control part. Under a given switching rule, the mathematical induction is used to prove the convergence of ILC tracking error in each subsystem. It is demonstrated that the convergence of ILC tracking error is dependent on the feedforward control gain, but the feedback control can speed up the convergence process of ILC by a suitable selection of feedback control gain. A switched freeway traffic system is used to illustrate the effectiveness of the proposed ILC law.

Nonlinear adaptive control of an elastic robotic arm

NASA Technical Reports Server (NTRS)

Singh, S. N.

1986-01-01

An approach to control of a class of nonlinear flexible robotic systems is presented. For simplicity, a robot arm (PUMA-type) with three rotational joints is considered. The third link is assumed to be elastic. An adaptive torquer control law is derived for controlling the joint angles. This controller includes a dynamic system in the feedback path, requires only joint angle and rate for feedback, and asymptotically decomposes the elastic dynamics into two subsystems representing the transverse vibrations of the elastic link in two orthogonal planes. To damp out the elastic vibration, a force control law using modal feedback is synthesized. The combination of the torque and force control laws accomplishes joint angle control and elastic mode stabilization.

Integrated Flight/Structural Mode Control for Very Flexible Aircraft Using L1 Adaptive Output Feedback Controller

NASA Technical Reports Server (NTRS)

Che, Jiaxing; Cao, Chengyu; Gregory, Irene M.

2012-01-01

This paper explores application of adaptive control architecture to a light, high-aspect ratio, flexible aircraft configuration that exhibits strong rigid body/flexible mode coupling. Specifically, an L(sub 1) adaptive output feedback controller is developed for a semi-span wind tunnel model capable of motion. The wind tunnel mount allows the semi-span model to translate vertically and pitch at the wing root, resulting in better simulation of an aircraft s rigid body motion. The control objective is to design a pitch control with altitude hold while suppressing body freedom flutter. The controller is an output feedback nominal controller (LQG) augmented by an L(sub 1) adaptive loop. A modification to the L(sub 1) output feedback is proposed to make it more suitable for flexible structures. The new control law relaxes the required bounds on the unmatched uncertainty and allows dependence on the state as well as time, i.e. a more general unmatched nonlinearity. The paper presents controller development and simulated performance responses. Simulation is conducted by using full state flexible wing models derived from test data at 10 different dynamic pressure conditions. An L(sub 1) adaptive output feedback controller is designed for a single test point and is then applied to all the test cases. The simulation results show that the L(sub 1) augmented controller can stabilize and meet the performance requirements for all 10 test conditions ranging from 30 psf to 130 psf dynamic pressure.

Application of variable-gain output feedback for high-alpha control

NASA Technical Reports Server (NTRS)

Ostroff, Aaron J.

1990-01-01

A variable-gain, optimal, discrete, output feedback design approach that is applied to a nonlinear flight regime is described. The flight regime covers a wide angle-of-attack range that includes stall and post stall. The paper includes brief descriptions of the variable-gain formulation, the discrete-control structure and flight equations used to apply the design approach, and the high performance airplane model used in the application. Both linear and nonlinear analysis are shown for a longitudinal four-model design case with angles of attack of 5, 15, 35, and 60 deg. Linear and nonlinear simulations are compared for a single-point longitudinal design at 60 deg angle of attack. Nonlinear simulations for the four-model, multi-mode, variable-gain design include a longitudinal pitch-up and pitch-down maneuver and high angle-of-attack regulation during a lateral maneuver.

SuperSpike: Supervised Learning in Multilayer Spiking Neural Networks.

PubMed

Zenke, Friedemann; Ganguli, Surya

2018-06-01

A vast majority of computation in the brain is performed by spiking neural networks. Despite the ubiquity of such spiking, we currently lack an understanding of how biological spiking neural circuits learn and compute in vivo, as well as how we can instantiate such capabilities in artificial spiking circuits in silico. Here we revisit the problem of supervised learning in temporally coding multilayer spiking neural networks. First, by using a surrogate gradient approach, we derive SuperSpike, a nonlinear voltage-based three-factor learning rule capable of training multilayer networks of deterministic integrate-and-fire neurons to perform nonlinear computations on spatiotemporal spike patterns. Second, inspired by recent results on feedback alignment, we compare the performance of our learning rule under different credit assignment strategies for propagating output errors to hidden units. Specifically, we test uniform, symmetric, and random feedback, finding that simpler tasks can be solved with any type of feedback, while more complex tasks require symmetric feedback. In summary, our results open the door to obtaining a better scientific understanding of learning and computation in spiking neural networks by advancing our ability to train them to solve nonlinear problems involving transformations between different spatiotemporal spike time patterns.

A megahertz-frequency tunable piecewise-linear electromechanical resonator realized via nonlinear feedback

NASA Astrophysics Data System (ADS)

Bajaj, Nikhil; Chiu, George T.-C.; Rhoads, Jeffrey F.

2018-07-01

Vibration-based sensing modalities traditionally have relied upon monitoring small shifts in natural frequency in order to detect structural changes (such as those in mass or stiffness). In contrast, bifurcation-based sensing schemes rely on the detection of a qualitative change in the behavior of a system as a parameter is varied. This can produce easy-to-detect changes in response amplitude with high sensitivity to structural change, but requires resonant devices with specific dynamic behavior which is not always easily reproduced. Desirable behavior for such devices can be produced reliably via nonlinear feedback circuitry, but has in past efforts been largely limited to sub-MHz operation, partially due to the time delay limitations present in certain nonlinear feedback circuits, such as multipliers. This work demonstrates the design and implementation of a piecewise-linear resonator realized via diode- and integrated circuit-based feedback electronics and a quartz crystal resonator. The proposed system is fabricated and characterized, and the creation and selective placement of the bifurcation points of the overall electromechanical system is demonstrated by tuning the circuit gains. The demonstrated circuit operates at 16 MHz. Preliminary modeling and analysis is presented that qualitatively agrees with the experimentally-observed behavior.

Closed-loop control of a fragile network: application to seizure-like dynamics of an epilepsy model

PubMed Central

Ehrens, Daniel; Sritharan, Duluxan; Sarma, Sridevi V.

2015-01-01

It has recently been proposed that the epileptic cortex is fragile in the sense that seizures manifest through small perturbations in the synaptic connections that render the entire cortical network unstable. Closed-loop therapy could therefore entail detecting when the network goes unstable, and then stimulating with an exogenous current to stabilize the network. In this study, a non-linear stochastic model of a neuronal network was used to simulate both seizure and non-seizure activity. In particular, synaptic weights between neurons were chosen such that the network's fixed point is stable during non-seizure periods, and a subset of these connections (the most fragile) were perturbed to make the same fixed point unstable to model seizure events; and, the model randomly transitions between these two modes. The goal of this study was to measure spike train observations from this epileptic network and then apply a feedback controller that (i) detects when the network goes unstable, and then (ii) applies a state-feedback gain control input to the network to stabilize it. The stability detector is based on a 2-state (stable, unstable) hidden Markov model (HMM) of the network, and detects the transition from the stable mode to the unstable mode from using the firing rate of the most fragile node in the network (which is the output of the HMM). When the unstable mode is detected, a state-feedback gain is applied to generate a control input to the fragile node bringing the network back to the stable mode. Finally, when the network is detected as stable again, the feedback control input is switched off. High performance was achieved for the stability detector, and feedback control suppressed seizures within 2 s after onset. PMID:25784851

Adaptive neural control of MIMO nonlinear systems with a block-triangular pure-feedback control structure.

PubMed

Chen, Zhenfeng; Ge, Shuzhi Sam; Zhang, Yun; Li, Yanan

2014-11-01

This paper presents adaptive neural tracking control for a class of uncertain multiinput-multioutput (MIMO) nonlinear systems in block-triangular form. All subsystems within these MIMO nonlinear systems are of completely nonaffine pure-feedback form and allowed to have different orders. To deal with the nonaffine appearance of the control variables, the mean value theorem is employed to transform the systems into a block-triangular strict-feedback form with control coefficients being couplings among various inputs and outputs. A systematic procedure is proposed for the design of a new singularity-free adaptive neural tracking control strategy. Such a design procedure can remove the couplings among subsystems and hence avoids the possible circular control construction problem. As a consequence, all the signals in the closed-loop system are guaranteed to be semiglobally uniformly ultimately bounded. Moreover, the outputs of the systems are ensured to converge to a small neighborhood of the desired trajectories. Simulation studies verify the theoretical findings revealed in this paper.

A Comparison of Climate Feedback Strength between CO2 Doubling and LGM Experiments

NASA Astrophysics Data System (ADS)

Yoshimori, M.; Yokohata, T.; Abe-Ouchi, A.

2008-12-01

Studies of past climate potentially provide a constraint on the uncertainty of climate sensitivity, but previous studies warn against a simple scaling to the future. The climate sensitivity is determined by various feedback processes and they may vary with climate states and forcings. In this study, we investigate similarities and differences of feedbacks for a CO2 doubling, a last glacial maximum (LGM), and LGM greenhouse gas (GHG) forcing experiments, using an atmospheric general circulation model coupled to a slab ocean model. After computing the radiative forcing, the individual feedback strengths: water vapor, lapse rate, albedo, and cloud feedbacks, are evaluated explicitly. For this particular model, the difference in the climate sensitivity among experiments is attributed to the shortwave cloud feedback in which there is a tendency that it becomes weaker or even negative in the cooling experiments. No significant difference is found in the water vapor feedback between warming and cooling experiments by GHGs despite the nonlinear dependence of the Clausius-Clapeyron relation on temperature. The weaker water vapor feedback in the LGM experiment due to a relatively weaker tropical forcing is compensated by the stronger lapse rate feedback due to a relatively stronger extratropical forcing. A hypothesis is proposed which explains the asymmetric cloud response between warming and cooling experiments associated with a displacement of the region of mixed- phase clouds. The difference in the total feedback strength between experiments is, however, relatively small compared to the current intermodel spread, and does not necessarily preclude the use of LGM climate as a future constraint.

A simple attitude control of quadrotor helicopter based on Ziegler-Nichols rules for tuning PD parameters.

PubMed

He, ZeFang; Zhao, Long

2014-01-01

An attitude control strategy based on Ziegler-Nichols rules for tuning PD (proportional-derivative) parameters of quadrotor helicopters is presented to solve the problem that quadrotor tends to be instable. This problem is caused by the narrow definition domain of attitude angles of quadrotor helicopters. The proposed controller is nonlinear and consists of a linear part and a nonlinear part. The linear part is a PD controller with PD parameters tuned by Ziegler-Nichols rules and acts on the quadrotor decoupled linear system after feedback linearization; the nonlinear part is a feedback linearization item which converts a nonlinear system into a linear system. It can be seen from the simulation results that the attitude controller proposed in this paper is highly robust, and its control effect is better than the other two nonlinear controllers. The nonlinear parts of the other two nonlinear controllers are the same as the attitude controller proposed in this paper. The linear part involves a PID (proportional-integral-derivative) controller with the PID controller parameters tuned by Ziegler-Nichols rules and a PD controller with the PD controller parameters tuned by GA (genetic algorithms). Moreover, this attitude controller is simple and easy to implement.

Decentralized Feedback Controllers for Exponential Stabilization of Hybrid Periodic Orbits: Application to Robotic Walking.

PubMed

Hamed, Kaveh Akbari; Gregg, Robert D

2016-07-01

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially stabilize periodic orbits for a class of hybrid dynamical systems arising from bipedal walking. The algorithm assumes a class of parameterized and nonlinear decentralized feedback controllers which coordinate lower-dimensional hybrid subsystems based on a common phasing variable. The exponential stabilization problem is translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities, which can be easily solved with available software packages. A set of sufficient conditions for the convergence of the iterative algorithm to a stabilizing decentralized feedback control solution is presented. The power of the algorithm is demonstrated by designing a set of local nonlinear controllers that cooperatively produce stable walking for a 3D autonomous biped with 9 degrees of freedom, 3 degrees of underactuation, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg.

Feedback linearization based control of a variable air volume air conditioning system for cooling applications.

PubMed

Thosar, Archana; Patra, Amit; Bhattacharyya, Souvik

2008-07-01

Design of a nonlinear control system for a Variable Air Volume Air Conditioning (VAVAC) plant through feedback linearization is presented in this article. VAVAC systems attempt to reduce building energy consumption while maintaining the primary role of air conditioning. The temperature of the space is maintained at a constant level by establishing a balance between the cooling load generated in the space and the air supply delivered to meet the load. The dynamic model of a VAVAC plant is derived and formulated as a MIMO bilinear system. Feedback linearization is applied for decoupling and linearization of the nonlinear model. Simulation results for a laboratory scale plant are presented to demonstrate the potential of keeping comfort and maintaining energy optimal performance by this methodology. Results obtained with a conventional PI controller and a feedback linearizing controller are compared and the superiority of the proposed approach is clearly established.

Feedback linearizing control of a MIMO power system

NASA Astrophysics Data System (ADS)

Ilyes, Laszlo

Prior research has demonstrated that either the mechanical or electrical subsystem of a synchronous electric generator may be controlled using single-input single-output (SISO) nonlinear feedback linearization. This research suggests a new approach which applies nonlinear feedback linearization to a multi-input multi-output (MIMO) model of the synchronous electric generator connected to an infinite bus load model. In this way, the electrical and mechanical subsystems may be linearized and simultaneously decoupled through the introduction of a pair of auxiliary inputs. This allows well known, linear, SISO control methods to be effectively applied to the resulting systems. The derivation of the feedback linearizing control law is presented in detail, including a discussion on the use of symbolic math processing as a development tool. The linearizing and decoupling properties of the control law are validated through simulation. And finally, the robustness of the control law is demonstrated.

Decentralized Feedback Controllers for Exponential Stabilization of Hybrid Periodic Orbits: Application to Robotic Walking*

PubMed Central

Hamed, Kaveh Akbari; Gregg, Robert D.

2016-01-01

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially stabilize periodic orbits for a class of hybrid dynamical systems arising from bipedal walking. The algorithm assumes a class of parameterized and nonlinear decentralized feedback controllers which coordinate lower-dimensional hybrid subsystems based on a common phasing variable. The exponential stabilization problem is translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities, which can be easily solved with available software packages. A set of sufficient conditions for the convergence of the iterative algorithm to a stabilizing decentralized feedback control solution is presented. The power of the algorithm is demonstrated by designing a set of local nonlinear controllers that cooperatively produce stable walking for a 3D autonomous biped with 9 degrees of freedom, 3 degrees of underactuation, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg. PMID:27990059

Regular network model for the sea ice-albedo feedback in the Arctic.

PubMed

Müller-Stoffels, Marc; Wackerbauer, Renate

2011-03-01

The Arctic Ocean and sea ice form a feedback system that plays an important role in the global climate. The complexity of highly parameterized global circulation (climate) models makes it very difficult to assess feedback processes in climate without the concurrent use of simple models where the physics is understood. We introduce a two-dimensional energy-based regular network model to investigate feedback processes in an Arctic ice-ocean layer. The model includes the nonlinear aspect of the ice-water phase transition, a nonlinear diffusive energy transport within a heterogeneous ice-ocean lattice, and spatiotemporal atmospheric and oceanic forcing at the surfaces. First results for a horizontally homogeneous ice-ocean layer show bistability and related hysteresis between perennial ice and perennial open water for varying atmospheric heat influx. Seasonal ice cover exists as a transient phenomenon. We also find that ocean heat fluxes are more efficient than atmospheric heat fluxes to melt Arctic sea ice.

Combined feedforward and feedback control of a redundant, nonlinear, dynamic musculoskeletal system.

PubMed

Blana, Dimitra; Kirsch, Robert F; Chadwick, Edward K

2009-05-01

A functional electrical stimulation controller is presented that uses a combination of feedforward and feedback for arm control in high-level injury. The feedforward controller generates the muscle activations nominally required for desired movements, and the feedback controller corrects for errors caused by muscle fatigue and external disturbances. The feedforward controller is an artificial neural network (ANN) which approximates the inverse dynamics of the arm. The feedback loop includes a PID controller in series with a second ANN representing the nonlinear properties and biomechanical interactions of muscles and joints. The controller was designed and tested using a two-joint musculoskeletal model of the arm that includes four mono-articular and two bi-articular muscles. Its performance during goal-oriented movements of varying amplitudes and durations showed a tracking error of less than 4 degrees in ideal conditions, and less than 10 degrees even in the case of considerable fatigue and external disturbances.

United States Air Force Research Initiation Program. 1985 Technical Report. Volume 3.

DTIC Science & Technology

1987-04-01

miners exposed to airborne radon (7). Thus the major health effect associated with radon is thought to be production of lung cancers by radon decay...Based Instruction: Effect Dr. Linda J. Buehner of Cognitive Style, Instructional Format, and Subject-Matter Content 160-OMG-085 9 Nonlinear Feedback...Instrumentation 760-OMG-042 16 Investigation of the Effects of Dr. David R. Cochran an Applied Electric Field on the InP Melt 760-OMG-014 17 Below-Melt

Simulating Eastern- and Central-Pacific Type ENSO Using a Simple Coupled Model

NASA Astrophysics Data System (ADS)

Fang, Xianghui; Zheng, Fei

2018-06-01

Severe biases exist in state-of-the-art general circulation models (GCMs) in capturing realistic central-Pacific (CP) El Niño structures. At the same time, many observational analyses have emphasized that thermocline (TH) feedback and zonal advective (ZA) feedback play dominant roles in the development of eastern-Pacific (EP) and CP El Niño-Southern Oscillation (ENSO), respectively. In this work, a simple linear air-sea coupled model, which can accurately depict the strength distribution of the TH and ZA feedbacks in the equatorial Pacific, is used to investigate these two types of El Niño. The results indicate that the model can reproduce the main characteristics of CP ENSO if the TH feedback is switched off and the ZA feedback is retained as the only positive feedback, confirming the dominant role played by ZA feedback in the development of CP ENSO. Further experiments indicate that, through a simple nonlinear control approach, many ENSO characteristics, including the existence of both CP and EP El Niño and the asymmetries between El Niño and La Niña, can be successfully captured using the simple linear air-sea coupled model. These analyses indicate that an accurate depiction of the climatological sea surface temperature distribution and the related ZA feedback, which are the subject of severe biases in GCMs, is very important in simulating a realistic CP El Niño.

Coevolution of nonlinear trends in vegetation, soils, and topography with elevation and slope aspect: A case study in the sky islands of southern Arizona

NASA Astrophysics Data System (ADS)

Pelletier, Jon D.; Barron-Gafford, Greg A.; Breshears, David D.; Brooks, Paul D.; Chorover, Jon; Durcik, Matej; Harman, Ciaran J.; Huxman, Travis E.; Lohse, Kathleen A.; Lybrand, Rebecca; Meixner, Tom; McIntosh, Jennifer C.; Papuga, Shirley A.; Rasmussen, Craig; Schaap, Marcel; Swetnam, Tyson L.; Troch, Peter A.

2013-06-01

among vegetation dynamics, pedogenesis, and topographic development affect the "critical zone"—the living filter for Earth's hydrologic, biogeochemical, and rock/sediment cycles. Assessing the importance of such feedbacks, which may be particularly pronounced in water-limited systems, remains a fundamental interdisciplinary challenge. The sky islands of southern Arizona offer an unusually well-defined natural experiment involving such feedbacks because mean annual precipitation varies by a factor of five over distances of approximately 10 km in areas of similar rock type (granite) and tectonic history. Here we compile high-resolution, spatially distributed data for Effective Energy and Mass Transfer (EEMT: the energy available to drive bedrock weathering), above-ground biomass, soil thickness, hillslope-scale topographic relief, and drainage density in two such mountain ranges (Santa Catalina: SCM; Pinaleño: PM). Strong correlations exist among vegetation-soil-topography variables, which vary nonlinearly with elevation, such that warm, dry, low-elevation portions of these ranges are characterized by relatively low above-ground biomass, thin soils, minimal soil organic matter, steep slopes, and high drainage densities; conversely, cooler, wetter, higher elevations have systematically higher biomass, thicker organic-rich soils, gentler slopes, and lower drainage densities. To test if eco-pedo-geomorphic feedbacks drive this pattern, we developed a landscape evolution model that couples pedogenesis and topographic development over geologic time scales, with rates explicitly dependent on vegetation density. The model self-organizes into states similar to those observed in SCM and PM. Our results highlight the potential importance of eco-pedo-geomorphic feedbacks, mediated by soil thickness, in water-limited systems.

Fuzzy distributed cooperative tracking for a swarm of unmanned aerial vehicles with heterogeneous goals

NASA Astrophysics Data System (ADS)

Kladis, Georgios P.; Menon, Prathyush P.; Edwards, Christopher

2016-12-01

This article proposes a systematic analysis for a tracking problem which ensures cooperation amongst a swarm of unmanned aerial vehicles (UAVs), modelled as nonlinear systems with linear and angular velocity constraints, in order to achieve different goals. A distributed Takagi-Sugeno (TS) framework design is adopted for the representation of the nonlinear model of the dynamics of the UAVs. The distributed control law which is introduced is composed of both node and network level information. Firstly, feedback gains are synthesised using a parallel distributed compensation (PDC) control law structure, for a collection of isolated UAVs; ignoring communications among the swarm. Then secondly, based on an alternation-like procedure, the resulting feedback gains are used to determine Lyapunov matrices which are utilised at network level to incorporate into the control law, the relative differences in the states of the vehicles, and to induce cooperative behaviour. Eventually stability is guaranteed for the entire swarm. The control synthesis is performed using tools from linear control theory: in particular the design criteria are posed as linear matrix inequalities (LMIs). An example based on a UAV tracking scenario is included to outline the efficacy of the approach.

Overexpression of human kynurenine-3-monooxygenase protects against 3-hydroxykynurenine-mediated apoptosis through bidirectional nonlinear feedback.

PubMed

Wilson, K; Auer, M; Binnie, M; Zheng, X; Pham, N T; Iredale, J P; Webster, S P; Mole, D J

2016-04-14

Kynurenine 3-monooxygenase (KMO) is a critical regulator of inflammation. The preferred KMO substrate, kynurenine, is converted to 3-hydroxykynurenine (3HK), and this product exhibits cytotoxicity through mechanisms that culminate in apoptosis. Here, we report that overexpression of human KMO with orthotopic localisation to mitochondria creates a metabolic environment during which the cell exhibits increased tolerance for exogenous 3HK-mediated cellular injury. Using the selective KMO inhibitor Ro61-8048, we show that KMO enzyme function is essential for cellular protection. Pan-caspase inhibition with Z-VAD-FMK confirmed apoptosis as the mode of cell death. By defining expression of pathway components upstream and downstream of KMO, we observed alterations in other key kynurenine pathway components, particularly tryptophan-2,3-dioxygenase upregulation, through bidirectional nonlinear feedback. KMO overexpression also increased expression of inducible nitric oxide synthase (iNOS). These changes in gene expression are functionally relevant, because siRNA knockdown of the pathway components kynureninase and quinolinate phosphoribosyl transferase caused cells to revert to a state of susceptibility to 3HK-mediated apoptosis. In summary, KMO overexpression, and importantly KMO activity, have metabolic repercussions that fundamentally affect resistance to cell stress.

Overexpression of human kynurenine-3-monooxygenase protects against 3-hydroxykynurenine-mediated apoptosis through bidirectional nonlinear feedback

PubMed Central

Wilson, K; Auer, M; Binnie, M; Zheng, X; Pham, N T; Iredale, J P; Webster, S P; Mole, D J

2016-01-01

Kynurenine 3-monooxygenase (KMO) is a critical regulator of inflammation. The preferred KMO substrate, kynurenine, is converted to 3-hydroxykynurenine (3HK), and this product exhibits cytotoxicity through mechanisms that culminate in apoptosis. Here, we report that overexpression of human KMO with orthotopic localisation to mitochondria creates a metabolic environment during which the cell exhibits increased tolerance for exogenous 3HK-mediated cellular injury. Using the selective KMO inhibitor Ro61-8048, we show that KMO enzyme function is essential for cellular protection. Pan-caspase inhibition with Z-VAD-FMK confirmed apoptosis as the mode of cell death. By defining expression of pathway components upstream and downstream of KMO, we observed alterations in other key kynurenine pathway components, particularly tryptophan-2,3-dioxygenase upregulation, through bidirectional nonlinear feedback. KMO overexpression also increased expression of inducible nitric oxide synthase (iNOS). These changes in gene expression are functionally relevant, because siRNA knockdown of the pathway components kynureninase and quinolinate phosphoribosyl transferase caused cells to revert to a state of susceptibility to 3HK-mediated apoptosis. In summary, KMO overexpression, and importantly KMO activity, have metabolic repercussions that fundamentally affect resistance to cell stress. PMID:27077813

Fibrous nonlinear elasticity enables positive mechanical feedback between cells and ECMs

PubMed Central

Hall, Matthew S.; Alisafaei, Farid; Ban, Ehsan; Feng, Xinzeng; Hui, Chung-Yuen; Shenoy, Vivek B.; Wu, Mingming

2016-01-01

In native states, animal cells of many types are supported by a fibrous network that forms the main structural component of the ECM. Mechanical interactions between cells and the 3D ECM critically regulate cell function, including growth and migration. However, the physical mechanism that governs the cell interaction with fibrous 3D ECM is still not known. In this article, we present single-cell traction force measurements using breast tumor cells embedded within 3D collagen matrices. We recreate the breast tumor mechanical environment by controlling the microstructure and density of type I collagen matrices. Our results reveal a positive mechanical feedback loop: cells pulling on collagen locally align and stiffen the matrix, and stiffer matrices, in return, promote greater cell force generation and a stiffer cell body. Furthermore, cell force transmission distance increases with the degree of strain-induced fiber alignment and stiffening of the collagen matrices. These findings highlight the importance of the nonlinear elasticity of fibrous matrices in regulating cell–ECM interactions within a 3D context, and the cell force regulation principle that we uncover may contribute to the rapid mechanical tissue stiffening occurring in many diseases, including cancer and fibrosis. PMID:27872289

Flatness-based embedded adaptive fuzzy control of turbocharged diesel engines

NASA Astrophysics Data System (ADS)

Rigatos, Gerasimos; Siano, Pierluigi; Arsie, Ivan

2014-10-01

In this paper nonlinear embedded control for turbocharged Diesel engines is developed with the use of Differential flatness theory and adaptive fuzzy control. It is shown that the dynamic model of the turbocharged Diesel engine is differentially flat and admits dynamic feedback linearization. It is also shown that the dynamic model can be written in the linear Brunovsky canonical form for which a state feedback controller can be easily designed. To compensate for modeling errors and external disturbances an adaptive fuzzy control scheme is implemanted making use of the transformed dynamical system of the diesel engine that is obtained through the application of differential flatness theory. Since only the system's output is measurable the complete state vector has to be reconstructed with the use of a state observer. It is shown that a suitable learning law can be defined for neuro-fuzzy approximators, which are part of the controller, so as to preserve the closed-loop system stability. With the use of Lyapunov stability analysis it is proven that the proposed observer-based adaptive fuzzy control scheme results in H∞ tracking performance.

Mathematical Modeling and Nonlinear Dynamical Analysis of Cell Growth in Response to Antibiotics

NASA Astrophysics Data System (ADS)

Jin, Suoqin; Niu, Lili; Wang, Gang; Zou, Xiufen

2015-06-01

This study is devoted to the revelation of the dynamical mechanisms of cell growth in response to antibiotics. We establish a mathematical model of ordinary differential equations for an antibiotic-resistant growth system with one positive feedback loop. We perform a dynamical analysis of the behavior of this model system. We present adequate sets of conditions that can guarantee the existence and stability of biologically-reasonable steady states. Using bifurcation analysis and numerical simulation, we show that the relative growth rate, which is defined as the ratio of the cell growth rate to the basal cell growth rate in the absence of antibiotics, can exhibit bistable behavior in an extensive range of parameters that correspond to a growth state and a nongrowth state in biology. We discover that both antibiotic and antibiotic resistance genes can cooperatively enhance bistability, whereas the cooperative coefficient of feedback can contribute to the onset of bistability. These results would contribute to a better understanding of not only the evolution of antibiotics but also the emergence of drug resistance in other diseases.

Nonlinear SVM-DTC for induction motor drive using input-output feedback linearization and high order sliding mode control.

PubMed

Ammar, Abdelkarim; Bourek, Amor; Benakcha, Abdelhamid

2017-03-01

This paper presents a nonlinear Direct Torque Control (DTC) strategy with Space Vector Modulation (SVM) for an induction motor. A nonlinear input-output feedback linearization (IOFL) is implemented to achieve a decoupled torque and flux control and the SVM is employed to reduce high torque and flux ripples. Furthermore, the control scheme performance is improved by inserting a super twisting speed controller in the outer loop and a load torque observer to enhance the speed regulation. The combining of dual nonlinear strategies ensures a good dynamic and robustness against parameters variation and disturbance. The system stability has been analyzed using Lyapunov stability theory. The effectiveness of the control algorithm is investigated by simulation and experimental validation using Matlab/Simulink software with real-time interface based on dSpace 1104. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

A semi-active H∞ control strategy with application to the vibration suppression of nonlinear high-rise building under earthquake excitations.

PubMed

Yan, Guiyun; Chen, Fuquan; Wu, Yingxiong

2016-01-01

Different from previous researches which mostly focused on linear response control of seismically excited high-rise buildings, this study aims to control nonlinear seismic response of high-rise buildings. To this end, a semi-active control strategy, in which H∞ control algorithm is used and magneto-rheological dampers are employed for an actuator, is presented to suppress the nonlinear vibration. In this strategy, a modified Kalman-Bucy observer which is suitable for the proposed semi-active strategy is developed to obtain the state vector from the measured semi-active control force and acceleration feedback, taking into account of the effects of nonlinearity, disturbance and uncertainty of controlled system parameters by the observed nonlinear accelerations. Then, the proposed semi-active H∞ control strategy is applied to the ASCE 20-story benchmark building when subjected to earthquake excitation and compared with the other control approaches by some control criteria. It is indicated that the proposed semi-active H∞ control strategy provides much better control performances by comparison with the semi-active MPC and Clipped-LQG control approaches, and can reduce nonlinear seismic response and minimize the damage in the buildings. Besides, it enhances the reliability of the control performance when compared with the active control strategy. Thus, the proposed semi-active H∞ control strategy is suitable for suppressing the nonlinear vibration of high-rise buildings.

Feedback control laws for highly maneuverable aircraft

NASA Technical Reports Server (NTRS)

Garrard, William L.; Balas, Gary J.

1992-01-01

The results of a study of the application of H infinity and mu synthesis techniques to the design of feedback control laws for the longitudinal dynamics of the High Angle of Attack Research Vehicle (HARV) are presented. The objective of this study is to develop methods for the design of feedback control laws which cause the closed loop longitudinal dynamics of the HARV to meet handling quality specifications over the entire flight envelope. Control law designs are based on models of the HARV linearized at various flight conditions. The control laws are evaluated by both linear and nonlinear simulations of typical maneuvers. The fixed gain control laws resulting from both the H infinity and mu synthesis techniques result in excellent performance even when the aircraft performs maneuvers in which the system states vary significantly from their equilibrium design values. Both the H infinity and mu synthesis control laws result in performance which compares favorably with an existing baseline longitudinal control law.

Nonlinear automatic landing control of unmanned aerial vehicles on moving platforms via a 3D laser radar

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hervas, Jaime Rubio; Tang, Hui; Reyhanoglu, Mahmut

2014-12-10

This paper presents a motion tracking and control system for automatically landing Unmanned Aerial Vehicles (UAVs) on an oscillating platform using Laser Radar (LADAR) observations. The system itself is assumed to be mounted on a ship deck. A full nonlinear mathematical model is first introduced for the UAV. The ship motion is characterized by a Fourier transform based method which includes a realistic characterization of the sea waves. LADAR observation models are introduced and an algorithm to process those observations for yielding the relative state between the vessel and the UAV is presented, from which the UAV's state relative tomore » an inertial frame can be obtained and used for feedback purposes. A sliding mode control algorithm is derived for tracking a landing trajectory defined by a set of desired waypoints. An extended Kalman filter (EKF) is proposed to account for process and observation noises in the design of a state estimator. The effectiveness of the control algorithm is illustrated through a simulation example.« less

Effects of CO2 Physiological Forcing on Amazon Climate

NASA Astrophysics Data System (ADS)

Halladay, K.; Good, P.; Kay, G.; Betts, R.

2014-12-01

Earth system models provide us with an opportunity to examine the complex interactions and feedbacks between land surface, vegetation and atmosphere. A more thorough understanding of these interactions is essential in reducing uncertainty surrounding the potential impacts of climate and environmental change on the future state and extent of the Amazon rainforest. This forest is a important resource for the region and globally in terms of ecosystem services, hydrology and biodiversity. We aim to investigate the effect of CO2 physiological forcing on the Amazon rainforest and its feedback on regional climate by using the CMIP5 idealised 1% CO2 simulations with a focus on HadGEM2-ES. In these simulations, the atmospheric CO2 concentration is increased by 1% per year for 140 years, reaching around 1150ppm at the end of the simulation. The use of idealised simulations allows the effect of CO2 to be separated from other forcings and the sensitivities to be quantified. In particular, it enables non-linear feedbacks to be identified. In addition to the fully coupled 1% CO2 simulation, in which all schemes respond to the forcing, we use simulations in which (a) only the biochemistry scheme sees the rising CO2 concentration, and (b) in which rising CO2 is only seen by the radiation scheme. With these simulations we examine the degree to which CO2 effects are additive or non-linear when in combination. We also show regional differences in climate and vegetation response, highlighting areas of increased sensitivity.

Stabilizing detached Bridgman melt crystal growth: Proportional-integral feedback control

NASA Astrophysics Data System (ADS)

Yeckel, Andrew; Daoutidis, Prodromos; Derby, Jeffrey J.

2012-10-01

The dynamics, operability limits, and tuning of a proportional-integral feedback controller to stabilize detached vertical Bridgman crystal growth are analyzed using a capillary model of shape stability. The manipulated variable is the pressure difference between upper and lower vapor spaces, and the controlled variable is the gap width at the triple-phase line. Open and closed loop dynamics of step changes in these state variables are analyzed under both shape stable and shape unstable growth conditions. Effects of step changes in static contact angle and growth angle are also studied. Proportional and proportional-integral control can stabilize unstable growth, but only within tight operability limits imposed by the narrow range of allowed meniscus shapes. These limits are used to establish safe operating ranges of controller gain. Strong nonlinearity of the capillary model restricts the range of perturbations that can be stabilized, and under some circumstances, stabilizes a spurious operating state far from the set point. Stabilizing detachment at low growth angle proves difficult and becomes impossible at zero growth angle.

Complex Nonlinear Dynamic System of Oligopolies Price Game with Heterogeneous Players Under Noise

NASA Astrophysics Data System (ADS)

Liu, Feng; Li, Yaguang

A nonlinear four oligopolies price game with heterogeneous players, that are boundedly rational and adaptive, is built using two different special demand costs. Based on the theory of complex discrete dynamical system, the stability and the existing equilibrium point are investigated. The complex dynamic behavior is presented via bifurcation diagrams, the Lyapunov exponents to show equilibrium state, bifurcation and chaos with the variation in parameters. As disturbance is ubiquitous in economic systems, this paper focuses on the analysis of delay feedback control method under noise circumstances. Stable dynamics is confirmed to depend mainly on the low price adjustment speed, and if all four players have limited opportunities to stabilize the market, the new adaptive player facing profits of scale are found to be higher than the incumbents of bounded rational.

Adaptive neural control for a class of nonlinear time-varying delay systems with unknown hysteresis.

PubMed

Liu, Zhi; Lai, Guanyu; Zhang, Yun; Chen, Xin; Chen, Chun Lung Philip

2014-12-01

This paper investigates the fusion of unknown direction hysteresis model with adaptive neural control techniques in face of time-delayed continuous time nonlinear systems without strict-feedback form. Compared with previous works on the hysteresis phenomenon, the direction of the modified Bouc-Wen hysteresis model investigated in the literature is unknown. To reduce the computation burden in adaptation mechanism, an optimized adaptation method is successfully applied to the control design. Based on the Lyapunov-Krasovskii method, two neural-network-based adaptive control algorithms are constructed to guarantee that all the system states and adaptive parameters remain bounded, and the tracking error converges to an adjustable neighborhood of the origin. In final, some numerical examples are provided to validate the effectiveness of the proposed control methods.

Computational alternatives to obtain time optimal jet engine control. M.S. Thesis

NASA Technical Reports Server (NTRS)

Basso, R. J.; Leake, R. J.

1976-01-01

Two computational methods to determine an open loop time optimal control sequence for a simple single spool turbojet engine are described by a set of nonlinear differential equations. Both methods are modifications of widely accepted algorithms which can solve fixed time unconstrained optimal control problems with a free right end. Constrained problems to be considered have fixed right ends and free time. Dynamic programming is defined on a standard problem and it yields a successive approximation solution to the time optimal problem of interest. A feedback control law is obtained and it is then used to determine the corresponding open loop control sequence. The Fletcher-Reeves conjugate gradient method has been selected for adaptation to solve a nonlinear optimal control problem with state variable and control constraints.

Commande de vol non lineaire d'un drone a voilure fixe par la methode du backstepping

NASA Astrophysics Data System (ADS)

Finoki, Edouard

This thesis describes the design of a non-linear controller for a UAV using the backstepping method. It is a fixed-wing UAV, the NexSTAR ARF from HobbicoRTM. The aim is to find the expressions of the aileron, the elevator, and the rudder deflection in order to command the flight path angle, the heading angle and the sideslip angle. Controlling the flight path angle allows a steady, climb or descent flight, controlling the heading cap allows to choose the heading and annul the sideslip angle allows an efficient flight. A good technical control has to ensure the stability of the system and provide optimal performances. Backstepping interlaces the choice of a Lyapunov function with the design of feedback control. This control technique works with the true non-linear model without any approximation. The procedure is to transform intermediate state variables into virtual inputs which will control other state variables. Advantages of this technique are its recursivity, its minimum control effort and its cascaded structure that allows dividing a high order system into several simpler lower order systems. To design this non-linear controller, a non-linear model of the UAV was used. Equations of motion are very accurate, aerodynamic coefficients result from interpolations between several essential variables in flight. The controller has been implemented in Matlab/Simulink and FlightGear.

A robust hybrid fuzzy-simulated annealing-intelligent water drops approach for tuning a distribution static compensator nonlinear controller in a distribution system

NASA Astrophysics Data System (ADS)

Bagheri Tolabi, Hajar; Hosseini, Rahil; Shakarami, Mahmoud Reza

2016-06-01

This article presents a novel hybrid optimization approach for a nonlinear controller of a distribution static compensator (DSTATCOM). The DSTATCOM is connected to a distribution system with the distributed generation units. The nonlinear control is based on partial feedback linearization. Two proportional-integral-derivative (PID) controllers regulate the voltage and track the output in this control system. In the conventional scheme, the trial-and-error method is used to determine the PID controller coefficients. This article uses a combination of a fuzzy system, simulated annealing (SA) and intelligent water drops (IWD) algorithms to optimize the parameters of the controllers. The obtained results reveal that the response of the optimized controlled system is effectively improved by finding a high-quality solution. The results confirm that using the tuning method based on the fuzzy-SA-IWD can significantly decrease the settling and rising times, the maximum overshoot and the steady-state error of the voltage step response of the DSTATCOM. The proposed hybrid tuning method for the partial feedback linearizing (PFL) controller achieved better regulation of the direct current voltage for the capacitor within the DSTATCOM. Furthermore, in the event of a fault the proposed controller tuned by the fuzzy-SA-IWD method showed better performance than the conventional controller or the PFL controller without optimization by the fuzzy-SA-IWD method with regard to both fault duration and clearing times.

A boundary PDE feedback control approach for the stabilization of mortgage price dynamics

NASA Astrophysics Data System (ADS)

Rigatos, G.; Siano, P.; Sarno, D.

2017-11-01

Several transactions taking place in financial markets are dependent on the pricing of mortgages (loans for the purchase of residences, land or farms). In this article, a method for stabilization of mortgage price dynamics is developed. It is considered that mortgage prices follow a PDE model which is equivalent to a multi-asset Black-Scholes PDE. Actually it is a diffusion process evolving in a 2D assets space, where the first asset is the house price and the second asset is the interest rate. By applying semi-discretization and a finite differences scheme this multi-asset PDE is transformed into a state-space model consisting of ordinary nonlinear differential equations. For the local subsystems, into which the mortgage PDE is decomposed, it becomes possible to apply boundary-based feedback control. The controller design proceeds by showing that the state-space model of the mortgage price PDE stands for a differentially flat system. Next, for each subsystem which is related to a nonlinear ODE, a virtual control input is computed, that can invert the subsystem's dynamics and can eliminate the subsystem's tracking error. From the last row of the state-space description, the control input (boundary condition) that is actually applied to the multi-factor mortgage price PDE system is found. This control input contains recursively all virtual control inputs which were computed for the individual ODE subsystems associated with the previous rows of the state-space equation. Thus, by tracing the rows of the state-space model backwards, at each iteration of the control algorithm, one can finally obtain the control input that should be applied to the mortgage price PDE system so as to assure that all its state variables will converge to the desirable setpoints. By showing the feasibility of such a control method it is also proven that through selected modification of the PDE boundary conditions the price of the mortgage can be made to converge and stabilize at specific reference values.

Constitutive modeling and control of 1D smart composite structures

NASA Astrophysics Data System (ADS)

Briggs, Jonathan P.; Ostrowski, James P.; Ponte-Castaneda, Pedro

1998-07-01

Homogenization techniques for determining effective properties of composite materials may provide advantages for control of stiffness and strain in systems using hysteretic smart actuators embedded in a soft matrix. In this paper, a homogenized model of a 1D composite structure comprised of shape memory alloys and a rubber-like matrix is presented. With proportional and proportional/integral feedback, using current as the input state and global strain as an error state, implementation scenarios include the use of tractions on the boundaries and a nonlinear constitutive law for the matrix. The result is a simple model which captures the nonlinear behavior of the smart composite material system and is amenable to experiments with various control paradigms. The success of this approach in the context of the 1D model suggests that the homogenization method may prove useful in investigating control of more general smart structures. Applications of such materials could include active rehabilitation aids, e.g. wrist braces, as well as swimming/undulating robots, or adaptive molds for manufacturing processes.

H∞ control for switched fuzzy systems via dynamic output feedback: Hybrid and switched approaches

NASA Astrophysics Data System (ADS)

Xiang, Weiming; Xiao, Jian; Iqbal, Muhammad Naveed

2013-06-01

Fuzzy T-S model has been proven to be a practical and effective way to deal with the analysis and synthesis problems for complex nonlinear systems. As for switched nonlinear system, describing its subsystems as fuzzy T-S models, namely switched fuzzy system, naturally is an alternative method to conventional control approaches. In this paper, the H∞ control problem for a class of switched fuzzy systems is addressed. Hybrid and switched design approaches are proposed with different availability of switching signal information at switching instant. The hybrid control strategy includes two parts: fuzzy controllers for subsystems and state updating controller at switching instant, and the switched control strategy contains the controllers for subsystems. It is demonstrated that the conservativeness is reduced by introducing the state updating behavior but its cost is an online prediction of switching signal. Numerical examples are given to illustrate the effectiveness of proposed approaches and compare the conservativeness of two approaches.

Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity.

PubMed

Oden, Jérémy; Lavrov, Roman; Chembo, Yanne K; Larger, Laurent

2017-11-01

We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity

NASA Astrophysics Data System (ADS)

Oden, Jérémy; Lavrov, Roman; Chembo, Yanne K.; Larger, Laurent

2017-11-01

We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

Investigation of a Nonlinear Control System

NASA Technical Reports Server (NTRS)

Flugge-Lotz, I; Taylor, C F; Lindberg, H E

1958-01-01

A discontinuous variation of coefficients of the differential equation describing the linear control system before nonlinear elements are added is studied in detail. The nonlinear feedback is applied to a second-order system. Simulation techniques are used to study performance of the nonlinear control system and to compare it with the linear system for a wide variety of inputs. A detailed quantitative study of the influence of relay delays and of a transport delay is presented.

Dynamic output feedback control of a flexible air-breathing hypersonic vehicle via T-S fuzzy approach

NASA Astrophysics Data System (ADS)

Hu, Xiaoxiang; Wu, Ligang; Hu, Changhua; Wang, Zhaoqiang; Gao, Huijun

2014-08-01

By utilising Takagi-Sugeno (T-S) fuzzy set approach, this paper addresses the robust H∞ dynamic output feedback control for the non-linear longitudinal model of flexible air-breathing hypersonic vehicles (FAHVs). The flight control of FAHVs is highly challenging due to the unique dynamic characteristics, and the intricate couplings between the engine and fight dynamics and external disturbance. Because of the dynamics' enormous complexity, currently, only the longitudinal dynamics models of FAHVs have been used for controller design. In this work, T-S fuzzy modelling technique is utilised to approach the non-linear dynamics of FAHVs, then a fuzzy model is developed for the output tracking problem of FAHVs. The fuzzy model contains parameter uncertainties and disturbance, which can approach the non-linear dynamics of FAHVs more exactly. The flexible models of FAHVs are difficult to measure because of the complex dynamics and the strong couplings, thus a full-order dynamic output feedback controller is designed for the fuzzy model. A robust H∞ controller is designed for the obtained closed-loop system. By utilising the Lyapunov functional approach, sufficient solvability conditions for such controllers are established in terms of linear matrix inequalities. Finally, the effectiveness of the proposed T-S fuzzy dynamic output feedback control method is demonstrated by numerical simulations.

Feedforward-Feedback Hybrid Control for Magnetic Shape Memory Alloy Actuators Based on the Krasnosel'skii-Pokrovskii Model

PubMed Central

Zhou, Miaolei; Zhang, Qi; Wang, Jingyuan

2014-01-01

As a new type of smart material, magnetic shape memory alloy has the advantages of a fast response frequency and outstanding strain capability in the field of microdrive and microposition actuators. The hysteresis nonlinearity in magnetic shape memory alloy actuators, however, limits system performance and further application. Here we propose a feedforward-feedback hybrid control method to improve control precision and mitigate the effects of the hysteresis nonlinearity of magnetic shape memory alloy actuators. First, hysteresis nonlinearity compensation for the magnetic shape memory alloy actuator is implemented by establishing a feedforward controller which is an inverse hysteresis model based on Krasnosel'skii-Pokrovskii operator. Secondly, the paper employs the classical Proportion Integration Differentiation feedback control with feedforward control to comprise the hybrid control system, and for further enhancing the adaptive performance of the system and improving the control accuracy, the Radial Basis Function neural network self-tuning Proportion Integration Differentiation feedback control replaces the classical Proportion Integration Differentiation feedback control. Utilizing self-learning ability of the Radial Basis Function neural network obtains Jacobian information of magnetic shape memory alloy actuator for the on-line adjustment of parameters in Proportion Integration Differentiation controller. Finally, simulation results show that the hybrid control method proposed in this paper can greatly improve the control precision of magnetic shape memory alloy actuator and the maximum tracking error is reduced from 1.1% in the open-loop system to 0.43% in the hybrid control system. PMID:24828010

Feedforward-feedback hybrid control for magnetic shape memory alloy actuators based on the Krasnosel'skii-Pokrovskii model.

PubMed

Zhou, Miaolei; Zhang, Qi; Wang, Jingyuan

2014-01-01

As a new type of smart material, magnetic shape memory alloy has the advantages of a fast response frequency and outstanding strain capability in the field of microdrive and microposition actuators. The hysteresis nonlinearity in magnetic shape memory alloy actuators, however, limits system performance and further application. Here we propose a feedforward-feedback hybrid control method to improve control precision and mitigate the effects of the hysteresis nonlinearity of magnetic shape memory alloy actuators. First, hysteresis nonlinearity compensation for the magnetic shape memory alloy actuator is implemented by establishing a feedforward controller which is an inverse hysteresis model based on Krasnosel'skii-Pokrovskii operator. Secondly, the paper employs the classical Proportion Integration Differentiation feedback control with feedforward control to comprise the hybrid control system, and for further enhancing the adaptive performance of the system and improving the control accuracy, the Radial Basis Function neural network self-tuning Proportion Integration Differentiation feedback control replaces the classical Proportion Integration Differentiation feedback control. Utilizing self-learning ability of the Radial Basis Function neural network obtains Jacobian information of magnetic shape memory alloy actuator for the on-line adjustment of parameters in Proportion Integration Differentiation controller. Finally, simulation results show that the hybrid control method proposed in this paper can greatly improve the control precision of magnetic shape memory alloy actuator and the maximum tracking error is reduced from 1.1% in the open-loop system to 0.43% in the hybrid control system.

Dynamics of the Coupled Human-climate System Resulting from Closed-loop Control of Solar Geoengineering

DOE Office of Scientific and Technical Information (OSTI.GOV)

MacMartin, Douglas; Kravitz, Benjamin S.; Keith, David

2014-07-08

If solar radiation management (SRM) were ever implemented, feedback of the observed climate state might be used to adjust the radiative forcing of SRM, in order to compensate for uncertainty in either the forcing or the climate response; this would also compensate for unexpected changes in the system, e.g. a nonlinear change in climate sensitivity. This feedback creates an emergent coupled human-climate system, with entirely new dynamics. In addition to the intended response to greenhouse-gas induced changes, the use of feedback would also result in a geoengineering response to natural climate variability. We use a simple box-diffusion dynamic model tomore » understand how changing feedback-control parameters and time delay affect the behavior of this coupled natural-human system, and verify these predictions using the HadCM3L general circulation model. In particular, some amplification of natural variability is unavoidable; any time delay (e.g., to average out natural variability, or due to decision-making) exacerbates this amplification, with oscillatory behavior possible if there is a desire for rapid correction (high feedback gain), but a delayed response needed for decision making. Conversely, the need for feedback to compensate for uncertainty, combined with a desire to avoid excessive amplification, results in a limit on how rapidly SRM could respond to uncertain changes.« less

The Trade-Off Mechanism in Mammalian Circadian Clock Model with Two Time Delays

NASA Astrophysics Data System (ADS)

Yan, Jie; Kang, Xiaxia; Yang, Ling

Circadian clock is an autonomous oscillator which orchestrates the daily rhythms of physiology and behaviors. This study is devoted to explore how a positive feedback loop affects the dynamics of mammalian circadian clock. We simplify an experimentally validated mathematical model in our previous work, to a nonlinear differential equation with two time delays. This simplified mathematical model incorporates the pacemaker of mammalian circadian clock, a negative primary feedback loop, and a critical positive auxiliary feedback loop, Rev-erbα/Cry1 loop. We perform analytical studies of the system. Delay-dependent conditions for the asymptotic stability of the nontrivial positive steady state of the model are investigated. We also prove the existence of Hopf bifurcation, which leads to self-sustained oscillation of mammalian circadian clock. Our theoretical analyses show that the oscillatory regime is reduced upon the participation of the delayed positive auxiliary loop. However, further simulations reveal that the auxiliary loop can enable the circadian clock gain widely adjustable amplitudes and robust period. Thus, the positive auxiliary feedback loop may provide a trade-off mechanism, to use the small loss in the robustness of oscillation in exchange for adaptable flexibility in mammalian circadian clock. The results obtained from the model may gain new insights into the dynamics of biological oscillators with interlocked feedback loops.

Shaping Microwave Fields Using Nonlinear Unsolicited Feedback: Application to Enhance Energy Harvesting

NASA Astrophysics Data System (ADS)

del Hougne, Philipp; Fink, Mathias; Lerosey, Geoffroy

2017-12-01

Wave-front shaping has emerged over the past decade as a powerful tool to control wave propagation through complex media, initially in optics and more recently also in the microwave domain with important applications in telecommunication, imaging, and energy transfer. The crux of implementing wave-front shaping concepts in real life is often its need for (direct) feedback, requiring access to the target to focus on. Here, we present the shaping of a microwave field based on indirect, unsolicited, and blind feedback which may be the pivotal step towards practical implementations. With the example of a radio-frequency harvester in a metallic cavity, we demonstrate tenfold enhancement of the harvested power by wave-front shaping based on nonlinear signals detected at an arbitrary position away from the harvesting device.

Structural Properties and Estimation of Delay Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Kwong, R. H. S.

1975-01-01

Two areas in the theory of delay systems were studied: structural properties and their applications to feedback control, and optimal linear and nonlinear estimation. The concepts of controllability, stabilizability, observability, and detectability were investigated. The property of pointwise degeneracy of linear time-invariant delay systems is considered. Necessary and sufficient conditions for three dimensional linear systems to be made pointwise degenerate by delay feedback were obtained, while sufficient conditions for this to be possible are given for higher dimensional linear systems. These results were applied to obtain solvability conditions for the minimum time output zeroing control problem by delay feedback. A representation theorem is given for conditional moment functionals of general nonlinear stochastic delay systems, and stochastic differential equations are derived for conditional moment functionals satisfying certain smoothness properties.

A Simple Attitude Control of Quadrotor Helicopter Based on Ziegler-Nichols Rules for Tuning PD Parameters

PubMed Central

He, ZeFang

2014-01-01

An attitude control strategy based on Ziegler-Nichols rules for tuning PD (proportional-derivative) parameters of quadrotor helicopters is presented to solve the problem that quadrotor tends to be instable. This problem is caused by the narrow definition domain of attitude angles of quadrotor helicopters. The proposed controller is nonlinear and consists of a linear part and a nonlinear part. The linear part is a PD controller with PD parameters tuned by Ziegler-Nichols rules and acts on the quadrotor decoupled linear system after feedback linearization; the nonlinear part is a feedback linearization item which converts a nonlinear system into a linear system. It can be seen from the simulation results that the attitude controller proposed in this paper is highly robust, and its control effect is better than the other two nonlinear controllers. The nonlinear parts of the other two nonlinear controllers are the same as the attitude controller proposed in this paper. The linear part involves a PID (proportional-integral-derivative) controller with the PID controller parameters tuned by Ziegler-Nichols rules and a PD controller with the PD controller parameters tuned by GA (genetic algorithms). Moreover, this attitude controller is simple and easy to implement. PMID:25614879

Multi-Window Controllers for Autonomous Space Systems

NASA Technical Reports Server (NTRS)

Lurie, B, J.; Hadaegh, F. Y.

1997-01-01

Multi-window controllers select between elementary linear controllers using nonlinear windows based on the amplitude and frequency content of the feedback error. The controllers are relatively simple to implement and perform much better than linear controllers. The commanders for such controllers only order the destination point and are freed from generating the command time-profiles. The robotic missions rely heavily on the tasks of acquisition and tracking. For autonomous and optimal control of the spacecraft, the control bandwidth must be larger while the feedback can (and, therefore, must) be reduced.. Combining linear compensators via multi-window nonlinear summer guarantees minimum phase character of the combined transfer function. It is shown that the solution may require using several parallel branches and windows. Several examples of multi-window nonlinear controller applications are presented.

Stimulated Brillouin scattering in ultra-long distributed feedback Bragg gratings in standard optical fiber.

PubMed

Loranger, Sébastien; Lambin-Iezzi, Victor; Wahbeh, Mamoun; Kashyap, Raman

2016-04-15

Distributed feedback (DFB) fiber Bragg gratings (FBG) are widely used as narrow-band filters and single-mode cavities for lasers. Recently, a nonlinear generation has been shown in 10-20 cm DFB gratings in a highly nonlinear fiber. First, we show in this Letter a novel fabrication technique of ultra-long DFBs in a standard fiber (SMF-28). Second, we demonstrate nonlinear generation in such gratings. A particular inscription technique was used to fabricate all-in-phase ultra-long FBG and to implement reproducible phase shift to form a DFB mode. We demonstrate stimulated Brillouin scattering (SBS) emission from this DFB mode and characterize the resulting laser. It seems that such a SBS based DFB laser stabilizes a pump's jittering and reduces its linewidth.

Efferent feedback can explain many hearing phenomena

NASA Astrophysics Data System (ADS)

Holmes, W. Harvey; Flax, Matthew R.

2015-12-01

The mixed mode cochlear amplifier (MMCA) model was presented at the last Mechanics of Hearing workshop [4]. The MMCA consists principally of a nonlinear feedback loop formed when an efferent-controlled outer hair cell (OHC) is combined with the cochlear mechanics and the rest of the relevant neurobiology. Essential elements of this model are efferent control of the OHC motility and a delay in the feedback to the OHC. The input to the MMCA is the passive travelling wave. In the MMCA amplification is localized where both the neural and tuned mechanical systems meet in the Organ of Corti (OoC). The simplest model based on this idea is a nonlinear delay line resonator (DLR), which is mathematically described by a nonlinear delay-differential equation (DDE). This model predicts possible Hopf bifurcations and exhibits its most interesting behaviour when operating near a bifurcation. This contribution presents some simulation results using the DLR model. These show that various observed hearing phenomena can be accounted for by this model, at least qualitatively, including compression effects, two-tone suppression and some forms of otoacoustic emissions (OAEs).

Generation of “gigantic” ultra-short microwave pulses based on passive mode-locking effect in electron oscillators with saturable absorber in the feedback loop

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ginzburg, N. S., E-mail: ginzburg@appl.sci-nnov.ru; Denisov, G. G.; Vilkov, M. N.

2016-05-15

A periodic train of powerful ultrashort microwave pulses can be generated in electron oscillators with a non-linear saturable absorber installed in the feedback loop. This method of pulse formation resembles the passive mode-locking widely used in laser physics. Nevertheless, there is a specific feature in the mechanism of pulse amplification when consecutive energy extraction from different fractions of a stationary electron beam takes place due to pulse slippage over the beam caused by the difference between the wave group velocity and the electron axial velocity. As a result, the peak power of generated “gigantic” pulses can exceed not only themore » level of steady-state generation but also, in the optimal case, the power of the driving electron beam.« less

General theory of feedback control of a nuclear spin ensemble in quantum dots

NASA Astrophysics Data System (ADS)

Yang, Wen; Sham, L. J.

2013-12-01

We present a microscopic theory of the nonequilibrium nuclear spin dynamics driven by the electron and/or hole under continuous-wave pumping in a quantum dot. We show the correlated dynamics of the nuclear spin ensemble and the electron and/or hole under optical excitation as a quantum feedback loop and investigate the dynamics of the many nuclear spins as a nonlinear collective motion. This gives rise to three observable effects: (i) hysteresis, (ii) locking (avoidance) of the pump absorption strength to (from) the natural resonance, and (iii) suppression (amplification) of the fluctuation of weakly polarized nuclear spins, leading to prolonged (shortened) electron-spin coherence time. A single nonlinear feedback function is constructed which determines the different outcomes of the three effects listed above depending on the feedback being negative or positive. The general theory also helps to put in perspective the wide range of existing theories on the problem of a single electron spin in a nuclear spin bath.

Chaotic oscillations and noise transformations in a simple dissipative system with delayed feedback

NASA Astrophysics Data System (ADS)

Zverev, V. V.; Rubinstein, B. Ya.

1991-04-01

We analyze the statistical behavior of signals in nonlinear circuits with delayed feedback in the presence of external Markovian noise. For the special class of circuits with intense phase mixing we develop an approach for the computation of the probability distributions and multitime correlation functions based on the random phase approximation. Both Gaussian and Kubo-Andersen models of external noise statistics are analyzed and the existence of the stationary (asymptotic) random process in the long-time limit is shown. We demonstrate that a nonlinear system with chaotic behavior becomes a noise amplifier with specific statistical transformation properties.

Application of the MNA design method to a nonlinear turbofan engine. [multivariable Nyquist array method

NASA Technical Reports Server (NTRS)

Leininger, G. G.

1981-01-01

Using nonlinear digital simulation as a representative model of the dynamic operation of the QCSEE turbofan engine, a feedback control system is designed by variable frequency design techniques. Transfer functions are generated for each of five power level settings covering the range of operation from approach power to full throttle (62.5% to 100% full power). These transfer functions are then used by an interactive control system design synthesis program to provide a closed loop feedback control using the multivariable Nyquist array and extensions to multivariable Bode diagrams and Nichols charts.

Alternatives for jet engine control

NASA Technical Reports Server (NTRS)

Sain, M. K.

1981-01-01

Research centered on basic topics in the modeling and feedback control of nonlinear dynamical systems is reported. Of special interest were the following topics: (1) the role of series descriptions, especially insofar as they relate to questions of scheduling, in the control of gas turbine engines; (2) the use of algebraic tensor theory as a technique for parameterizing such descriptions; (3) the relationship between tensor methodology and other parts of the nonlinear literature; (4) the improvement of interactive methods for parameter selection within a tensor viewpoint; and (5) study of feedback gain representation as a counterpart to these modeling and parameterization ideas.

Finite-Time Adaptive Control for a Class of Nonlinear Systems With Nonstrict Feedback Structure.

PubMed

Sun, Yumei; Chen, Bing; Lin, Chong; Wang, Honghong

2017-09-18

This paper focuses on finite-time adaptive neural tracking control for nonlinear systems in nonstrict feedback form. A semiglobal finite-time practical stability criterion is first proposed. Correspondingly, the finite-time adaptive neural control strategy is given by using this criterion. Unlike the existing results on adaptive neural/fuzzy control, the proposed adaptive neural controller guarantees that the tracking error converges to a sufficiently small domain around the origin in finite time, and other closed-loop signals are bounded. At last, two examples are used to test the validity of our results.

The Physical Origin of Long Gas Depletion Times in Galaxies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Semenov, Vadim A.; Kravtsov, Andrey V.; Gnedin, Nickolay Y.

2017-08-18

We present a model that elucidates why gas depletion times in galaxies are long compared to the time scales of the processes driving the evolution of the interstellar medium. We show that global depletion times are not set by any "bottleneck" in the process of gas evolution towards the star-forming state. Instead, depletion times are long because star-forming gas converts only a small fraction of its mass into stars before it is dispersed by dynamical and feedback processes. Thus, complete depletion requires that gas transitions between star-forming and non-star-forming states multiple times. Our model does not rely on the assumption of equilibrium and can be used to interpret trends of depletion times with the properties of observed galaxies and the parameters of star formation and feedback recipes in galaxy simulations. In particular, the model explains the mechanism by which feedback self-regulates star formation rate in simulations and makes it insensitive to the local star formation efficiency. We illustrate our model using the results of an isolatedmore » $$L_*$$-sized disk galaxy simulation that reproduces the observed Kennicutt-Schmidt relation for both molecular and atomic gas. Interestingly, the relation for molecular gas is close to linear on kiloparsec scales, even though a non-linear relation is adopted in simulation cells. This difference is due to stellar feedback, which breaks the self-similar scaling of the gas density PDF with the average gas surface density.« less

Adaptive critic designs for optimal control of uncertain nonlinear systems with unmatched interconnections.

PubMed

Yang, Xiong; He, Haibo

2018-05-26

In this paper, we develop a novel optimal control strategy for a class of uncertain nonlinear systems with unmatched interconnections. To begin with, we present a stabilizing feedback controller for the interconnected nonlinear systems by modifying an array of optimal control laws of auxiliary subsystems. We also prove that this feedback controller ensures a specified cost function to achieve optimality. Then, under the framework of adaptive critic designs, we use critic networks to solve the Hamilton-Jacobi-Bellman equations associated with auxiliary subsystem optimal control laws. The critic network weights are tuned through the gradient descent method combined with an additional stabilizing term. By using the newly established weight tuning rules, we no longer need the initial admissible control condition. In addition, we demonstrate that all signals in the closed-loop auxiliary subsystems are stable in the sense of uniform ultimate boundedness by using classic Lyapunov techniques. Finally, we provide an interconnected nonlinear plant to validate the present control scheme. Copyright © 2018 Elsevier Ltd. All rights reserved.

Analysis and design of gain scheduled control systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Shamma, Jeff S.

1988-01-01

Gain scheduling, as an idea, is to construct a global feedback control system for a time varying and/or nonlinear plant from a collection of local time invariant designs. However in the absence of a sound analysis, these designs come with no guarantees on the robustness, performance, or even nominal stability of the overall gain schedule design. Such an analysis is presented for three types of gain scheduling situations: (1) a linear parameter varying plant scheduling on its exogenous parameters, (2) a nonlinear plant scheduling on a prescribed reference trajectory, and (3) a nonlinear plant scheduling on the current plant output. Conditions are given which guarantee that the stability, robustness, and performance properties of the fixed operating point designs carry over to the global gain scheduled designs, such as the scheduling variable should vary slowly and capture the plants nonlinearities. Finally, an alternate design framework is proposed which removes the slowing varying restriction or gain scheduled systems. This framework addresses some fundamental feedback issues previously ignored in standard gain.

Steady-state bumpless transfer under controller uncertainty using the state/output feedback topology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zheng, K.; Lee, A.H.; Bentsman, J.

2006-01-15

Linear quadratic (LQ) bumpless transfer design introduced recently by Turner and Walker gives a very convenient and straightforward computational procedure for the steady-state bumpless transfer operator synthesis. It is, however, found to be incapable of providing convergence of the output of the offline controller to that of the online controller in several industrial applications, producing bumps in the plant output in the wake of controller transfer. An examination of this phenomenon reveals that the applications in question are characterized by a significant mismatch, further referred to as controller uncertainty, between the dynamics of the implemented controllers and their models usedmore » in the transfer operator computation. To address this problem, while retaining the convenience of the Turner and Walker design, a novel state/output feedback bumpless transfer topology is introduced that employs the nominal state of the offline controller and, through the use of an additional controller/model mismatch compensator, also the offline controller output. A corresponding steady-state bumpless transfer design procedure along with the supporting theory is developed for a large class of systems. Due to these features, it is demonstrated to solve a long-standing problem of high-quality steady-state bumpless transfer from the industry standard low-order nonlinear multiloop PID-based controllers to the modern multiinput-multioutput (MIMO) robust controllers in the megawatt/throttle pressure control of a typical coal-fired boiler/turbine unit.« less

Division by zero, pseudo-division by zero, Zhang dynamics method and Zhang-gradient method about control singularity conquering

NASA Astrophysics Data System (ADS)

Zhang, Yunong; Zhang, Yinyan; Chen, Dechao; Xiao, Zhengli; Yan, Xiaogang

2017-01-01

In this paper, the division-by-zero (DBO) problem in the field of nonlinear control, which is traditionally termed the control singularity problem (or specifically, controller singularity problem), is investigated by the Zhang dynamics (ZD) method and the Zhang-gradient (ZG) method. According to the impact of the DBO problem on the state variables of the controlled nonlinear system, the concepts of the pseudo-DBO problem and the true-DBO problem are proposed in this paper, which provide a new perspective for the researchers on the DBO problems as well as nonlinear control systems. Besides, the two classes of DBO problems are solved under the framework of the ZG method. Specific examples are shown and investigated in this paper to illustrate the two proposed concepts and the efficacy of the ZG method in conquering pseudo-DBO and true-DBO problems. The application of the ZG method to the tracking control of a two-wheeled mobile robot further substantiates the effectiveness of the ZG method. In addition, the ZG method is successfully applied to the tracking control of a pure-feedback nonlinear system.

Neural Networks for Rapid Design and Analysis

NASA Technical Reports Server (NTRS)

Sparks, Dean W., Jr.; Maghami, Peiman G.

1998-01-01

Artificial neural networks have been employed for rapid and efficient dynamics and control analysis of flexible systems. Specifically, feedforward neural networks are designed to approximate nonlinear dynamic components over prescribed input ranges, and are used in simulations as a means to speed up the overall time response analysis process. To capture the recursive nature of dynamic components with artificial neural networks, recurrent networks, which use state feedback with the appropriate number of time delays, as inputs to the networks, are employed. Once properly trained, neural networks can give very good approximations to nonlinear dynamic components, and by their judicious use in simulations, allow the analyst the potential to speed up the analysis process considerably. To illustrate this potential speed up, an existing simulation model of a spacecraft reaction wheel system is executed, first conventionally, and then with an artificial neural network in place.

Design Of Combined Stochastic Feedforward/Feedback Control

NASA Technical Reports Server (NTRS)

Halyo, Nesim

1989-01-01

Methodology accommodates variety of control structures and design techniques. In methodology for combined stochastic feedforward/feedback control, main objectives of feedforward and feedback control laws seen clearly. Inclusion of error-integral feedback, dynamic compensation, rate-command control structure, and like integral element of methodology. Another advantage of methodology flexibility to develop variety of techniques for design of feedback control with arbitrary structures to obtain feedback controller: includes stochastic output feedback, multiconfiguration control, decentralized control, or frequency and classical control methods. Control modes of system include capture and tracking of localizer and glideslope, crab, decrab, and flare. By use of recommended incremental implementation, control laws simulated on digital computer and connected with nonlinear digital simulation of aircraft and its systems.

A minimal mathematical model combining several regulatory cycles from the budding yeast cell cycle.

PubMed

Sriram, K; Bernot, G; Képès, F

2007-11-01

A novel topology of regulatory networks abstracted from the budding yeast cell cycle is studied by constructing a simple nonlinear model. A ternary positive feedback loop with only positive regulations is constructed with elements that activates the subsequent element in a clockwise fashion. A ternary negative feedback loop with only negative regulations is constructed with the elements that inhibit the subsequent element in an anticlockwise fashion. Positive feedback loop exhibits bistability, whereas the negative feedback loop exhibits limit cycle oscillations. The novelty of the topology is that the corresponding elements in these two homogeneous feedback loops are linked by the binary positive feedback loops with only positive regulations. This results in the emergence of mixed feedback loops in the network that displays complex behaviour like the coexistence of multiple steady states, relaxation oscillations and chaos. Importantly, the arrangement of the feedback loops brings in the notion of checkpoint in the model. The model also exhibits domino-like behaviour, where the limit cycle oscillations take place in a stepwise fashion. As the aforementioned topology is abstracted from the budding yeast cell cycle, the events that govern the cell cycle are considered for the present study. In budding yeast, the sequential activation of the transcription factors, cyclins and their inhibitors form mixed feedback loops. The transcription factors that involve in the positive regulation in a clockwise orientation generates ternary positive feedback loop, while the cyclins and their inhibitors that involve in the negative regulation in an anticlockwise orientation generates ternary negative feedback loop. The mutual regulation between the corresponding elements in the transcription factors and the cyclins and their inhibitors generates binary positive feedback loops. The bifurcation diagram constructed for the whole system can be related to the different events of the cell cycle in terms of dynamical system theory. The checkpoint mechanism that plays an important role in different phases of the cell cycle are accounted for by silencing appropriate feedback loops in the model.

Passivity-Based Control for Two-Wheeled Robot Stabilization

NASA Astrophysics Data System (ADS)

Uddin, Nur; Aryo Nugroho, Teguh; Agung Pramudito, Wahyu

2018-04-01

A passivity-based control system design for two-wheeled robot (TWR) stabilization is presented. A TWR is a statically-unstable non-linear system. A control system is applied to actively stabilize the TWR. Passivity-based control method is applied to design the control system. The design results in a state feedback control law that makes the TWR closed loop system globally asymptotically stable (GAS). The GAS is proven mathematically. The TWR stabilization is demonstrated through computer simulation. The simulation results show that the designed control system is able to stabilize the TWR.

Revival of oscillations from deaths in diffusively coupled nonlinear systems: Theory and experiment

NASA Astrophysics Data System (ADS)

Zou, Wei; Sebek, Michael; Kiss, István Z.; Kurths, Jürgen

2017-06-01

Amplitude death (AD) and oscillation death (OD) are two structurally different oscillation quenching phenomena in coupled nonlinear systems. As a reverse issue of AD and OD, revival of oscillations from deaths attracts an increasing attention recently. In this paper, we clearly disclose that a time delay in the self-feedback component of the coupling destabilizes not only AD but also OD, and even the AD to OD transition in paradigmatic models of coupled Stuart-Landau oscillators under diverse death configurations. Using a rigorous analysis, the effectiveness of this self-feedback delay in revoking AD is theoretically proved to be valid in an arbitrary network of coupled Stuart-Landau oscillators with generally distributed propagation delays. Moreover, the role of self-feedback delay in reviving oscillations from AD is experimentally verified in two delay-coupled electrochemical reactions.

Revival of oscillations from deaths in diffusively coupled nonlinear systems: Theory and experiment.

PubMed

Zou, Wei; Sebek, Michael; Kiss, István Z; Kurths, Jürgen

2017-06-01

Amplitude death (AD) and oscillation death (OD) are two structurally different oscillation quenching phenomena in coupled nonlinear systems. As a reverse issue of AD and OD, revival of oscillations from deaths attracts an increasing attention recently. In this paper, we clearly disclose that a time delay in the self-feedback component of the coupling destabilizes not only AD but also OD, and even the AD to OD transition in paradigmatic models of coupled Stuart-Landau oscillators under diverse death configurations. Using a rigorous analysis, the effectiveness of this self-feedback delay in revoking AD is theoretically proved to be valid in an arbitrary network of coupled Stuart-Landau oscillators with generally distributed propagation delays. Moreover, the role of self-feedback delay in reviving oscillations from AD is experimentally verified in two delay-coupled electrochemical reactions.

Sensorless H∞ speed-tracking synthesis for surface-mount permanent magnet synchronous motor.

PubMed

Ramírez-Villalobos, Ramón; Aguilar, Luis T; Coria, Luis N

2017-03-01

In this paper, a sensorless speed tracking control is proposed for a surface-mount permanent magnet synchronous motor by using a nonlinear H ∞ -controller via stator currents measurements for feedback. An output feedback nonlinear H ∞ -controller was designed such that the undisturbed system is uniformly asymptotically stable around the desired speed reference, while also the effects of external vanishing and non-vanishing disturbances, noise, and input backlash were attenuated locally. The rotor position was calculated from the causal dynamic output feedback compensator and from the desired speed reference. The existence of the proper solutions of the perturbed differential Riccati equations ensures stabilizability and detectability of the control system. The efficiency of the proposed sensorless controller was supported by numerical simulations. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Stability of uncertain systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Blankenship, G. L.

1971-01-01

The asymptotic properties of feedback systems are discussed, containing uncertain parameters and subjected to stochastic perturbations. The approach is functional analytic in flavor and thereby avoids the use of Markov techniques and auxiliary Lyapunov functionals characteristic of the existing work in this area. The results are given for the probability distributions of the accessible signals in the system and are proved using the Prohorov theory of the convergence of measures. For general nonlinear systems, a result similar to the small loop-gain theorem of deterministic stability theory is given. Boundedness is a property of the induced distributions of the signals and not the usual notion of boundedness in norm. For the special class of feedback systems formed by the cascade of a white noise, a sector nonlinearity and convolution operator conditions are given to insure the total boundedness of the overall feedback system.

Output feedback control of a quadrotor UAV using neural networks.

PubMed

Dierks, Travis; Jagannathan, Sarangapani

2010-01-01

In this paper, a new nonlinear controller for a quadrotor unmanned aerial vehicle (UAV) is proposed using neural networks (NNs) and output feedback. The assumption on the availability of UAV dynamics is not always practical, especially in an outdoor environment. Therefore, in this work, an NN is introduced to learn the complete dynamics of the UAV online, including uncertain nonlinear terms like aerodynamic friction and blade flapping. Although a quadrotor UAV is underactuated, a novel NN virtual control input scheme is proposed which allows all six degrees of freedom (DOF) of the UAV to be controlled using only four control inputs. Furthermore, an NN observer is introduced to estimate the translational and angular velocities of the UAV, and an output feedback control law is developed in which only the position and the attitude of the UAV are considered measurable. It is shown using Lyapunov theory that the position, orientation, and velocity tracking errors, the virtual control and observer estimation errors, and the NN weight estimation errors for each NN are all semiglobally uniformly ultimately bounded (SGUUB) in the presence of bounded disturbances and NN functional reconstruction errors while simultaneously relaxing the separation principle. The effectiveness of proposed output feedback control scheme is then demonstrated in the presence of unknown nonlinear dynamics and disturbances, and simulation results are included to demonstrate the theoretical conjecture.

Optimal estimation and scheduling in aquifer management using the rapid feedback control method

NASA Astrophysics Data System (ADS)

Ghorbanidehno, Hojat; Kokkinaki, Amalia; Kitanidis, Peter K.; Darve, Eric

2017-12-01

Management of water resources systems often involves a large number of parameters, as in the case of large, spatially heterogeneous aquifers, and a large number of "noisy" observations, as in the case of pressure observation in wells. Optimizing the operation of such systems requires both searching among many possible solutions and utilizing new information as it becomes available. However, the computational cost of this task increases rapidly with the size of the problem to the extent that textbook optimization methods are practically impossible to apply. In this paper, we present a new computationally efficient technique as a practical alternative for optimally operating large-scale dynamical systems. The proposed method, which we term Rapid Feedback Controller (RFC), provides a practical approach for combined monitoring, parameter estimation, uncertainty quantification, and optimal control for linear and nonlinear systems with a quadratic cost function. For illustration, we consider the case of a weakly nonlinear uncertain dynamical system with a quadratic objective function, specifically a two-dimensional heterogeneous aquifer management problem. To validate our method, we compare our results with the linear quadratic Gaussian (LQG) method, which is the basic approach for feedback control. We show that the computational cost of the RFC scales only linearly with the number of unknowns, a great improvement compared to the basic LQG control with a computational cost that scales quadratically. We demonstrate that the RFC method can obtain the optimal control values at a greatly reduced computational cost compared to the conventional LQG algorithm with small and controllable losses in the accuracy of the state and parameter estimation.

Loudspeakers: Modeling and control

NASA Astrophysics Data System (ADS)

Al-Ali, Khalid Mohammad

This thesis documented a comprehensive study of loudspeaker modeling and control. A lumped-parameter model for a voice-coil loudspeaker in a vented enclosure was presented that derived from a consideration of physical principles. In addition, a low-frequency (20 Hz to 100 Hz), feedback control method designed to improve the nonlinear performance of the loudspeaker and a suitable performance measure for use in design and evaluation were proposed. Data from experiments performed on a variety of actual loudspeakers confirmed the practicality of the theory developed in this work. The lumped-parameter loudspeaker model, although simple, captured much of the nonlinear behavior of the loudspeaker. In addition, the model formulation allowed a straightforward application of modern control system methods and lent itself well to modern parametric identification techniques. The nonlinear performance of the loudspeaker system was evaluated using a suitable distortion measure that was proposed and compared with other distortion measures currently used in practice. Furthermore, the linearizing effect of feedback using a linear controller (both static and dynamic) was studied on a class of nonlinear systems. The results illustrated that the distortion reduction was potentially significant and a useful upper bound on the closed-loop distortion was found based on the sensitivity function of the system's linearization. A feedback scheme based on robust control theory was chosen for application to the loudspeaker system. Using the pressure output of the loudspeaker system for feedback, the technique offered significant advantages over those previously attempted. Illustrative examples were presented that proved the applicability of the theory developed in this dissertation to a variety of loudspeaker systems. The examples included a vented loudspeaker model and actual loudspeakers enclosed in both vented and sealed configurations. In each example, predictable and measurable distortion reduction at the output of the closed-loop system was recorded.

Focus scanning with feedback control for fiber-optic nonlinear endomicroscopy (Conference Presentation)

NASA Astrophysics Data System (ADS)

Li, Ang; Liang, Wenxuan; Li, Xingde

2017-02-01

Fiber-optic nonlinear endomicroscopy represents a strong promise to enable translation of nonlinear microscopy technologies to in vivo applications, particularly imaging of internal organs. Two-dimensional imaging beam scanning has been accomplished by using fiber-optic scanners or MEMS scanners. Yet nonlinear endomicroscopy still cannot perform rapid and reliable depth or focus scanning while maintaining a small form factor. Shape memory alloy (SMA) wire had shown promise in extending 2D endoscopic imaging to the third dimension. By Joule heating, the SMA wire would contract and move the endomicroscope optics to change beam focus. However, this method suffered from hysteresis, and was susceptible to change in ambient temperature, making it difficult to achieve accurate and reliable depth scanning. Here we present a feedback-controlled SMA actuator which addressed these challenges. The core of the feedback loop was a Hall effect sensor. By measuring the magnetic flux density from a tiny magnet attached to the SMA wire, contraction distance of the SMA wire could be tracked in real time. The distance was then fed to the PID algorithm running in a microprocessor, which computed the error between the command position and the current position of the actuator. The current running through the SMA wire was adjusted accordingly. Our feedback-controlled SMA actuator had a tube-like shape with outer diameter of 5.5 mm and length of 25 mm, and was designed to house the endomicroscope inside. Initial test showed that it allowed more than 300 microns of travel distance, with an average positioning error of less than 2 microns. 3D imaging experiments with the endomicroscope is underway, and its imaging performance will be assessed and discussed.

Reinforcement-learning-based output-feedback control of nonstrict nonlinear discrete-time systems with application to engine emission control.

PubMed

Shih, Peter; Kaul, Brian C; Jagannathan, Sarangapani; Drallmeier, James A

2009-10-01

A novel reinforcement-learning-based output adaptive neural network (NN) controller, which is also referred to as the adaptive-critic NN controller, is developed to deliver the desired tracking performance for a class of nonlinear discrete-time systems expressed in nonstrict feedback form in the presence of bounded and unknown disturbances. The adaptive-critic NN controller consists of an observer, a critic, and two action NNs. The observer estimates the states and output, and the two action NNs provide virtual and actual control inputs to the nonlinear discrete-time system. The critic approximates a certain strategic utility function, and the action NNs minimize the strategic utility function and control inputs. All NN weights adapt online toward minimization of a performance index, utilizing the gradient-descent-based rule, in contrast with iteration-based adaptive-critic schemes. Lyapunov functions are used to show the stability of the closed-loop tracking error, weights, and observer estimates. Separation and certainty equivalence principles, persistency of excitation condition, and linearity in the unknown parameter assumption are not needed. Experimental results on a spark ignition (SI) engine operating lean at an equivalence ratio of 0.75 show a significant (25%) reduction in cyclic dispersion in heat release with control, while the average fuel input changes by less than 1% compared with the uncontrolled case. Consequently, oxides of nitrogen (NO(x)) drop by 30%, and unburned hydrocarbons drop by 16% with control. Overall, NO(x)'s are reduced by over 80% compared with stoichiometric levels.

Improved methods in neural network-based adaptive output feedback control, with applications to flight control

NASA Astrophysics Data System (ADS)

Kim, Nakwan

Utilizing the universal approximation property of neural networks, we develop several novel approaches to neural network-based adaptive output feedback control of nonlinear systems, and illustrate these approaches for several flight control applications. In particular, we address the problem of non-affine systems and eliminate the fixed point assumption present in earlier work. All of the stability proofs are carried out in a form that eliminates an algebraic loop in the neural network implementation. An approximate input/output feedback linearizing controller is augmented with a neural network using input/output sequences of the uncertain system. These approaches permit adaptation to both parametric uncertainty and unmodeled dynamics. All physical systems also have control position and rate limits, which may either deteriorate performance or cause instability for a sufficiently high control bandwidth. Here we apply a method for protecting an adaptive process from the effects of input saturation and time delays, known as "pseudo control hedging". This method was originally developed for the state feedback case, and we provide a stability analysis that extends its domain of applicability to the case of output feedback. The approach is illustrated by the design of a pitch-attitude flight control system for a linearized model of an R-50 experimental helicopter, and by the design of a pitch-rate control system for a 58-state model of a flexible aircraft consisting of rigid body dynamics coupled with actuator and flexible modes. A new approach to augmentation of an existing linear controller is introduced. It is especially useful when there is limited information concerning the plant model, and the existing controller. The approach is applied to the design of an adaptive autopilot for a guided munition. Design of a neural network adaptive control that ensures asymptotically stable tracking performance is also addressed.

Endogenous Molecular-Cellular Network Cancer Theory: A Systems Biology Approach.

PubMed

Wang, Gaowei; Yuan, Ruoshi; Zhu, Xiaomei; Ao, Ping

2018-01-01

In light of ever apparent limitation of the current dominant cancer mutation theory, a quantitative hypothesis for cancer genesis and progression, endogenous molecular-cellular network hypothesis has been proposed from the systems biology perspective, now for more than 10 years. It was intended to include both the genetic and epigenetic causes to understand cancer. Its development enters the stage of meaningful interaction with experimental and clinical data and the limitation of the traditional cancer mutation theory becomes more evident. Under this endogenous network hypothesis, we established a core working network of hepatocellular carcinoma (HCC) according to the hypothesis and quantified the working network by a nonlinear dynamical system. We showed that the two stable states of the working network reproduce the main known features of normal liver and HCC at both the modular and molecular levels. Using endogenous network hypothesis and validated working network, we explored genetic mutation pattern in cancer and potential strategies to cure or relieve HCC from a totally new perspective. Patterns of genetic mutations have been traditionally analyzed by posteriori statistical association approaches in light of traditional cancer mutation theory. One may wonder the possibility of a priori determination of any mutation regularity. Here, we found that based on the endogenous network theory the features of genetic mutations in cancers may be predicted without any prior knowledge of mutation propensities. Normal hepatocyte and cancerous hepatocyte stable states, specified by distinct patterns of expressions or activities of proteins in the network, provide means to directly identify a set of most probable genetic mutations and their effects in HCC. As the key proteins and main interactions in the network are conserved through cell types in an organism, similar mutational features may also be found in other cancers. This analysis yielded straightforward and testable predictions on an accumulated and preferred mutation spectrum in normal tissue. The validation of predicted cancer state mutation patterns demonstrates the usefulness and potential of a causal dynamical framework to understand and predict genetic mutations in cancer. We also obtained the following implication related to HCC therapy, (1) specific positive feedback loops are responsible for the maintenance of normal liver and HCC; (2) inhibiting proliferation and inflammation-related positive feedback loops, and simultaneously inducing liver-specific positive feedback loop is predicated as the potential strategy to cure or relieve HCC; (3) the genesis and regression of HCC is asymmetric. In light of the characteristic property of the nonlinear dynamical system, we demonstrate that positive feedback loops must be existed as a simple and general molecular basis for the maintenance of phenotypes such as normal liver and HCC, and regulating the positive feedback loops directly or indirectly provides potential strategies to cure or relieve HCC.

QCL-based nonlinear sensing of independent targets dynamics.

PubMed

Mezzapesa, F P; Columbo, L L; Dabbicco, M; Brambilla, M; Scamarcio, G

2014-03-10

We demonstrate a common-path interferometer to measure the independent displacement of multiple targets through nonlinear frequency mixing in a quantum-cascade laser (QCL). The sensing system exploits the unique stability of QCLs under strong optical feedback to access the intrinsic nonlinearity of the active medium. The experimental results using an external dual cavity are in excellent agreement with the numerical simulations based on the Lang-Kobayashi equations.

Design and evaluation of a Stochastic Optimal Feed-forward and Feedback Technology (SOFFT) flight control architecture

NASA Technical Reports Server (NTRS)

Ostroff, Aaron J.; Proffitt, Melissa S.

1994-01-01

This paper describes the design and evaluation of a stochastic optimal feed-forward and feedback technology (SOFFT) control architecture with emphasis on the feed-forward controller design. The SOFFT approach allows the designer to independently design the feed-forward and feedback controllers to meet separate objectives and then integrate the two controllers. The feed-forward controller has been integrated with an existing high-angle-of-attack (high-alpha) feedback controller. The feed-forward controller includes a variable command model with parameters selected to satisfy level 1 flying qualities with a high-alpha adjustment to achieve desired agility guidelines, a nonlinear interpolation approach that scales entire matrices for approximation of the plant model, and equations for calculating feed-forward gains developed for perfect plant-model tracking. The SOFFT design was applied to a nonlinear batch simulation model of an F/A-18 aircraft modified for thrust vectoring. Simulation results show that agility guidelines are met and that the SOFFT controller filters undesired pilot-induced frequencies more effectively during a tracking task than a flight controller that has the same feedback control law but does not have the SOFFT feed-forward control.

Optimizing the feedback control of Galvo scanners for laser manufacturing systems

NASA Astrophysics Data System (ADS)

Mirtchev, Theodore; Weeks, Robert; Minko, Sergey

2010-06-01

This paper summarizes the factors that limit the performance of moving-magnet galvo scanners driven by closed-loop digital servo amplifiers: torsional resonances, drifts, nonlinearities, feedback noise and friction. Then it describes a detailed Simulink® simulator that takes into account these factors and can be used to automatically tune the controller for best results with given galvo type and trajectory patterns. It allows for rapid testing of different control schemes, for instance combined position/velocity PID loops and displays the corresponding output in terms of torque, angular position and feedback sensor signal. The tool is configurable and can either use a dynamical state-space model of galvo's open-loop response, or can import the experimentally measured frequency domain transfer function. Next a drive signal digital pre-filtering technique is discussed. By performing a real-time Fourier analysis of the raw command signal it can be pre-warped to minimize all harmonics around the torsional resonances while boosting other non-resonant high frequencies. The optimized waveform results in much smaller overshoot and better settling time. Similar performance gain cannot be extracted from the servo controller alone.

Nonlinear threshold behavior during the loss of Arctic sea ice.

PubMed

Eisenman, I; Wettlaufer, J S

2009-01-06

In light of the rapid recent retreat of Arctic sea ice, a number of studies have discussed the possibility of a critical threshold (or "tipping point") beyond which the ice-albedo feedback causes the ice cover to melt away in an irreversible process. The focus has typically been centered on the annual minimum (September) ice cover, which is often seen as particularly susceptible to destabilization by the ice-albedo feedback. Here, we examine the central physical processes associated with the transition from ice-covered to ice-free Arctic Ocean conditions. We show that although the ice-albedo feedback promotes the existence of multiple ice-cover states, the stabilizing thermodynamic effects of sea ice mitigate this when the Arctic Ocean is ice covered during a sufficiently large fraction of the year. These results suggest that critical threshold behavior is unlikely during the approach from current perennial sea-ice conditions to seasonally ice-free conditions. In a further warmed climate, however, we find that a critical threshold associated with the sudden loss of the remaining wintertime-only sea ice cover may be likely.

Nonlinear threshold behavior during the loss of Arctic sea ice

PubMed Central

Eisenman, I.; Wettlaufer, J. S.

2009-01-01

In light of the rapid recent retreat of Arctic sea ice, a number of studies have discussed the possibility of a critical threshold (or “tipping point”) beyond which the ice–albedo feedback causes the ice cover to melt away in an irreversible process. The focus has typically been centered on the annual minimum (September) ice cover, which is often seen as particularly susceptible to destabilization by the ice–albedo feedback. Here, we examine the central physical processes associated with the transition from ice-covered to ice-free Arctic Ocean conditions. We show that although the ice–albedo feedback promotes the existence of multiple ice-cover states, the stabilizing thermodynamic effects of sea ice mitigate this when the Arctic Ocean is ice covered during a sufficiently large fraction of the year. These results suggest that critical threshold behavior is unlikely during the approach from current perennial sea-ice conditions to seasonally ice-free conditions. In a further warmed climate, however, we find that a critical threshold associated with the sudden loss of the remaining wintertime-only sea ice cover may be likely. PMID:19109440

Winning in Time: Enabling Naturalistic Decision Making in Command and Control

DTIC Science & Technology

2000-11-01

non-linear with non-linearity defined as a condition master chess player , the NBA basketball player , the in which a system disobeys principles of great...are made up of basic others identified in the successive sectors, are feedback structures which have known behavioral points of leverage for policy

Fuzzy attitude control of solar sail via linear matrix inequalities

NASA Astrophysics Data System (ADS)

Baculi, Joshua; Ayoubi, Mohammad A.

2017-09-01

This study presents a fuzzy tracking controller based on the Takagi-Sugeno (T-S) fuzzy model of the solar sail. First, the T-S fuzzy model is constructed by linearizing the existing nonlinear equations of motion of the solar sail. Then, the T-S fuzzy model is used to derive the state feedback controller gains for the Twin Parallel Distributed Compensation (TPDC) technique. The TPDC tracks and stabilizes the attitude of the solar sail to any desired state in the presence of parameter uncertainties and external disturbances while satisfying actuator constraints. The performance of the TPDC is compared to a PID controller that is tuned using the Ziegler-Nichols method. Numerical simulation shows the TPDC outperforms the PID controller when stabilizing the solar sail to a desired state.

Control of Vibratory Energy Harvesters in the Presence of Nonlinearities and Power-Flow Constraints

NASA Astrophysics Data System (ADS)

Cassidy, Ian L.

Over the past decade, a significant amount of research activity has been devoted to developing electromechanical systems that can convert ambient mechanical vibrations into usable electric power. Such systems, referred to as vibratory energy harvesters, have a number of useful of applications, ranging in scale from self-powered wireless sensors for structural health monitoring in bridges and buildings to energy harvesting from ocean waves. One of the most challenging aspects of this technology concerns the efficient extraction and transmission of power from transducer to storage. Maximizing the rate of power extraction from vibratory energy harvesters is further complicated by the stochastic nature of the disturbance. The primary purpose of this dissertation is to develop feedback control algorithms which optimize the average power generated from stochastically-excited vibratory energy harvesters. This dissertation will illustrate the performance of various controllers using two vibratory energy harvesting systems: an electromagnetic transducer embedded within a flexible structure, and a piezoelectric bimorph cantilever beam. Compared with piezoelectric systems, large-scale electromagnetic systems have received much less attention in the literature despite their ability to generate power at the watt--kilowatt scale. Motivated by this observation, the first part of this dissertation focuses on developing an experimentally validated predictive model of an actively controlled electromagnetic transducer. Following this experimental analysis, linear-quadratic-Gaussian control theory is used to compute unconstrained state feedback controllers for two ideal vibratory energy harvesting systems. This theory is then augmented to account for competing objectives, nonlinearities in the harvester dynamics, and non-quadratic transmission loss models in the electronics. In many vibratory energy harvesting applications, employing a bi-directional power electronic drive to actively control the harvester is infeasible due to the high levels of parasitic power required to operate the drive. For the case where a single-directional drive is used, a constraint on the directionality of power-flow is imposed on the system, which necessitates the use of nonlinear feedback. As such, a sub-optimal controller for power-flow-constrained vibratory energy harvesters is presented, which is analytically guaranteed to outperform the optimal static admittance controller. Finally, the last section of this dissertation explores a numerical approach to compute optimal discretized control manifolds for systems with power-flow constraints. Unlike the sub-optimal nonlinear controller, the numerical controller satisfies the necessary conditions for optimality by solving the stochastic Hamilton-Jacobi equation.

Time-optimal Aircraft Pursuit-evasion with a Weapon Envelope Constraint

NASA Technical Reports Server (NTRS)

Menon, P. K. A.

1990-01-01

The optimal pursuit-evasion problem between two aircraft including a realistic weapon envelope is analyzed using differential game theory. Six order nonlinear point mass vehicle models are employed and the inclusion of an arbitrary weapon envelope geometry is allowed. The performance index is a linear combination of flight time and the square of the vehicle acceleration. Closed form solution to this high-order differential game is then obtained using feedback linearization. The solution is in the form of a feedback guidance law together with a quartic polynomial for time-to-go. Due to its modest computational requirements, this nonlinear guidance law is useful for on-board real-time implementation.

Output Feedback-Based Boundary Control of Uncertain Coupled Semilinear Parabolic PDE Using Neurodynamic Programming.

PubMed

Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

2018-04-01

In this paper, neurodynamic programming-based output feedback boundary control of distributed parameter systems governed by uncertain coupled semilinear parabolic partial differential equations (PDEs) under Neumann or Dirichlet boundary control conditions is introduced. First, Hamilton-Jacobi-Bellman (HJB) equation is formulated in the original PDE domain and the optimal control policy is derived using the value functional as the solution of the HJB equation. Subsequently, a novel observer is developed to estimate the system states given the uncertain nonlinearity in PDE dynamics and measured outputs. Consequently, the suboptimal boundary control policy is obtained by forward-in-time estimation of the value functional using a neural network (NN)-based online approximator and estimated state vector obtained from the NN observer. Novel adaptive tuning laws in continuous time are proposed for learning the value functional online to satisfy the HJB equation along system trajectories while ensuring the closed-loop stability. Local uniformly ultimate boundedness of the closed-loop system is verified by using Lyapunov theory. The performance of the proposed controller is verified via simulation on an unstable coupled diffusion reaction process.

Robustness of linear quadratic state feedback designs in the presence of system uncertainty. [applied to STOL autopilot design

NASA Technical Reports Server (NTRS)

Patel, R. V.; Toda, M.; Sridhar, B.

1977-01-01

In connection with difficulties concerning an accurate mathematical representation of a linear quadratic state feedback (LQSF) system, it is often necessary to investigate the robustness (stability) of an LQSF design in the presence of system uncertainty and obtain some quantitative measure of the perturbations which such a design can tolerate. A study is conducted concerning the problem of expressing the robustness property of an LQSF design quantitatively in terms of bounds on the perturbations (modeling errors or parameter variations) in the system matrices. Bounds are obtained for the general case of nonlinear, time-varying perturbations. It is pointed out that most of the presented results are readily applicable to practical situations for which a designer has estimates of the bounds on the system parameter perturbations. Relations are provided which help the designer to select appropriate weighting matrices in the quadratic performance index to attain a robust design. The developed results are employed in the design of an autopilot logic for the flare maneuver of the Augmentor Wing Jet STOL Research Aircraft.

Nonlinear dynamics of autonomous vehicles with limits on acceleration

NASA Astrophysics Data System (ADS)

Davis, L. C.

2014-07-01

The stability of autonomous vehicle platoons with limits on acceleration and deceleration is determined. If the leading-vehicle acceleration remains within the limits, all vehicles in the platoon remain within the limits when the relative-velocity feedback coefficient is equal to the headway time constant [k=1/h]. Furthermore, if the sensitivity α>1/h, no collisions occur. String stability for small perturbations is assumed and the initial condition is taken as the equilibrium state. Other values of k and α that give stability with no collisions are found from simulations. For vehicles with non-negligible mechanical response, simulations indicate that the acceleration-feedback-control gain might have to be dynamically adjusted to obtain optimal performance as the response time changes with engine speed. Stability is demonstrated for some perturbations that cause initial acceleration or deceleration greater than the limits, yet do not cause collisions.

Mixed Poisson distributions in exact solutions of stochastic autoregulation models.

PubMed

Iyer-Biswas, Srividya; Jayaprakash, C

2014-11-01

In this paper we study the interplay between stochastic gene expression and system design using simple stochastic models of autoactivation and autoinhibition. Using the Poisson representation, a technique whose particular usefulness in the context of nonlinear gene regulation models we elucidate, we find exact results for these feedback models in the steady state. Further, we exploit this representation to analyze the parameter spaces of each model, determine which dimensionless combinations of rates are the shape determinants for each distribution, and thus demarcate where in the parameter space qualitatively different behaviors arise. These behaviors include power-law-tailed distributions, bimodal distributions, and sub-Poisson distributions. We also show how these distribution shapes change when the strength of the feedback is tuned. Using our results, we reexamine how well the autoinhibition and autoactivation models serve their conventionally assumed roles as paradigms for noise suppression and noise exploitation, respectively.

The application of LQR synthesis techniques to the turboshaft engine control problem

NASA Technical Reports Server (NTRS)

Pfeil, W. H.; De Los Reyes, G.; Bobula, G. A.

1984-01-01

A power turbine governor was designed for a recent-technology turboshaft engine coupled to a modern, articulated rotor system using Linear Quadratic Regulator (LQR) and Kalman Filter (KF) techniques. A linear, state-space model of the engine and rotor system was derived for six engine power settings from flight idle to maximum continuous. An integrator was appended to the fuel flow input to reduce the steady-state governor error to zero. Feedback gains were calculated for the system states at each power setting using the LQR technique. The main rotor tip speed state is not measurable, so a Kalman Filter of the rotor was used to estimate this state. The crossover of the system was increased to 10 rad/s compared to 2 rad/sec for a current governor. Initial computer simulations with a nonlinear engine model indicate a significant decrease in power turbine speed variation with the LQR governor compared to a conventional governor.

An LMI approach to design H(infinity) controllers for discrete-time nonlinear systems based on unified models.

PubMed

Liu, Meiqin; Zhang, Senlin

2008-10-01

A unified neural network model termed standard neural network model (SNNM) is advanced. Based on the robust L(2) gain (i.e. robust H(infinity) performance) analysis of the SNNM with external disturbances, a state-feedback control law is designed for the SNNM to stabilize the closed-loop system and eliminate the effect of external disturbances. The control design constraints are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms (e.g. interior-point algorithms) to determine the control law. Most discrete-time recurrent neural network (RNNs) and discrete-time nonlinear systems modelled by neural networks or Takagi and Sugeno (T-S) fuzzy models can be transformed into the SNNMs to be robust H(infinity) performance analyzed or robust H(infinity) controller synthesized in a unified SNNM's framework. Finally, some examples are presented to illustrate the wide application of the SNNMs to the nonlinear systems, and the proposed approach is compared with related methods reported in the literature.

Polarization chaos and random bit generation in nonlinear fiber optics induced by a time-delayed counter-propagating feedback loop.

PubMed

Morosi, J; Berti, N; Akrout, A; Picozzi, A; Guasoni, M; Fatome, J

2018-01-22

In this manuscript, we experimentally and numerically investigate the chaotic dynamics of the state-of-polarization in a nonlinear optical fiber due to the cross-interaction between an incident signal and its intense backward replica generated at the fiber-end through an amplified reflective delayed loop. Thanks to the cross-polarization interaction between the two-delayed counter-propagating waves, the output polarization exhibits fast temporal chaotic dynamics, which enable a powerful scrambling process with moving speeds up to 600-krad/s. The performance of this all-optical scrambler was then evaluated on a 10-Gbit/s On/Off Keying telecom signal achieving an error-free transmission. We also describe how these temporal and chaotic polarization fluctuations can be exploited as an all-optical random number generator. To this aim, a billion-bit sequence was experimentally generated and successfully confronted to the dieharder benchmarking statistic tools. Our experimental analysis are supported by numerical simulations based on the resolution of counter-propagating coupled nonlinear propagation equations that confirm the observed behaviors.

Feedback Robust Cubature Kalman Filter for Target Tracking Using an Angle Sensor.

PubMed

Wu, Hao; Chen, Shuxin; Yang, Binfeng; Chen, Kun

2016-05-09

The direction of arrival (DOA) tracking problem based on an angle sensor is an important topic in many fields. In this paper, a nonlinear filter named the feedback M-estimation based robust cubature Kalman filter (FMR-CKF) is proposed to deal with measurement outliers from the angle sensor. The filter designs a new equivalent weight function with the Mahalanobis distance to combine the cubature Kalman filter (CKF) with the M-estimation method. Moreover, by embedding a feedback strategy which consists of a splitting and merging procedure, the proper sub-filter (the standard CKF or the robust CKF) can be chosen in each time index. Hence, the probability of the outliers' misjudgment can be reduced. Numerical experiments show that the FMR-CKF performs better than the CKF and conventional robust filters in terms of accuracy and robustness with good computational efficiency. Additionally, the filter can be extended to the nonlinear applications using other types of sensors.

Active muscle response using feedback control of a finite element human arm model.

PubMed

Östh, Jonas; Brolin, Karin; Happee, Riender

2012-01-01

Mathematical human body models (HBMs) are important research tools that are used to study the human response in car crash situations. Development of automotive safety systems requires the implementation of active muscle response in HBM, as novel safety systems also interact with vehicle occupants in the pre-crash phase. In this study, active muscle response was implemented using feedback control of a nonlinear muscle model in the right upper extremity of a finite element (FE) HBM. Hill-type line muscle elements were added, and the active and passive properties were assessed. Volunteer tests with low impact loading resulting in elbow flexion motions were performed. Simulations of posture maintenance in a gravity field and the volunteer tests were successfully conducted. It was concluded that feedback control of a nonlinear musculoskeletal model can be used to obtain posture maintenance and human-like reflexive responses in an FE HBM.

Development of a helicopter rotor/propulsion system dynamics analysis

NASA Technical Reports Server (NTRS)

Warmbrodt, W.; Hull, R.

1982-01-01

A time-domain analysis of coupled engine/drive train/rotor dynamics of a twin-engine, single main rotor helicopter model has been performed. The analysis incorporates an existing helicopter model with nonlinear simulations of a helicopter turboshaft engine and its fuel controller. System dynamic behavior is studied using the resulting simulation which included representations for the two engines and their fuel controllers, drive system, main rotor, tail rotor, and aircraft rigid body motions. Time histories of engine and rotor RPM response to pilot control inputs are studied for a baseline rotor and propulsion system model. Sensitivity of rotor RPM droop to fuel controller gain changes and collective input feed-forward gain changes are studied. Torque-load-sharing between the two engines is investigated by making changes in the fuel controller feedback paths. A linear engine model is derived from the nonlinear engine simulation and used in the coupled system analysis. This four-state linear engine model is then reduced to a three-state model. The effect of this simplification on coupled system behavior is shown.

Robust fuzzy output feedback controller for affine nonlinear systems via T-S fuzzy bilinear model: CSTR benchmark.

PubMed

Hamdy, M; Hamdan, I

2015-07-01

In this paper, a robust H∞ fuzzy output feedback controller is designed for a class of affine nonlinear systems with disturbance via Takagi-Sugeno (T-S) fuzzy bilinear model. The parallel distributed compensation (PDC) technique is utilized to design a fuzzy controller. The stability conditions of the overall closed loop T-S fuzzy bilinear model are formulated in terms of Lyapunov function via linear matrix inequality (LMI). The control law is robustified by H∞ sense to attenuate external disturbance. Moreover, the desired controller gains can be obtained by solving a set of LMI. A continuous stirred tank reactor (CSTR), which is a benchmark problem in nonlinear process control, is discussed in detail to verify the effectiveness of the proposed approach with a comparative study. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Analysis of the faster-than-Nyquist optimal linear multicarrier system

NASA Astrophysics Data System (ADS)

Marquet, Alexandre; Siclet, Cyrille; Roque, Damien

2017-02-01

Faster-than-Nyquist signalization enables a better spectral efficiency at the expense of an increased computational complexity. Regarding multicarrier communications, previous work mainly relied on the study of non-linear systems exploiting coding and/or equalization techniques, with no particular optimization of the linear part of the system. In this article, we analyze the performance of the optimal linear multicarrier system when used together with non-linear receiving structures (iterative decoding and direct feedback equalization), or in a standalone fashion. We also investigate the limits of the normality assumption of the interference, used for implementing such non-linear systems. The use of this optimal linear system leads to a closed-form expression of the bit-error probability that can be used to predict the performance and help the design of coded systems. Our work also highlights the great performance/complexity trade-off offered by decision feedback equalization in a faster-than-Nyquist context. xml:lang="fr"

Learning-Based Adaptive Optimal Tracking Control of Strict-Feedback Nonlinear Systems.

PubMed

Gao, Weinan; Jiang, Zhong-Ping; Weinan Gao; Zhong-Ping Jiang; Gao, Weinan; Jiang, Zhong-Ping

2018-06-01

This paper proposes a novel data-driven control approach to address the problem of adaptive optimal tracking for a class of nonlinear systems taking the strict-feedback form. Adaptive dynamic programming (ADP) and nonlinear output regulation theories are integrated for the first time to compute an adaptive near-optimal tracker without any a priori knowledge of the system dynamics. Fundamentally different from adaptive optimal stabilization problems, the solution to a Hamilton-Jacobi-Bellman (HJB) equation, not necessarily a positive definite function, cannot be approximated through the existing iterative methods. This paper proposes a novel policy iteration technique for solving positive semidefinite HJB equations with rigorous convergence analysis. A two-phase data-driven learning method is developed and implemented online by ADP. The efficacy of the proposed adaptive optimal tracking control methodology is demonstrated via a Van der Pol oscillator with time-varying exogenous signals.

How linear response shaped models of neural circuits and the quest for alternatives.

PubMed

Herfurth, Tim; Tchumatchenko, Tatjana

2017-10-01

In the past decades, many mathematical approaches to solve complex nonlinear systems in physics have been successfully applied to neuroscience. One of these tools is the concept of linear response functions. However, phenomena observed in the brain emerge from fundamentally nonlinear interactions and feedback loops rather than from a composition of linear filters. Here, we review the successes achieved by applying the linear response formalism to topics, such as rhythm generation and synchrony and by incorporating it into models that combine linear and nonlinear transformations. We also discuss the challenges encountered in the linear response applications and argue that new theoretical concepts are needed to tackle feedback loops and non-equilibrium dynamics which are experimentally observed in neural networks but are outside of the validity regime of the linear response formalism. Copyright © 2017 Elsevier Ltd. All rights reserved.

Model-based Optimization and Feedback Control of the Current Density Profile Evolution in NSTX-U

NASA Astrophysics Data System (ADS)

Ilhan, Zeki Okan

Nuclear fusion research is a highly challenging, multidisciplinary field seeking contributions from both plasma physics and multiple engineering areas. As an application of plasma control engineering, this dissertation mainly explores methods to control the current density profile evolution within the National Spherical Torus eXperiment-Upgrade (NSTX-U), which is a substantial upgrade based on the NSTX device, which is located in Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ. Active control of the toroidal current density profile is among those plasma control milestones that the NSTX-U program must achieve to realize its next-step operational goals, which are characterized by high-performance, long-pulse, MHD-stable plasma operation with neutral beam heating. Therefore, the aim of this work is to develop model-based, feedforward and feedback controllers that can enable time regulation of the current density profile in NSTX-U by actuating the total plasma current, electron density, and the powers of the individual neutral beam injectors. Motivated by the coupled, nonlinear, multivariable, distributed-parameter plasma dynamics, the first step towards control design is the development of a physics-based, control-oriented model for the current profile evolution in NSTX-U in response to non-inductive current drives and heating systems. Numerical simulations of the proposed control-oriented model show qualitative agreement with the high-fidelity physics code TRANSP. The next step is to utilize the proposed control-oriented model to design an open-loop actuator trajectory optimizer. Given a desired operating state, the optimizer produces the actuator trajectories that can steer the plasma to such state. The objective of the feedforward control design is to provide a more systematic approach to advanced scenario planning in NSTX-U since the development of such scenarios is conventionally carried out experimentally by modifying the tokamak's actuator trajectories and analyzing the resulting plasma evolution. Finally, the proposed control-oriented model is embedded in feedback control schemes based on optimal control and Model Predictive Control (MPC) approaches. Integrators are added to the standard Linear Quadratic Gaussian (LQG) and MPC formulations to provide robustness against various modeling uncertainties and external disturbances. The effectiveness of the proposed feedback controllers in regulating the current density profile in NSTX-U is demonstrated in closed-loop nonlinear simulations. Moreover, the optimal feedback control algorithm has been implemented successfully in closed-loop control simulations within TRANSP through the recently developed Expert routine. (Abstract shortened by ProQuest.).

A new RISE-based adaptive control of PKMs: design, stability analysis and experiments

NASA Astrophysics Data System (ADS)

Bennehar, M.; Chemori, A.; Bouri, M.; Jenni, L. F.; Pierrot, F.

2018-03-01

This paper deals with the development of a new adaptive control scheme for parallel kinematic manipulators (PKMs) based on Rrbust integral of the sign of the error (RISE) control theory. Original RISE control law is only based on state feedback and does not take advantage of the modelled dynamics of the manipulator. Consequently, the overall performance of the resulting closed-loop system may be poor compared to modern advanced model-based control strategies. We propose in this work to extend RISE by including the nonlinear dynamics of the PKM in the control loop to improve its overall performance. More precisely, we augment original RISE control scheme with a model-based adaptive control term to account for the inherent nonlinearities in the closed-loop system. To demonstrate the relevance of the proposed controller, real-time experiments are conducted on the Delta robot, a three-degree-of-freedom (3-DOF) PKM.

Robustness of delayed multistable systems with application to droop-controlled inverter-based microgrids

NASA Astrophysics Data System (ADS)

Efimov, Denis; Schiffer, Johannes; Ortega, Romeo

2016-05-01

Motivated by the problem of phase-locking in droop-controlled inverter-based microgrids with delays, the recently developed theory of input-to-state stability (ISS) for multistable systems is extended to the case of multistable systems with delayed dynamics. Sufficient conditions for ISS of delayed systems are presented using Lyapunov-Razumikhin functions. It is shown that ISS multistable systems are robust with respect to delays in a feedback. The derived theory is applied to two examples. First, the ISS property is established for the model of a nonlinear pendulum and delay-dependent robustness conditions are derived. Second, it is shown that, under certain assumptions, the problem of phase-locking analysis in droop-controlled inverter-based microgrids with delays can be reduced to the stability investigation of the nonlinear pendulum. For this case, corresponding delay-dependent conditions for asymptotic phase-locking are given.

Nonlinear gearshifts control of dual-clutch transmissions during inertia phase.

PubMed

Hu, Yunfeng; Tian, Lu; Gao, Bingzhao; Chen, Hong

2014-07-01

In this paper, a model-based nonlinear gearshift controller is designed by the backstepping method to improve the shift quality of vehicles with a dual-clutch transmission (DCT). Considering easy-implementation, the controller is rearranged into a concise structure which contains a feedforward control and a feedback control. Then, robustness of the closed-loop error system is discussed in the framework of the input to state stability (ISS) theory, where model uncertainties are considered as the additive disturbance inputs. Furthermore, due to the application of the backstepping method, the closed-loop error system is ordered as a linear system. Using the linear system theory, a guideline for selecting the controller parameters is deduced which could reduce the workload of parameters tuning. Finally, simulation results and Hardware in the Loop (HiL) simulation are presented to validate the effectiveness of the designed controller. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Fuzzy Adaptive Control Design and Discretization for a Class of Nonlinear Uncertain Systems.

PubMed

Zhao, Xudong; Shi, Peng; Zheng, Xiaolong

2016-06-01

In this paper, tracking control problems are investigated for a class of uncertain nonlinear systems in lower triangular form. First, a state-feedback controller is designed by using adaptive backstepping technique and the universal approximation ability of fuzzy logic systems. During the design procedure, a developed method with less computation is proposed by constructing one maximum adaptive parameter. Furthermore, adaptive controllers with nonsymmetric dead-zone are also designed for the systems. Then, a sampled-data control scheme is presented to discretize the obtained continuous-time controller by using the forward Euler method. It is shown that both proposed continuous and discrete controllers can ensure that the system output tracks the target signal with a small bounded error and the other closed-loop signals remain bounded. Two simulation examples are presented to verify the effectiveness and applicability of the proposed new design techniques.

Phase Matching in Presence of Feedback: Higher Order Terms and Enhancement of Nonlinear Interactions

DTIC Science & Technology

2003-12-01

Papers submitted for publication: M. Centini, G. D’Aguanno, L. Sciscione, C. Sibilia, M. Bertolotti, M. Scalora , M. Bloemer: “Phase matching in the...M. Centini, G. D’Aguanno, L. Sciscione, C. Sibilia, M. Bertolotti, M. Scalora , M. Bloemer: “Phase matching in the presence of feedback: High order

A new decentralised controller design method for a class of strongly interconnected systems

NASA Astrophysics Data System (ADS)

Duan, Zhisheng; Jiang, Zhong-Ping; Huang, Lin

2017-02-01

In this paper, two interconnected structures are first discussed, under which some closed-loop subsystems must be unstable to make the whole interconnected system stable, which can be viewed as a kind of strongly interconnected systems. Then, comparisons with small gain theorem are discussed and large gain interconnected characteristics are shown. A new approach for the design of decentralised controllers is presented by determining the Lyapunov function structure previously, which allows the existence of unstable subsystems. By fully utilising the orthogonal space information of input matrix, some new understandings are presented for the construction of Lyapunov matrix. This new method can deal with decentralised state feedback, static output feedback and dynamic output feedback controllers in a unified framework. Furthermore, in order to reduce the design conservativeness and deal with robustness, a new robust decentralised controller design method is given by combining with the parameter-dependent Lyapunov function method. Some basic rules are provided for the choice of initial variables in Lyapunov matrix or new introduced slack matrices. As byproducts, some linear matrix inequality based sufficient conditions are established for centralised static output feedback stabilisation. Effects of unstable subsystems in nonlinear Lur'e systems are further discussed. The corresponding decentralised controller design method is presented for absolute stability. The examples illustrate that the new method is significantly effective.

Adaptive and neuroadaptive control for nonnegative and compartmental dynamical systems

NASA Astrophysics Data System (ADS)

Volyanskyy, Kostyantyn Y.

Neural networks have been extensively used for adaptive system identification as well as adaptive and neuroadaptive control of highly uncertain systems. The goal of adaptive and neuroadaptive control is to achieve system performance without excessive reliance on system models. To improve robustness and the speed of adaptation of adaptive and neuroadaptive controllers several controller architectures have been proposed in the literature. In this dissertation, we develop a new neuroadaptive control architecture for nonlinear uncertain dynamical systems. The proposed framework involves a novel controller architecture with additional terms in the update laws that are constructed using a moving window of the integrated system uncertainty. These terms can be used to identify the ideal system weights of the neural network as well as effectively suppress system uncertainty. Linear and nonlinear parameterizations of the system uncertainty are considered and state and output feedback neuroadaptive controllers are developed. Furthermore, we extend the developed framework to discrete-time dynamical systems. To illustrate the efficacy of the proposed approach we apply our results to an aircraft model with wing rock dynamics, a spacecraft model with unknown moment of inertia, and an unmanned combat aerial vehicle undergoing actuator failures, and compare our results with standard neuroadaptive control methods. Nonnegative systems are essential in capturing the behavior of a wide range of dynamical systems involving dynamic states whose values are nonnegative. A sub-class of nonnegative dynamical systems are compartmental systems. These systems are derived from mass and energy balance considerations and are comprised of homogeneous interconnected microscopic subsystems or compartments which exchange variable quantities of material via intercompartmental flow laws. In this dissertation, we develop direct adaptive and neuroadaptive control framework for stabilization, disturbance rejection and noise suppression for nonnegative and compartmental dynamical systems with noise and exogenous system disturbances. We then use the developed framework to control the infusion of the anesthetic drug propofol for maintaining a desired constant level of depth of anesthesia for surgery in the face of continuing hemorrhage and hemodilution. Critical care patients, whether undergoing surgery or recovering in intensive care units, require drug administration to regulate physiological variables such as blood pressure, cardiac output, heart rate, and degree of consciousness. The rate of infusion of each administered drug is critical, requiring constant monitoring and frequent adjustments. In this dissertation, we develop a neuroadaptive output feedback control framework for nonlinear uncertain nonnegative and compartmental systems with nonnegative control inputs and noisy measurements. The proposed framework is Lyapunov-based and guarantees ultimate boundedness of the error signals. In addition, the neuroadaptive controller guarantees that the physical system states remain in the nonnegative orthant of the state space. Finally, the developed approach is used to control the infusion of the anesthetic drug propofol for maintaining a desired constant level of depth of anesthesia for surgery in the face of noisy electroencephalographic (EEG) measurements. Clinical trials demonstrate excellent regulation of unconsciousness allowing for a safe and effective administration of the anesthetic agent propofol. Furthermore, a neuroadaptive output feedback control architecture for nonlinear nonnegative dynamical systems with input amplitude and integral constraints is developed. Specifically, the neuroadaptive controller guarantees that the imposed amplitude and integral input constraints are satisfied and the physical system states remain in the nonnegative orthant of the state space. The proposed approach is used to control the infusion of the anesthetic drug propofol for maintaining a desired constant level of depth of anesthesia for noncardiac surgery in the face of infusion rate constraints and a drug dosing constraint over a specified period. In addition, the aforementioned control architecture is used to control lung volume and minute ventilation with input pressure constraints that also accounts for spontaneous breathing by the patient. Specifically, we develop a pressure- and work-limited neuroadaptive controller for mechanical ventilation based on a nonlinear multi-compartmental lung model. The control framework does not rely on any averaged data and is designed to automatically adjust the input pressure to the patient's physiological characteristics capturing lung resistance and compliance modeling uncertainty. Moreover, the controller accounts for input pressure constraints as well as work of breathing constraints. The effect of spontaneous breathing is incorporated within the lung model and the control framework. Finally, a neural network hybrid adaptive control framework for nonlinear uncertain hybrid dynamical systems is developed. The proposed hybrid adaptive control framework is Lyapunov-based and guarantees partial asymptotic stability of the closed-loop hybrid system; that is, asymptotic stability with respect to part of the closed-loop system states associated with the hybrid plant states. A numerical example is provided to demonstrate the efficacy of the proposed hybrid adaptive stabilization approach.

Adaptive non-predictor control of lower triangular uncertain nonlinear systems with an unknown time-varying delay in the input

NASA Astrophysics Data System (ADS)

Koo, Min-Sung; Choi, Ho-Lim

2018-01-01

In this paper, we consider a control problem for a class of uncertain nonlinear systems in which there exists an unknown time-varying delay in the input and lower triangular nonlinearities. Usually, in the existing results, input delays have been coupled with feedforward (or upper triangular) nonlinearities; in other words, the combination of lower triangular nonlinearities and input delay has been rare. Motivated by the existing controller for input-delayed chain of integrators with nonlinearity, we show that the control of input-delayed nonlinear systems with two particular types of lower triangular nonlinearities can be done. As a control solution, we propose a newly designed feedback controller whose main features are its dynamic gain and non-predictor approach. Three examples are given for illustration.

Linearization of microwave photonic link based on nonlinearity of distributed feedback laser

NASA Astrophysics Data System (ADS)

Kang, Zi-jian; Gu, Yi-ying; Zhu, Wen-wu; Fan, Feng; Hu, Jing-jing; Zhao, Ming-shan

2016-02-01

A microwave photonic link (MPL) with spurious-free dynamic range (SFDR) improvement utilizing the nonlinearity of a distributed feedback (DFB) laser is proposed and demonstrated. First, the relationship between the bias current and nonlinearity of a semiconductor DFB laser is experimentally studied. On this basis, the proposed linear optimization of MPL is realized by the combination of the external intensity Mach-Zehnder modulator (MZM) modulation MPL and the direct modulation MPL with the nonlinear operation of the DFB laser. In the external modulation MPL, the MZM is biased at the linear point to achieve the radio frequency (RF) signal transmission. In the direct modulation MPL, the third-order intermodulation (IMD3) components are generated for enhancing the SFDR of the external modulation MPL. When the center frequency of the input RF signal is 5 GHz and the two-tone signal interval is 10 kHz, the experimental results show that IMD3 of the system is effectively suppressed by 29.3 dB and the SFDR is increased by 7.7 dB.

Developing an active artificial hair cell using nonlinear feedback control

NASA Astrophysics Data System (ADS)

Joyce, Bryan S.; Tarazaga, Pablo A.

2015-09-01

The hair cells in the mammalian cochlea convert sound-induced vibrations into electrical signals. These cells have inspired a variety of artificial hair cells (AHCs) to serve as biologically inspired sound, fluid flow, and acceleration sensors and could one day replace damaged hair cells in humans. Most of these AHCs rely on passive transduction of stimulus while it is known that the biological cochlea employs active processes to amplify sound-induced vibrations and improve sound detection. In this work, an active AHC mimics the active, nonlinear behavior of the cochlea. The AHC consists of a piezoelectric bimorph beam subjected to a base excitation. A feedback control law is used to reduce the linear damping of the beam and introduce a cubic damping term which gives the AHC the desired nonlinear behavior. Model and experimental results show the AHC amplifies the response due to small base accelerations, has a higher frequency sensitivity than the passive system, and exhibits a compressive nonlinearity like that of the mammalian cochlea. This bio-inspired accelerometer could lead to new sensors with lower thresholds of detection, improved frequency sensitivities, and wider dynamic ranges.

Sensitivity analysis of primary resonances and bifurcations of a controlled piecewise-smooth system with negative stiffness

NASA Astrophysics Data System (ADS)

Huang, Dongmei; Xu, Wei

2017-11-01

In this paper, the combination of the cubic nonlinearity and time delay is proposed to improve the performance of a piecewise-smooth (PWS) system with negative stiffness. Dynamical properties, feedback control performance and symmetry-breaking bifurcation are mainly considered for a PWS system with negative stiffness under nonlinear position and velocity feedback control. For the free vibration system, the homoclinic-like orbits are firstly derived. Then, the amplitude-frequency response of the controlled system is obtained analytically in aspect of the Lindstedt-Poincaré method and the method of multiple scales, which is also verified through the numerical results. In this regard, a softening-type behavior, which directly leads to the multi-valued responses, is illustrated over the negative position feedback. Especially, the five-valued responses in which three branches of them are stable are found. And complex multi-valued characteristics are also observed in the force-amplitude responses. Furthermore, for explaining the effectiveness of feedback control, the equivalent damping and stiffness are also introduced. Sensitivity of the system response to the feedback gain and time delay is comprehensively considered and interesting dynamical properties are found. Relatively, from the perspective of suppressing the maximum amplitude and controlling the resonance stability, the selection of the feedback parameters is discussed. Finally, the symmetry-breaking bifurcation and chaotic motion are considered.

The Cloud Feedback Model Intercomparison Project (CFMIP) contribution to CMIP6

DOE PAGES

Webb, Mark J.; Andrews, Timothy; Bodas-Salcedo, Alejandro; ...

2017-01-01

Our primary objective of CFMIP is to inform future assessments of cloud feedbacks through improved understanding of cloud–climate feedback mechanisms and better evaluation of cloud processes and cloud feedbacks in climate models. But, the CFMIP approach is also increasingly being used to understand other aspects of climate change, and so a second objective has now been introduced, to improve understanding of circulation, regional-scale precipitation, and non-linear changes. CFMIP is supporting ongoing model inter-comparison activities by coordinating a hierarchy of targeted experiments for CMIP6, along with a set of cloud-related output diagnostics. CFMIP contributes primarily to addressing the CMIP6 questions Howmore » does the Earth system respond to forcing? and What are the origins and consequences of systematic model biases? and supports the activities of the WCRP Grand Challenge on Clouds, Circulation and Climate Sensitivity.A compact set of Tier 1 experiments is proposed for CMIP6 to address this question: (1) what are the physical mechanisms underlying the range of cloud feedbacks and cloud adjustments predicted by climate models, and which models have the most credible cloud feedbacks? Additional Tier 2 experiments are proposed to address the following questions. (2) Are cloud feedbacks consistent for climate cooling and warming, and if not, why? (3) How do cloud-radiative effects impact the structure, the strength and the variability of the general atmospheric circulation in present and future climates? (4) How do responses in the climate system due to changes in solar forcing differ from changes due to CO 2, and is the response sensitive to the sign of the forcing? (5) To what extent is regional climate change per CO 2 doubling state-dependent (non-linear), and why? (6) Are climate feedbacks during the 20th century different to those acting on long-term climate change and climate sensitivity? (7) How do regional climate responses (e.g. in precipitation) and their uncertainties in coupled models arise from the combination of different aspects of CO 2 forcing and sea surface warming?CFMIP also proposes a number of additional model outputs in the CMIP DECK, CMIP6 Historical and CMIP6 CFMIP experiments, including COSP simulator outputs and process diagnostics to address the following questions. How well do clouds and other relevant variables simulated by models agree with observations?What physical processes and mechanisms are important for a credible simulation of clouds, cloud feedbacks and cloud adjustments in climate models?Which models have the most credible representations of processes relevant to the simulation of clouds?How do clouds and their changes interact with other elements of the climate system?« less

The Cloud Feedback Model Intercomparison Project (CFMIP) contribution to CMIP6.

NASA Technical Reports Server (NTRS)

Webb, Mark J.; Andrews, Timothy; Bodas-Salcedo, Alejandro; Bony, Sandrine; Bretherton, Christopher S.; Chadwick, Robin; Chepfer, Helene; Douville, Herve; Good, Peter; Kay, Jennifer E.;

The Cloud Feedback Model Intercomparison Project (CFMIP) contribution to CMIP6

DOE Office of Scientific and Technical Information (OSTI.GOV)

Webb, Mark J.; Andrews, Timothy; Bodas-Salcedo, Alejandro

Our primary objective of CFMIP is to inform future assessments of cloud feedbacks through improved understanding of cloud–climate feedback mechanisms and better evaluation of cloud processes and cloud feedbacks in climate models. But, the CFMIP approach is also increasingly being used to understand other aspects of climate change, and so a second objective has now been introduced, to improve understanding of circulation, regional-scale precipitation, and non-linear changes. CFMIP is supporting ongoing model inter-comparison activities by coordinating a hierarchy of targeted experiments for CMIP6, along with a set of cloud-related output diagnostics. CFMIP contributes primarily to addressing the CMIP6 questions Howmore » does the Earth system respond to forcing? and What are the origins and consequences of systematic model biases? and supports the activities of the WCRP Grand Challenge on Clouds, Circulation and Climate Sensitivity.A compact set of Tier 1 experiments is proposed for CMIP6 to address this question: (1) what are the physical mechanisms underlying the range of cloud feedbacks and cloud adjustments predicted by climate models, and which models have the most credible cloud feedbacks? Additional Tier 2 experiments are proposed to address the following questions. (2) Are cloud feedbacks consistent for climate cooling and warming, and if not, why? (3) How do cloud-radiative effects impact the structure, the strength and the variability of the general atmospheric circulation in present and future climates? (4) How do responses in the climate system due to changes in solar forcing differ from changes due to CO 2, and is the response sensitive to the sign of the forcing? (5) To what extent is regional climate change per CO 2 doubling state-dependent (non-linear), and why? (6) Are climate feedbacks during the 20th century different to those acting on long-term climate change and climate sensitivity? (7) How do regional climate responses (e.g. in precipitation) and their uncertainties in coupled models arise from the combination of different aspects of CO 2 forcing and sea surface warming?CFMIP also proposes a number of additional model outputs in the CMIP DECK, CMIP6 Historical and CMIP6 CFMIP experiments, including COSP simulator outputs and process diagnostics to address the following questions. How well do clouds and other relevant variables simulated by models agree with observations?What physical processes and mechanisms are important for a credible simulation of clouds, cloud feedbacks and cloud adjustments in climate models?Which models have the most credible representations of processes relevant to the simulation of clouds?How do clouds and their changes interact with other elements of the climate system?« less

Cross scale interactions, nonlinearities, and forecasting catastrophic events

USGS Publications Warehouse

Peters, Debra P.C.; Pielke, Roger A.; Bestelmeyer, Brandon T.; Allen, Craig D.; Munson-McGee, Stuart; Havstad, Kris M.

2004-01-01

Catastrophic events share characteristic nonlinear behaviors that are often generated by cross-scale interactions and feedbacks among system elements. These events result in surprises that cannot easily be predicted based on information obtained at a single scale. Progress on catastrophic events has focused on one of the following two areas: nonlinear dynamics through time without an explicit consideration of spatial connectivity [Holling, C. S. (1992) Ecol. Monogr. 62, 447–502] or spatial connectivity and the spread of contagious processes without a consideration of cross-scale interactions and feedbacks [Zeng, N., Neeling, J. D., Lau, L. M. & Tucker, C. J. (1999) Science 286, 1537–1540]. These approaches rarely have ventured beyond traditional disciplinary boundaries. We provide an interdisciplinary, conceptual, and general mathematical framework for understanding and forecasting nonlinear dynamics through time and across space. We illustrate the generality and usefulness of our approach by using new data and recasting published data from ecology (wildfires and desertification), epidemiology (infectious diseases), and engineering (structural failures). We show that decisions that minimize the likelihood of catastrophic events must be based on cross-scale interactions, and such decisions will often be counterintuitive. Given the continuing challenges associated with global change, approaches that cross disciplinary boundaries to include interactions and feedbacks at multiple scales are needed to increase our ability to predict catastrophic events and develop strategies for minimizing their occurrence and impacts. Our framework is an important step in developing predictive tools and designing experiments to examine cross-scale interactions.

Adaptive integral feedback controller for pitch and yaw channels of an AUV with actuator saturations.

PubMed

Sarhadi, Pouria; Noei, Abolfazl Ranjbar; Khosravi, Alireza

2016-11-01

Input saturations and uncertain dynamics are among the practical challenges in control of autonomous vehicles. Adaptive control is known as a proper method to deal with the uncertain dynamics of these systems. Therefore, incorporating the ability to confront with input saturation in adaptive controllers can be valuable. In this paper, an adaptive autopilot is presented for the pitch and yaw channels of an autonomous underwater vehicle (AUV) in the presence of input saturations. This will be performed by combination of a model reference adaptive control (MRAC) with integral state feedback with a modern anti-windup (AW) compensator. MRAC with integral state feedback is commonly used in autonomous vehicles. However, some proper modifications need to be taken into account in order to cope with the saturation problem. To this end, a Riccati-based anti-windup (AW) compensator is employed. The presented technique is applied to the non-linear six degrees of freedom (DOF) model of an AUV and the obtained results are compared with that of its baseline method. Several simulation scenarios are executed in the pitch and yaw channels to evaluate the controller performance. Moreover, effectiveness of proposed adaptive controller is comprehensively investigated by implementing Monte Carlo simulations. The obtained results verify the performance of proposed method. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

A guidance and navigation system for continuous low-thrust vehicles. M.S. Thesis

NASA Technical Reports Server (NTRS)

Jack-Chingtse, C.

1973-01-01

A midcourse guidance and navigation system for continuous low thrust vehicles was developed. The equinoctial elements are the state variables. Uncertainties are modelled statistically by random vector and stochastic processes. The motion of the vehicle and the measurements are described by nonlinear stochastic differential and difference equations respectively. A minimum time trajectory is defined; equations of motion and measurements are linearized about this trajectory. An exponential cost criterion is constructed and a linear feedback quidance law is derived. An extended Kalman filter is used for state estimation. A short mission using this system is simulated. It is indicated that this system is efficient for short missions, but longer missions require accurate trajectory and ground based measurements.

A theoretical model of strong and moderate El Niño regimes

NASA Astrophysics Data System (ADS)

Takahashi, Ken; Karamperidou, Christina; Dewitte, Boris

2018-02-01

The existence of two regimes for El Niño (EN) events, moderate and strong, has been previously shown in the GFDL CM2.1 climate model and also suggested in observations. The two regimes have been proposed to originate from the nonlinearity in the Bjerknes feedback, associated with a threshold in sea surface temperature (T_c ) that needs to be exceeded for deep atmospheric convection to occur in the eastern Pacific. However, although the recent 2015-16 EN event provides a new data point consistent with the sparse strong EN regime, it is not enough to statistically reject the null hypothesis of a unimodal distribution based on observations alone. Nevertheless, we consider the possibility suggestive enough to explore it with a simple theoretical model based on the nonlinear Bjerknes feedback. In this study, we implemented this nonlinear mechanism in the recharge-discharge (RD) ENSO model and show that it is sufficient to produce the two EN regimes, i.e. a bimodal distribution in peak surface temperature (T) during EN events. The only modification introduced to the original RD model is that the net damping is suppressed when T exceeds T_c , resulting in a weak nonlinearity in the system. Due to the damping, the model is globally stable and it requires stochastic forcing to maintain the variability. The sustained low-frequency component of the stochastic forcing plays a key role for the onset of strong EN events (i.e. for T>T_c ), at least as important as the precursor positive heat content anomaly (h). High-frequency forcing helps some EN events to exceed T_c , increasing the number of strong events, but the rectification effect is small and the overall number of EN events is little affected by this forcing. Using the Fokker-Planck equation, we show how the bimodal probability distribution of EN events arises from the nonlinear Bjerknes feedback and also propose that the increase in the net feedback with increasing T is a necessary condition for bimodality in the RD model. We also show that the damping strength determines both the adjustment time-scale and equilibrium value of the ensemble spread associated with the stochastic forcing.

Ant Colony Optimization Analysis on Overall Stability of High Arch Dam Basis of Field Monitoring

PubMed Central

Liu, Xiaoli; Chen, Hong-Xin; Kim, Jinxie

2014-01-01

A dam ant colony optimization (D-ACO) analysis of the overall stability of high arch dams on complicated foundations is presented in this paper. A modified ant colony optimization (ACO) model is proposed for obtaining dam concrete and rock mechanical parameters. A typical dam parameter feedback problem is proposed for nonlinear back-analysis numerical model based on field monitoring deformation and ACO. The basic principle of the proposed model is the establishment of the objective function of optimizing real concrete and rock mechanical parameter. The feedback analysis is then implemented with a modified ant colony algorithm. The algorithm performance is satisfactory, and the accuracy is verified. The m groups of feedback parameters, used to run a nonlinear FEM code, and the displacement and stress distribution are discussed. A feedback analysis of the deformation of the Lijiaxia arch dam and based on the modified ant colony optimization method is also conducted. By considering various material parameters obtained using different analysis methods, comparative analyses were conducted on dam displacements, stress distribution characteristics, and overall dam stability. The comparison results show that the proposal model can effectively solve for feedback multiple parameters of dam concrete and rock material and basically satisfy assessment requirements for geotechnical structural engineering discipline. PMID:25025089

Control of nonlinear flexible space structures

NASA Astrophysics Data System (ADS)

Shi, Jianjun

With the advances made in computer technology and efficiency of numerical algorithms over last decade, the MPC strategies have become quite popular among control community. However, application of MPC or GPC to flexible space structure control has not been explored adequately in the literature. The work presented in this thesis primarily focuses on application of GPC to control of nonlinear flexible space structures. This thesis is particularly devoted to the development of various approximate dynamic models, design and assessment of candidate controllers, and extensive numerical simulations for a realistic multibody flexible spacecraft, namely, Jupiter Icy Moons Orbiter (JIMO)---a Prometheus class of spacecraft proposed by NASA for deep space exploratory missions. A stable GPC algorithm is developed for Multi-Input-Multi-Output (MIMO) systems. An end-point weighting (penalty) is used in the GPC cost function to guarantee the nominal stability of the closed-loop system. A method is given to compute the desired end-point state from the desired output trajectory. The methodologies based on Fake Algebraic Riccati Equation (FARE) and constrained nonlinear optimization, are developed for synthesis of state weighting matrix. This makes this formulation more practical. A stable reconfigurable GPC architecture is presented and its effectiveness is demonstrated on both aircraft as well as spacecraft model. A representative in-orbit maneuver is used for assessing the performance of various control strategies using various design models. Different approximate dynamic models used for analysis include linear single body flexible structure, nonlinear single body flexible structure, and nonlinear multibody flexible structure. The control laws evaluated include traditional GPC, feedback linearization-based GPC (FLGPC), reconfigurable GPC, and nonlinear dissipative control. These various control schemes are evaluated for robust stability and robust performance in the presence of parametric uncertainties and input disturbances. Finally, the conclusions are made with regard to the efficacy of these controllers and potential directions for future research.

Global output feedback control for a class of high-order feedforward nonlinear systems with input delay.

PubMed

Zha, Wenting; Zhai, Junyong; Fei, Shumin

2013-07-01

This paper investigates the problem of output feedback stabilization for a class of high-order feedforward nonlinear systems with time-varying input delay. First, a scaling gain is introduced into the system under a set of coordinate transformations. Then, the authors construct an observer and controller to make the nominal system globally asymptotically stable. Based on homogeneous domination approach and Lyapunov-Krasovskii functional, it is shown that the closed-loop system can be rendered globally asymptotically stable by the scaling gain. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed scheme. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Extending a Lippmann style seismometer's dynamic range by using a non-linear feedback circuit

NASA Astrophysics Data System (ADS)

Romeo, Giovanni; Spinelli, Giuseppe

2013-04-01

A Lippmann style seismometer uses a single-coil velocity-feedback method in order to extend toward lower frequencies a geophone's frequency response. Strong seismic signals may saturate the electronics, sometimes producing a characteristic whale-shaped recording. Adding a non linear feedback in the electronic circuit may avoid saturation, allowing the strong-motion use of the seismometer without affecting the usual performance. We show results from both simulations and experiments, using a Teledyne Geotech s13 as a mechanical part.

A case study in nonlinear dynamics and control of articulated spacecraft: The Space Station Freedom with a mobile remote manipulator system

NASA Technical Reports Server (NTRS)

Bennett, William H.; Kwatny, Harry G.; Lavigna, Chris; Blankenship, Gilmer

1994-01-01

The following topics are discussed: (1) modeling of articulated spacecraft as multi-flex-body systems; (2) nonlinear attitude control by adaptive partial feedback linearizing (PFL) control; (3) attitude dynamics and control for SSF/MRMS; and (4) performance analysis results for attitude control of SSF/MRMS.

Approaches to the Optimal Nonlinear Analysis of Microcalorimeter Pulses

NASA Astrophysics Data System (ADS)

Fowler, J. W.; Pappas, C. G.; Alpert, B. K.; Doriese, W. B.; O'Neil, G. C.; Ullom, J. N.; Swetz, D. S.

2018-03-01

We consider how to analyze microcalorimeter pulses for quantities that are nonlinear in the data, while preserving the signal-to-noise advantages of linear optimal filtering. We successfully apply our chosen approach to compute the electrothermal feedback energy deficit (the "Joule energy") of a pulse, which has been proposed as a linear estimator of the deposited photon energy.

Short-term forecasting of electric loads using nonlinear autoregressive artificial neural networks with exogenous vector inputs

DOE PAGES

Buitrago, Jaime; Asfour, Shihab

2017-01-01

Short-term load forecasting is crucial for the operations planning of an electrical grid. Forecasting the next 24 h of electrical load in a grid allows operators to plan and optimize their resources. The purpose of this study is to develop a more accurate short-term load forecasting method utilizing non-linear autoregressive artificial neural networks (ANN) with exogenous multi-variable input (NARX). The proposed implementation of the network is new: the neural network is trained in open-loop using actual load and weather data, and then, the network is placed in closed-loop to generate a forecast using the predicted load as the feedback input.more » Unlike the existing short-term load forecasting methods using ANNs, the proposed method uses its own output as the input in order to improve the accuracy, thus effectively implementing a feedback loop for the load, making it less dependent on external data. Using the proposed framework, mean absolute percent errors in the forecast in the order of 1% have been achieved, which is a 30% improvement on the average error using feedforward ANNs, ARMAX and state space methods, which can result in large savings by avoiding commissioning of unnecessary power plants. Finally, the New England electrical load data are used to train and validate the forecast prediction.« less

Short-term forecasting of electric loads using nonlinear autoregressive artificial neural networks with exogenous vector inputs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Buitrago, Jaime; Asfour, Shihab

Short-term load forecasting is crucial for the operations planning of an electrical grid. Forecasting the next 24 h of electrical load in a grid allows operators to plan and optimize their resources. The purpose of this study is to develop a more accurate short-term load forecasting method utilizing non-linear autoregressive artificial neural networks (ANN) with exogenous multi-variable input (NARX). The proposed implementation of the network is new: the neural network is trained in open-loop using actual load and weather data, and then, the network is placed in closed-loop to generate a forecast using the predicted load as the feedback input.more » Unlike the existing short-term load forecasting methods using ANNs, the proposed method uses its own output as the input in order to improve the accuracy, thus effectively implementing a feedback loop for the load, making it less dependent on external data. Using the proposed framework, mean absolute percent errors in the forecast in the order of 1% have been achieved, which is a 30% improvement on the average error using feedforward ANNs, ARMAX and state space methods, which can result in large savings by avoiding commissioning of unnecessary power plants. Finally, the New England electrical load data are used to train and validate the forecast prediction.« less

Flatness-Based Tracking Control and Nonlinear Observer for a Micro Aerial Quadcopter

NASA Astrophysics Data System (ADS)

Rivera, G.; Sawodny, O.

2010-09-01

This paper deals with the design of a nonlinear observer and a differential flat based path tracking controller for a mini aerial quadcopter. Taking into account that only the inertial coordinates and the yaw angle are available for measurements, it is shown, that the system is differentially flat, allowing a systematic design of a nonlinear tracking control in open and closed loop. A nonlinear observer is carried out to estimate the roll and pitch angle as well as all the linear and angular velocities. Finally the performance of the feedback controller and observer are illustrated in a computer simulation.

Synchronizing movements with the metronome: nonlinear error correction and unstable periodic orbits.

PubMed

Engbert, Ralf; Krampe, Ralf Th; Kurths, Jürgen; Kliegl, Reinhold

2002-02-01

The control of human hand movements is investigated in a simple synchronization task. We propose and analyze a stochastic model based on nonlinear error correction; a mechanism which implies the existence of unstable periodic orbits. This prediction is tested in an experiment with human subjects. We find that our experimental data are in good agreement with numerical simulations of our theoretical model. These results suggest that feedback control of the human motor systems shows nonlinear behavior. Copyright 2001 Elsevier Science (USA).

A mathematical model of the mevalonate cholesterol biosynthesis pathway.

PubMed

Pool, Frances; Currie, Richard; Sweby, Peter K; Salazar, José Domingo; Tindall, Marcus J

2018-04-14

We formulate, parameterise and analyse a mathematical model of the mevalonate pathway, a key pathway in the synthesis of cholesterol. Of high clinical importance, the pathway incorporates rate limiting enzymatic reactions with multiple negative feedbacks. In this work we investigate the pathway dynamics and demonstrate that rate limiting steps and negative feedbacks within it act in concert to tightly regulate intracellular cholesterol levels. Formulated using the theory of nonlinear ordinary differential equations and parameterised in the context of a hepatocyte, the governing equations are analysed numerically and analytically. Sensitivity and mathematical analysis demonstrate the importance of the two rate limiting enzymes 3-hydroxy-3-methylglutaryl-CoA reductase and squalene synthase in controlling the concentration of substrates within the pathway as well as that of cholesterol. The role of individual feedbacks, both global (between that of cholesterol and sterol regulatory element-binding protein 2; SREBP-2) and local internal (between substrates in the pathway) are investigated. We find that whilst the cholesterol SREBP-2 feedback regulates the overall system dynamics, local feedbacks activate within the pathway to tightly regulate the overall cellular cholesterol concentration. The network stability is analysed by constructing a reduced model of the full pathway and is shown to exhibit one real, stable steady-state. We close by addressing the biological question as to how farnesyl-PP levels are affected by CYP51 inhibition, and demonstrate that the regulatory mechanisms within the network work in unison to ensure they remain bounded. Copyright © 2018 Elsevier Ltd. All rights reserved.

Energetics and monsoon bifurcations

NASA Astrophysics Data System (ADS)

Seshadri, Ashwin K.

2017-01-01

Monsoons involve increases in dry static energy (DSE), with primary contributions from increased shortwave radiation and condensation of water vapor, compensated by DSE export via horizontal fluxes in monsoonal circulations. We introduce a simple box-model characterizing evolution of the DSE budget to study nonlinear dynamics of steady-state monsoons. Horizontal fluxes of DSE are stabilizing during monsoons, exporting DSE and hence weakening the monsoonal circulation. By contrast latent heat addition (LHA) due to condensation of water vapor destabilizes, by increasing the DSE budget. These two factors, horizontal DSE fluxes and LHA, are most strongly dependent on the contrast in tropospheric mean temperature between land and ocean. For the steady-state DSE in the box-model to be stable, the DSE flux should depend more strongly on the temperature contrast than LHA; stronger circulation then reduces DSE and thereby restores equilibrium. We present conditions for this to occur. The main focus of the paper is describing conditions for bifurcation behavior of simple models. Previous authors presented a minimal model of abrupt monsoon transitions and argued that such behavior can be related to a positive feedback called the `moisture advection feedback'. However, by accounting for the effect of vertical lapse rate of temperature on the DSE flux, we show that bifurcations are not a generic property of such models despite these fluxes being nonlinear in the temperature contrast. We explain the origin of this behavior and describe conditions for a bifurcation to occur. This is illustrated for the case of the July-mean monsoon over India. The default model with mean parameter estimates does not contain a bifurcation, but the model admits bifurcation as parameters are varied.

Theory of cortical function

PubMed Central

Heeger, David J.

2017-01-01

Most models of sensory processing in the brain have a feedforward architecture in which each stage comprises simple linear filtering operations and nonlinearities. Models of this form have been used to explain a wide range of neurophysiological and psychophysical data, and many recent successes in artificial intelligence (with deep convolutional neural nets) are based on this architecture. However, neocortex is not a feedforward architecture. This paper proposes a first step toward an alternative computational framework in which neural activity in each brain area depends on a combination of feedforward drive (bottom-up from the previous processing stage), feedback drive (top-down context from the next stage), and prior drive (expectation). The relative contributions of feedforward drive, feedback drive, and prior drive are controlled by a handful of state parameters, which I hypothesize correspond to neuromodulators and oscillatory activity. In some states, neural responses are dominated by the feedforward drive and the theory is identical to a conventional feedforward model, thereby preserving all of the desirable features of those models. In other states, the theory is a generative model that constructs a sensory representation from an abstract representation, like memory recall. In still other states, the theory combines prior expectation with sensory input, explores different possible perceptual interpretations of ambiguous sensory inputs, and predicts forward in time. The theory, therefore, offers an empirically testable framework for understanding how the cortex accomplishes inference, exploration, and prediction. PMID:28167793

Generation of chaotic radiation in a driven traveling wave tube amplifier with time-delayed feedback

NASA Astrophysics Data System (ADS)

Marchewka, Chad; Larsen, Paul; Bhattacharjee, Sudeep; Booske, John; Sengele, Sean; Ryskin, Nikita; Titov, Vladimir

2006-01-01

The application of chaos in communications and radar offers new and interesting possibilities. This article describes investigations on the generation of chaos in a traveling wave tube (TWT) amplifier and the experimental parameters responsible for sustaining stable chaos. Chaos is generated in a TWT amplifier when it is made to operate in a highly nonlinear regime by recirculating a fraction of the TWT output power back to the input in a delayed feedback configuration. A driver wave provides a constant external force to the system making it behave like a forced nonlinear oscillator. The effects of the feedback bandwidth, intensity, and phase are described. The study illuminates the different transitions to chaos and the effect of parameters such as the frequency and intensity of the driver wave. The detuning frequency, i.e., difference frequency between the driver wave and the natural oscillation of the system, has been identified as being an important physical parameter for controlling evolution to chaos. Among the observed routes to chaos, besides the more common period doubling, a new route called loss of frequency locking occurs when the driving frequency is adjacent to a natural oscillation mode. The feedback bandwidth controls the nonlinear dynamics of the system, particularly the number of natural oscillation modes. A computational model has been developed to simulate the experiments and reasonably good agreement is obtained between them. Experiments are described that demonstrate the feasibility of chaotic communications using two TWTs, where one is operated as a driven chaotic oscillator and the other as a time-delayed, open-loop amplifier.

Neural network based adaptive control for nonlinear dynamic regimes

NASA Astrophysics Data System (ADS)

Shin, Yoonghyun

Adaptive control designs using neural networks (NNs) based on dynamic inversion are investigated for aerospace vehicles which are operated at highly nonlinear dynamic regimes. NNs play a key role as the principal element of adaptation to approximately cancel the effect of inversion error, which subsequently improves robustness to parametric uncertainty and unmodeled dynamics in nonlinear regimes. An adaptive control scheme previously named 'composite model reference adaptive control' is further developed so that it can be applied to multi-input multi-output output feedback dynamic inversion. It can have adaptive elements in both the dynamic compensator (linear controller) part and/or in the conventional adaptive controller part, also utilizing state estimation information for NN adaptation. This methodology has more flexibility and thus hopefully greater potential than conventional adaptive designs for adaptive flight control in highly nonlinear flight regimes. The stability of the control system is proved through Lyapunov theorems, and validated with simulations. The control designs in this thesis also include the use of 'pseudo-control hedging' techniques which are introduced to prevent the NNs from attempting to adapt to various actuation nonlinearities such as actuator position and rate saturations. Control allocation is introduced for the case of redundant control effectors including thrust vectoring nozzles. A thorough comparison study of conventional and NN-based adaptive designs for a system under a limit cycle, wing-rock, is included in this research, and the NN-based adaptive control designs demonstrate their performances for two highly maneuverable aerial vehicles, NASA F-15 ACTIVE and FQM-117B unmanned aerial vehicle (UAV), operated under various nonlinearities and uncertainties.

Research in the Optical Sciences

DTIC Science & Technology

1990-03-12

organics for guided wave devices; nonlinear propagation and wave mixing in sodium vapor: gain/feedback approach to optical instabilities; conical... SODIUM VAPOR: GAIN/FEEDBACK APPROACH TO OPTICAL INSTABILITIES; CONICAL EMISSION; KALEIDOSCOPIC SPATIAL INSTABILITY G. Khitrova and H . M . Gibbs...Falco, "Ex situ characterization of MBE-grown molybdenum silicide thin films, The 8th Annual Symposium of the Arizona chapter of The American Vacuum

Adaptive Fuzzy Bounded Control for Consensus of Multiple Strict-Feedback Nonlinear Systems.

PubMed

Wang, Wei; Tong, Shaocheng

2018-02-01

This paper studies the adaptive fuzzy bounded control problem for leader-follower multiagent systems, where each follower is modeled by the uncertain nonlinear strict-feedback system. Combining the fuzzy approximation with the dynamic surface control, an adaptive fuzzy control scheme is developed to guarantee the output consensus of all agents under directed communication topologies. Different from the existing results, the bounds of the control inputs are known as a priori, and they can be determined by the feedback control gains. To realize smooth and fast learning, a predictor is introduced to estimate each error surface, and the corresponding predictor error is employed to learn the optimal fuzzy parameter vector. It is proved that the developed adaptive fuzzy control scheme guarantees the uniformly ultimate boundedness of the closed-loop systems, and the tracking error converges to a small neighborhood of the origin. The simulation results and comparisons are provided to show the validity of the control strategy presented in this paper.

Nonlinear friction modelling and compensation control of hysteresis phenomena for a pair of tendon-sheath actuated surgical robots

NASA Astrophysics Data System (ADS)

Do, T. N.; Tjahjowidodo, T.; Lau, M. W. S.; Phee, S. J.

2015-08-01

Natural Orifice Transluminal Endoscopic Surgery (NOTES) is a special method that allows surgical operations via natural orifices like mouth, anus, and vagina, without leaving visible scars. The use of flexible tendon-sheath mechanism (TSM) is common in these systems because of its light weight in structure, flexibility, and easy transmission of power. However, nonlinear friction and backlash hysteresis pose many challenges to control of such systems; in addition, they do not provide haptic feedback to assist the surgeon in the operation of the systems. In this paper, we propose a new dynamic friction model and backlash hysteresis nonlinearity for a pair of TSM to deal with these problems. The proposed friction model, unlike current approaches in the literature, is smooth and able to capture the force at near zero velocity when the system is stationary or operates at small motion. This model can be used to estimate the friction force for haptic feedback purpose. To improve the system tracking performances, a backlash hysteresis model will be introduced, which can be used in a feedforward controller scheme. The controller involves a simple computation of the inverse hysteresis model. The proposed models are configuration independent and able to capture the nonlinearities for arbitrary tendon-sheath shapes. A representative experimental setup is used to validate the proposed models and to demonstrate the improvement in position tracking accuracy and the possibility of providing desired force information at the distal end of a pair of TSM slave manipulator for haptic feedback to the surgeons.

Non-linear interactions between CO_2 radiative and physiological effects on Amazonian evapotranspiration in an Earth system model

NASA Astrophysics Data System (ADS)

Halladay, Kate; Good, Peter

2017-10-01

We present a detailed analysis of mechanisms underlying the evapotranspiration response to increased CO_2 in HadGEM2-ES, focussed on western Amazonia. We use three simulations from CMIP5 in which atmospheric CO_2 increases at 1% per year reaching approximately four times pre-industrial levels after 140 years. Using 3-hourly data, we found that evapotranspiration (ET) change was dominated by decreased stomatal conductance (g_s), and to a lesser extent by decreased canopy water and increased moisture gradient (specific humidity difference between surface and near-surface). There were large, non-linear decreases in ET in the simulation in which radiative and physiological forcings could interact. This non-linearity arises from non-linearity in the conductance term (includes aerodynamic and stomatal resistance and partitioning between the two, which is determined by canopy water availability), the moisture gradient, and negative correlation between these two terms. The conductance term is non-linear because GPP responds non-linearly to temperature and GPP is the dominant control on g_s in HadGEM2-ES. In addition, canopy water declines, mainly due to increases in potential evaporation, which further decrease the conductance term. The moisture gradient responds non-linearly owing to the non-linear response of temperature to CO_2 increases, which increases the Bowen ratio. Moisture gradient increases resulting from ET decline increase ET and thus constitute a negative feedback. This analysis highlights the importance of the g_s parametrisation in determining the ET response and the potential differences between offline and online simulations owing to feedbacks on ET via the atmosphere, some of which would not occur in an offline simulation.

Highly Stable Nanolattice Structures using Nonlinear Laser Lithography

NASA Astrophysics Data System (ADS)

Yavuz, Ozgun; Tokel, Onur; Ergecen, Emre; Pavlov, Ihor; Makey, Ghaith; Ilday, Fatih Omer

Periodic nanopatterning is crucial for multiple technologies, including photovoltaics and display technologies. Conventional optical lithography techniques require complex masks, while e-beam and ion-beam lithography require expensive equipment. With the Nonlinear Laser Lithography (NLL) technique, we had recently shown that various surfaces can be covered with extremely periodic nanopatterns with ultrafast lasers through a single-step, maskless and inexpensive method. Here, we expand NLL nanopatterns to flexible materials, and also present a fully predictive model for the formation of NLL nanostructures as confirmed with experiments. In NLL, a nonlocal positive feedback mechanism (dipole scattering) competes with a rate limiting negative feedback mechanism. Here, we show that judicious use of the laser polarisation can constrain the lattice symmetry, while the nonlinearities regulate periodicity. We experimentally demonstrate that in addition to one dimensional periodic stripes, two dimensional lattices can be produced on surfaces. In particular, hexagonal and square lattices were produced, which are highly desired for display technologies. Notably, with this approach, we can tile flexible substrates, which can find applications in next generation display technologies.

Synchronization controller design of two coupling permanent magnet synchronous motors system with nonlinear constraints.

PubMed

Deng, Zhenhua; Shang, Jing; Nian, Xiaohong

2015-11-01

In this paper, two coupling permanent magnet synchronous motors system with nonlinear constraints is studied. First of all, the mathematical model of the system is established according to the engineering practices, in which the dynamic model of motor and the nonlinear coupling effect between two motors are considered. In order to keep the two motors synchronization, a synchronization controller based on load observer is designed via cross-coupling idea and interval matrix. Moreover, speed, position and current signals of two motor all are taken as self-feedback signal as well as cross-feedback signal in the proposed controller, which is conducive to improving the dynamical performance and the synchronization performance of the system. The proposed control strategy is verified by simulation via Matlab/Simulink program. The simulation results show that the proposed control method has a better control performance, especially synchronization performance, than that of the conventional PI controller. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Self-organizing biochemical cycle in dynamic feedback with soil structure

NASA Astrophysics Data System (ADS)

Vasilyeva, Nadezda; Vladimirov, Artem; Smirnov, Alexander; Matveev, Sergey; Tyrtyshnikov, Evgeniy; Yudina, Anna; Milanovskiy, Evgeniy; Shein, Evgeniy

2016-04-01

In the present study we perform bifurcation analysis of a physically-based mathematical model of self-organized structures in soil (Vasilyeva et al., 2015). The state variables in this model included microbial biomass, two organic matter types, oxygen, carbon dioxide, water content and capillary pore size. According to our previous experimental studies, organic matter affinity to water is an important property affecting soil structure. Therefore, organic matter wettability was taken as principle distinction between organic matter types in this model. It considers general known biological feedbacks with soil physical properties formulated as a system of parabolic type non-linear partial differential equations with elements of discrete modeling for water and pore formation. The model shows complex behavior, involving emergence of temporal and spatial irregular auto-oscillations from initially homogeneous distributions. The energy of external impact on a system was defined by a constant oxygen level on the boundary. Non-linear as opposed to linear oxygen diffusion gives possibility of modeling anaerobic micro-zones formation (organic matter conservation mechanism). For the current study we also introduced population competition of three different types of microorganisms according to their mobility/feeding (diffusive, moving and fungal growth). The strongly non-linear system was solved and parameterized by time-optimized algorithm combining explicit and implicit (matrix form of Thomas algorithm) methods considering the time for execution of the evaluated time-step according to accuracy control. The integral flux of the CO2 state variable was used as a macroscopic parameter to describe system as a whole and validation was carried out on temperature series of moisture dependence for soil heterotrophic respiration data. Thus, soil heterotrophic respiration can be naturally modeled as an integral result of complex dynamics on microscale, arising from biological processes formulated as a sum of state variables products, with no need to introduce any saturation functions, such as Mikhaelis-Menten type kinetics, inside the model. Analyzed dynamic soil model is being further developed to describe soil structure formation and its effect on organic matter decomposition at macro-scale, to predict changes with external perturbations. To link micro- and macro-scales we additionally model soil particles aggregation process. The results from local biochemical soil organic matter cycle serve as inputs to aggregation process, while the output aggregate size distributions define physical properties in the soil profile, these in turn serve as dynamic parameters in local biochemical cycles. The additional formulation is a system of non-linear ordinary differential equations, including Smoluchowski-type equations for aggregation and reaction kinetics equations for coagulation/adsorption/adhesion processes. Vasilyeva N.A., Ingtem J.G., Silaev D.A. Nonlinear dynamical model of microbial growth in soil medium. Computational Mathematics and Modeling, vol. 49, p.31-44, 2015 (in Russian). English version is expected in corresponding vol.27, issue 2, 2016.

Nonlinear response of summer temperature to Holocene insolation forcing in Alaska.

PubMed

Clegg, Benjamin F; Kelly, Ryan; Clarke, Gina H; Walker, Ian R; Hu, Feng Sheng

2011-11-29

Regional climate responses to large-scale forcings, such as precessional changes in solar irradiation and increases in anthropogenic greenhouse gases, may be nonlinear as a result of complex interactions among earth system components. Such nonlinear behaviors constitute a major source of climate "surprises" with important socioeconomic and ecological implications. Paleorecords are key for elucidating patterns and mechanisms of nonlinear responses to radiative forcing, but their utility has been greatly limited by the paucity of quantitative temperature reconstructions. Here we present Holocene July temperature reconstructions on the basis of midge analysis of sediment cores from three Alaskan lakes. Results show that summer temperatures during 10,000-5,500 calibrated years (cal) B.P. were generally lower than modern and that peak summer temperatures around 5,000 were followed by a decreasing trend toward the present. These patterns stand in stark contrast with the trend of precessional insolation, which decreased by ∼10% from 10,000 y ago to the present. Cool summers before 5,500 cal B.P. coincided with extensive summer ice cover in the western Arctic Ocean, persistence of a positive phase of the Arctic Oscillation, predominantly La Niña-like conditions, and variation in the position of the Alaskan treeline. These results illustrate nonlinear responses of summer temperatures to Holocene insolation radiative forcing in the Alaskan sub-Arctic, possibly because of state changes in the Arctic Oscillation and El Niño-Southern Oscillation and associated land-atmosphere-ocean feedbacks.

Nonlinear response of summer temperature to Holocene insolation forcing in Alaska

PubMed Central

Clegg, Benjamin F.; Kelly, Ryan; Clarke, Gina H.; Walker, Ian R.; Hu, Feng Sheng

2011-01-01

Regional climate responses to large-scale forcings, such as precessional changes in solar irradiation and increases in anthropogenic greenhouse gases, may be nonlinear as a result of complex interactions among earth system components. Such nonlinear behaviors constitute a major source of climate “surprises” with important socioeconomic and ecological implications. Paleorecords are key for elucidating patterns and mechanisms of nonlinear responses to radiative forcing, but their utility has been greatly limited by the paucity of quantitative temperature reconstructions. Here we present Holocene July temperature reconstructions on the basis of midge analysis of sediment cores from three Alaskan lakes. Results show that summer temperatures during 10,000–5,500 calibrated years (cal) B.P. were generally lower than modern and that peak summer temperatures around 5,000 were followed by a decreasing trend toward the present. These patterns stand in stark contrast with the trend of precessional insolation, which decreased by ∼10% from 10,000 y ago to the present. Cool summers before 5,500 cal B.P. coincided with extensive summer ice cover in the western Arctic Ocean, persistence of a positive phase of the Arctic Oscillation, predominantly La Niña-like conditions, and variation in the position of the Alaskan treeline. These results illustrate nonlinear responses of summer temperatures to Holocene insolation radiative forcing in the Alaskan sub-Arctic, possibly because of state changes in the Arctic Oscillation and El Niño-Southern Oscillation and associated land–atmosphere–ocean feedbacks. PMID:22084085

Joystick With Cable Springs Offers Better Feel

NASA Technical Reports Server (NTRS)

Kerley, James; Ecklund, Wayne

1992-01-01

Improved joystick allows motion in 6 degrees of freedom, biased toward central position and orientation by 16 segments of cable serving as springs. Improvement in feel and control results from nonlinear compliance of cable-spring assembly. Nonlinear variations accommodate natural reactions of hand and brain. Operator functions as part of feedback control loop. More comfortable, increases ability to exert control and reduces fatigue.

Stochastic nonlinear dynamics pattern formation and growth models

PubMed Central

Yaroslavsky, Leonid P

2007-01-01

Stochastic evolutionary growth and pattern formation models are treated in a unified way in terms of algorithmic models of nonlinear dynamic systems with feedback built of a standard set of signal processing units. A number of concrete models is described and illustrated by numerous examples of artificially generated patterns that closely imitate wide variety of patterns found in the nature. PMID:17908341

Real Time Digital Control of a Magnetostrictive Actuator

NASA Technical Reports Server (NTRS)

Zrostlik, Rick L.; Hall, David L.; Flatau, Alison B.

1996-01-01

The use of the magnetostrictive material Terfenol-D as a motion source in active vibration control (AVC) systems are being studied. Currently it is of limited use due to the nonlinear nature of the strain versus magnetization curve and the magnetic hysteresis in the Terfenol-D. One manifestation of these nonlinearities is waveform distortion in the output velocity of the transducer. For Terfenol-D to be used in ever greater numbers of AVC systems, these nonlinearities must be addressed. In this study the nonlinearities are treated as disturbances to a linear system. The acceleration output is used in simple analog and digital feedback control schemes to improve linearity of the transducer. In addition, the use of a Terfenol-D actuator in an AVC system is verified. Both analog and digital controllers are implemented and results compared. A cantilever beam system is considered for AVC applications. The second thrust of this presentation is the reduction of harmonic distortions. Two conclusions can be reached from this work. One, the linearization of Terfenol-D transducers is possible with the use of feedback controllers, both digital and analog. Second, Terfenol-D is a viable motion source in active vibration control systems utilizing either analog or digital controllers.

Optimal Fault-Tolerant Control for Discrete-Time Nonlinear Strict-Feedback Systems Based on Adaptive Critic Design.

PubMed

Wang, Zhanshan; Liu, Lei; Wu, Yanming; Zhang, Huaguang

2018-06-01

This paper investigates the problem of optimal fault-tolerant control (FTC) for a class of unknown nonlinear discrete-time systems with actuator fault in the framework of adaptive critic design (ACD). A pivotal highlight is the adaptive auxiliary signal of the actuator fault, which is designed to offset the effect of the fault. The considered systems are in strict-feedback forms and involve unknown nonlinear functions, which will result in the causal problem. To solve this problem, the original nonlinear systems are transformed into a novel system by employing the diffeomorphism theory. Besides, the action neural networks (ANNs) are utilized to approximate a predefined unknown function in the backstepping design procedure. Combined the strategic utility function and the ACD technique, a reinforcement learning algorithm is proposed to set up an optimal FTC, in which the critic neural networks (CNNs) provide an approximate structure of the cost function. In this case, it not only guarantees the stability of the systems, but also achieves the optimal control performance as well. In the end, two simulation examples are used to show the effectiveness of the proposed optimal FTC strategy.

Through-wafer optical probe characterization for microelectromechanical systems positional state monitoring and feedback control

NASA Astrophysics Data System (ADS)

Dawson, Jeremy M.; Chen, Jingdong; Brown, Kolin S.; Famouri, Parviz F.; Hornak, Lawrence A.

2000-12-01

Implementation of closed-loop microelectromechanical system (MEMS) control enables mechanical microsystems to adapt to the demands of the environment that they are actuating, opening a broad range of new opportunities for future MEMS applications. Integrated optical microsystems have the potential to enable continuous in situ optical interrogation of MEMS microstructure position fully decoupled from the means of mechanical actuation that is necessary for realization of feedback control. We present the results of initial research evaluating through-wafer optical microprobes for surface micromachined MEMS integrated optical position monitoring. Results from the through-wafer free-space optical probe of a lateral comb resonator fabricated using the multiuser MEMS process service (MUMPS) indicate significant positional information content with an achievable return probe signal dynamic range of up to 80% arising from film transmission contrast. Static and dynamic deflection analysis and experimental results indicate a through-wafer probe positional signal sensitivity of 40 mV/micrometers for the present setup or 10% signal change per micrometer. A simulation of the application of nonlinear sliding control is presented illustrating position control of the lateral comb resonator structure given the availability of positional state information.

Decentralized adaptive neural control for high-order interconnected stochastic nonlinear time-delay systems with unknown system dynamics.

PubMed

Si, Wenjie; Dong, Xunde; Yang, Feifei

2018-03-01

This paper is concerned with the problem of decentralized adaptive backstepping state-feedback control for uncertain high-order large-scale stochastic nonlinear time-delay systems. For the control design of high-order large-scale nonlinear systems, only one adaptive parameter is constructed to overcome the over-parameterization, and neural networks are employed to cope with the difficulties raised by completely unknown system dynamics and stochastic disturbances. And then, the appropriate Lyapunov-Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown unmatched time-delay interactions of high-order large-scale systems for the first time. At last, on the basis of Lyapunov stability theory, the decentralized adaptive neural controller was developed, and it decreases the number of learning parameters. The actual controller can be designed so as to ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges in the small neighborhood of zero. The simulation example is used to further show the validity of the design method. Copyright © 2018 Elsevier Ltd. All rights reserved.

Switched-Observer-Based Adaptive Neural Control of MIMO Switched Nonlinear Systems With Unknown Control Gains.

PubMed

Long, Lijun; Zhao, Jun

2017-07-01

In this paper, the problem of adaptive neural output-feedback control is addressed for a class of multi-input multioutput (MIMO) switched uncertain nonlinear systems with unknown control gains. Neural networks (NNs) are used to approximate unknown nonlinear functions. In order to avoid the conservativeness caused by adoption of a common observer for all subsystems, an MIMO NN switched observer is designed to estimate unmeasurable states. A new switched observer-based adaptive neural control technique for the problem studied is then provided by exploiting the classical average dwell time (ADT) method and the backstepping method and the Nussbaum gain technique. It effectively handles the obstacle about the coexistence of multiple Nussbaum-type function terms, and improves the classical ADT method, since the exponential decline property of Lyapunov functions for individual subsystems is no longer satisfied. It is shown that the technique proposed is able to guarantee semiglobal uniformly ultimately boundedness of all the signals in the closed-loop system under a class of switching signals with ADT, and the tracking errors converge to a small neighborhood of the origin. The effectiveness of the approach proposed is illustrated by its application to a two inverted pendulum system.

Neural network based online simultaneous policy update algorithm for solving the HJI equation in nonlinear H∞ control.

PubMed

Wu, Huai-Ning; Luo, Biao

2012-12-01

It is well known that the nonlinear H∞ state feedback control problem relies on the solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which is a nonlinear partial differential equation that has proven to be impossible to solve analytically. In this paper, a neural network (NN)-based online simultaneous policy update algorithm (SPUA) is developed to solve the HJI equation, in which knowledge of internal system dynamics is not required. First, we propose an online SPUA which can be viewed as a reinforcement learning technique for two players to learn their optimal actions in an unknown environment. The proposed online SPUA updates control and disturbance policies simultaneously; thus, only one iterative loop is needed. Second, the convergence of the online SPUA is established by proving that it is mathematically equivalent to Newton's method for finding a fixed point in a Banach space. Third, we develop an actor-critic structure for the implementation of the online SPUA, in which only one critic NN is needed for approximating the cost function, and a least-square method is given for estimating the NN weight parameters. Finally, simulation studies are provided to demonstrate the effectiveness of the proposed algorithm.

Neural node network and model, and method of teaching same

DOEpatents

Parlos, A.G.; Atiya, A.F.; Fernandez, B.; Tsai, W.K.; Chong, K.T.

1995-12-26

The present invention is a fully connected feed forward network that includes at least one hidden layer. The hidden layer includes nodes in which the output of the node is fed back to that node as an input with a unit delay produced by a delay device occurring in the feedback path (local feedback). Each node within each layer also receives a delayed output (crosstalk) produced by a delay unit from all the other nodes within the same layer. The node performs a transfer function operation based on the inputs from the previous layer and the delayed outputs. The network can be implemented as analog or digital or within a general purpose processor. Two teaching methods can be used: (1) back propagation of weight calculation that includes the local feedback and the crosstalk or (2) more preferably a feed forward gradient decent which immediately follows the output computations and which also includes the local feedback and the crosstalk. Subsequent to the gradient propagation, the weights can be normalized, thereby preventing convergence to a local optimum. Education of the network can be incremental both on and off-line. An educated network is suitable for modeling and controlling dynamic nonlinear systems and time series systems and predicting the outputs as well as hidden states and parameters. The educated network can also be further educated during on-line processing. 21 figs.

Neural node network and model, and method of teaching same

DOEpatents

Parlos, Alexander G.; Atiya, Amir F.; Fernandez, Benito; Tsai, Wei K.; Chong, Kil T.

1995-01-01

The present invention is a fully connected feed forward network that includes at least one hidden layer 16. The hidden layer 16 includes nodes 20 in which the output of the node is fed back to that node as an input with a unit delay produced by a delay device 24 occurring in the feedback path 22 (local feedback). Each node within each layer also receives a delayed output (crosstalk) produced by a delay unit 36 from all the other nodes within the same layer 16. The node performs a transfer function operation based on the inputs from the previous layer and the delayed outputs. The network can be implemented as analog or digital or within a general purpose processor. Two teaching methods can be used: (1) back propagation of weight calculation that includes the local feedback and the crosstalk or (2) more preferably a feed forward gradient decent which immediately follows the output computations and which also includes the local feedback and the crosstalk. Subsequent to the gradient propagation, the weights can be normalized, thereby preventing convergence to a local optimum. Education of the network can be incremental both on and off-line. An educated network is suitable for modeling and controlling dynamic nonlinear systems and time series systems and predicting the outputs as well as hidden states and parameters. The educated network can also be further educated during on-line processing.

Adaptive Neural Network Control of a Flapping Wing Micro Aerial Vehicle With Disturbance Observer.

PubMed

He, Wei; Yan, Zichen; Sun, Changyin; Chen, Yunan

2017-10-01

The research of this paper works out the attitude and position control of the flapping wing micro aerial vehicle (FWMAV). Neural network control with full state and output feedback are designed to deal with uncertainties in this complex nonlinear FWMAV dynamic system and enhance the system robustness. Meanwhile, we design disturbance observers which are exerted into the FWMAV system via feedforward loops to counteract the bad influence of disturbances. Then, a Lyapunov function is proposed to prove the closed-loop system stability and the semi-global uniform ultimate boundedness of all state variables. Finally, a series of simulation results indicate that proposed controllers can track desired trajectories well via selecting appropriate control gains. And the designed controllers possess potential applications in FWMAVs.

Quantitative implementation of the endogenous molecular-cellular network hypothesis in hepatocellular carcinoma.

PubMed

Wang, Gaowei; Zhu, Xiaomei; Gu, Jianren; Ao, Ping

2014-06-06

A quantitative hypothesis for cancer genesis and progression-the endogenous molecular-cellular network hypothesis, intended to include both genetic and epigenetic causes of cancer-has been proposed recently. Using this hypothesis, here we address the molecular basis for maintaining normal liver and hepatocellular carcinoma (HCC), and the potential strategy to cure or relieve HCC. First, we elaborate the basic assumptions of the hypothesis and establish a core working network of HCC according to the hypothesis. Second, we quantify the working network by a nonlinear dynamical system. We show that the working network reproduces the main known features of normal liver and HCC at both the modular and molecular levels. Lastly, the validated working network reveals that (i) specific positive feedback loops are responsible for the maintenance of normal liver and HCC; (ii) inhibiting proliferation and inflammation-related positive feedback loops and simultaneously inducing a liver-specific positive feedback loop is predicated as a potential strategy to cure or relieve HCC; and (iii) the genesis and regression of HCC are asymmetric. In light of the characteristic properties of the nonlinear dynamical system, we demonstrate that positive feedback loops must exist as a simple and general molecular basis for the maintenance of heritable phenotypes, such as normal liver and HCC, and regulating the positive feedback loops directly or indirectly provides potential strategies to cure or relieve HCC.

Event-Triggered Distributed Control of Nonlinear Interconnected Systems Using Online Reinforcement Learning With Exploration.

PubMed

Narayanan, Vignesh; Jagannathan, Sarangapani

2017-09-07

In this paper, a distributed control scheme for an interconnected system composed of uncertain input affine nonlinear subsystems with event triggered state feedback is presented by using a novel hybrid learning scheme-based approximate dynamic programming with online exploration. First, an approximate solution to the Hamilton-Jacobi-Bellman equation is generated with event sampled neural network (NN) approximation and subsequently, a near optimal control policy for each subsystem is derived. Artificial NNs are utilized as function approximators to develop a suite of identifiers and learn the dynamics of each subsystem. The NN weight tuning rules for the identifier and event-triggering condition are derived using Lyapunov stability theory. Taking into account, the effects of NN approximation of system dynamics and boot-strapping, a novel NN weight update is presented to approximate the optimal value function. Finally, a novel strategy to incorporate exploration in online control framework, using identifiers, is introduced to reduce the overall cost at the expense of additional computations during the initial online learning phase. System states and the NN weight estimation errors are regulated and local uniformly ultimately bounded results are achieved. The analytical results are substantiated using simulation studies.

Nonlinear multivariable design by total synthesis. [of gas turbine engine control systems

NASA Technical Reports Server (NTRS)

Sain, M. K.; Peczkowski, J. L.

1982-01-01

The Nominal Design Problem (NDP) is extended to nonlinear cases, and a new case study of robust feedback synthesis for gas turbine control design is presented. The discussion of NDP extends and builds on earlier Total Synthesis Problem theory and ideas. Some mathematical preliminaries are given in which a bijection from a set S onto a set T is considered, with T admitting the structure of an F-vector space. NDP is then discussed for a nonlinear plant, and nonlinear nominal design is defined and characterized. The design of local controllers for a turbojet and the scheduling of these controls into a global control are addressed.

Design of robust iterative learning control schemes for systems with polytopic uncertainties and sector-bounded nonlinearities

NASA Astrophysics Data System (ADS)

Boski, Marcin; Paszke, Wojciech

2017-01-01

This paper deals with designing of iterative learning control schemes for uncertain systems with static nonlinearities. More specifically, the nonlinear part is supposed to be sector bounded and system matrices are assumed to range in the polytope of matrices. For systems with such nonlinearities and uncertainties the repetitive process setting is exploited to develop a linear matrix inequality based conditions for computing the feedback and feedforward (learning) controllers. These controllers guarantee acceptable dynamics along the trials and ensure convergence of the trial-to-trial error dynamics, respectively. Numerical examples illustrate the theoretical results and confirm effectiveness of the designed control scheme.

The Physical Origin of Long Gas Depletion Times in Galaxies

NASA Astrophysics Data System (ADS)

Semenov, Vadim A.; Kravtsov, Andrey V.; Gnedin, Nickolay Y.

2017-08-01

We present a model that explains why galaxies form stars on a timescale significantly longer than the timescales of processes governing the evolution of interstellar gas. We show that gas evolves from a non-star-forming to a star-forming state on a relatively short timescale, and thus the rate of this evolution does not limit the star formation rate (SFR). Instead, the SFR is limited because only a small fraction of star-forming gas is converted into stars before star-forming regions are dispersed by feedback and dynamical processes. Thus, gas cycles into and out of a star-forming state multiple times, which results in a long timescale on which galaxies convert gas into stars. Our model does not rely on the assumption of equilibrium and can be used to interpret trends of depletion times with the properties of observed galaxies and the parameters of star formation and feedback recipes in simulations. In particular, the model explains how feedback self-regulates the SFR in simulations and makes it insensitive to the local star formation efficiency. We illustrate our model using the results of an isolated L *-sized galaxy simulation that reproduces the observed Kennicutt-Schmidt relation for both molecular and atomic gas. Interestingly, the relation for molecular gas is almost linear on kiloparsec scales, although a nonlinear relation is adopted in simulation cells. We discuss how a linear relation emerges from non-self-similar scaling of the gas density PDF with the average gas surface density.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Semenov, Vadim A.; Kravtsov, Andrey V.; Gnedin, Nickolay Y., E-mail: semenov@uchicago.edu

We present a model that explains why galaxies form stars on a timescale significantly longer than the timescales of processes governing the evolution of interstellar gas. We show that gas evolves from a non-star-forming to a star-forming state on a relatively short timescale, and thus the rate of this evolution does not limit the star formation rate (SFR). Instead, the SFR is limited because only a small fraction of star-forming gas is converted into stars before star-forming regions are dispersed by feedback and dynamical processes. Thus, gas cycles into and out of a star-forming state multiple times, which results inmore » a long timescale on which galaxies convert gas into stars. Our model does not rely on the assumption of equilibrium and can be used to interpret trends of depletion times with the properties of observed galaxies and the parameters of star formation and feedback recipes in simulations. In particular, the model explains how feedback self-regulates the SFR in simulations and makes it insensitive to the local star formation efficiency. We illustrate our model using the results of an isolated L {sub *}-sized galaxy simulation that reproduces the observed Kennicutt–Schmidt relation for both molecular and atomic gas. Interestingly, the relation for molecular gas is almost linear on kiloparsec scales, although a nonlinear relation is adopted in simulation cells. We discuss how a linear relation emerges from non-self-similar scaling of the gas density PDF with the average gas surface density.« less

A disturbance based control/structure design algorithm

NASA Technical Reports Server (NTRS)

Mclaren, Mark D.; Slater, Gary L.

1989-01-01

Some authors take a classical approach to the simultaneous structure/control optimization by attempting to simultaneously minimize the weighted sum of the total mass and a quadratic form, subject to all of the structural and control constraints. Here, the optimization will be based on the dynamic response of a structure to an external unknown stochastic disturbance environment. Such a response to excitation approach is common to both the structural and control design phases, and hence represents a more natural control/structure optimization strategy than relying on artificial and vague control penalties. The design objective is to find the structure and controller of minimum mass such that all the prescribed constraints are satisfied. Two alternative solution algorithms are presented which have been applied to this problem. Each algorithm handles the optimization strategy and the imposition of the nonlinear constraints in a different manner. Two controller methodologies, and their effect on the solution algorithm, will be considered. These are full state feedback and direct output feedback, although the problem formulation is not restricted solely to these forms of controller. In fact, although full state feedback is a popular choice among researchers in this field (for reasons that will become apparent), its practical application is severely limited. The controller/structure interaction is inserted by the imposition of appropriate closed-loop constraints, such as closed-loop output response and control effort constraints. Numerical results will be obtained for a representative flexible structure model to illustrate the effectiveness of the solution algorithms.

The Cloud Feedback Model Intercomparison Project (CFMIP) contribution to CMIP6

NASA Astrophysics Data System (ADS)

Webb, Mark J.; Andrews, Timothy; Bodas-Salcedo, Alejandro; Bony, Sandrine; Bretherton, Christopher S.; Chadwick, Robin; Chepfer, Hélène; Douville, Hervé; Good, Peter; Kay, Jennifer E.; Klein, Stephen A.; Marchand, Roger; Medeiros, Brian; Pier Siebesma, A.; Skinner, Christopher B.; Stevens, Bjorn; Tselioudis, George; Tsushima, Yoko; Watanabe, Masahiro

2017-01-01

The primary objective of CFMIP is to inform future assessments of cloud feedbacks through improved understanding of cloud-climate feedback mechanisms and better evaluation of cloud processes and cloud feedbacks in climate models. However, the CFMIP approach is also increasingly being used to understand other aspects of climate change, and so a second objective has now been introduced, to improve understanding of circulation, regional-scale precipitation, and non-linear changes. CFMIP is supporting ongoing model inter-comparison activities by coordinating a hierarchy of targeted experiments for CMIP6, along with a set of cloud-related output diagnostics. CFMIP contributes primarily to addressing the CMIP6 questions How does the Earth system respond to forcing? and What are the origins and consequences of systematic model biases? and supports the activities of the WCRP Grand Challenge on Clouds, Circulation and Climate Sensitivity.A compact set of Tier 1 experiments is proposed for CMIP6 to address this question: (1) what are the physical mechanisms underlying the range of cloud feedbacks and cloud adjustments predicted by climate models, and which models have the most credible cloud feedbacks? Additional Tier 2 experiments are proposed to address the following questions. (2) Are cloud feedbacks consistent for climate cooling and warming, and if not, why? (3) How do cloud-radiative effects impact the structure, the strength and the variability of the general atmospheric circulation in present and future climates? (4) How do responses in the climate system due to changes in solar forcing differ from changes due to CO2, and is the response sensitive to the sign of the forcing? (5) To what extent is regional climate change per CO2 doubling state-dependent (non-linear), and why? (6) Are climate feedbacks during the 20th century different to those acting on long-term climate change and climate sensitivity? (7) How do regional climate responses (e.g. in precipitation) and their uncertainties in coupled models arise from the combination of different aspects of CO2 forcing and sea surface warming?CFMIP also proposes a number of additional model outputs in the CMIP DECK, CMIP6 Historical and CMIP6 CFMIP experiments, including COSP simulator outputs and process diagnostics to address the following questions.

1. How well do clouds and other relevant variables simulated by models agree with observations?

2. What physical processes and mechanisms are important for a credible simulation of clouds, cloud feedbacks and cloud adjustments in climate models?

3. Which models have the most credible representations of processes relevant to the simulation of clouds?

4. How do clouds and their changes interact with other elements of the climate system?

The application of LQR synthesis techniques to the turboshaft engine control problem. [Linear Quadratic Regulator

NASA Technical Reports Server (NTRS)

Pfeil, W. H.; De Los Reyes, G.; Bobula, G. A.

1985-01-01

A power turbine governor was designed for a recent-technology turboshaft engine coupled to a modern, articulated rotor system using Linear Quadratic Regulator (LQR) and Kalman Filter (KF) techniques. A linear, state-space model of the engine and rotor system was derived for six engine power settings from flight idle to maximum continuous. An integrator was appended to the fuel flow input to reduce the steady-state governor error to zero. Feedback gains were calculated for the system states at each power setting using the LQR technique. The main rotor tip speed state is not measurable, so a Kalman Filter of the rotor was used to estimate this state. The crossover of the system was increased to 10 rad/s compared to 2 rad/sec for a current governor. Initial computer simulations with a nonlinear engine model indicate a significant decrease in power turbine speed variation with the LQR governor compared to a conventional governor.

Sensor fault detection and recovery in satellite attitude control

NASA Astrophysics Data System (ADS)

Nasrolahi, Seiied Saeed; Abdollahi, Farzaneh

2018-04-01

This paper proposes an integrated sensor fault detection and recovery for the satellite attitude control system. By introducing a nonlinear observer, the healthy sensor measurements are provided. Considering attitude dynamics and kinematic, a novel observer is developed to detect the fault in angular rate as well as attitude sensors individually or simultaneously. There is no limit on type and configuration of attitude sensors. By designing a state feedback based control signal and Lyapunov stability criterion, the uniformly ultimately boundedness of tracking errors in the presence of sensor faults is guaranteed. Finally, simulation results are presented to illustrate the performance of the integrated scheme.

Boiler-turbine control system design using a genetic algorithm

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dimeo, R.; Lee, K.Y.

1995-12-01

This paper discusses the application of a genetic algorithm to control system design for a boiler-turbine plant. In particular the authors study the ability of the genetic algorithm to develop a proportional-integral (PI) controller and a state feedback controller for a non-linear multi-input/multi-output (MIMO) plant model. The plant model is presented along with a discussion of the inherent difficulties in such controller development. A sketch of the genetic algorithm (GA) is presented and its strategy as a method of control system design is discussed. Results are presented for two different control systems that have been designed with the genetic algorithm.

Feedback and Acousto Optic Isolation Effects on Laser Stability.

DTIC Science & Technology

1977-03-01

This paper analyzes the effect of optical feedback on laser frequency stability and the acousto optic isolator concept, which was demonstrated...nonlinearity such as saturation in the laser medium. The analysis mathematically corroborates the initial acousto optic isolator concept and the...limited experimental data available. In the study of the acousto optic isolator, it was determined that an acceptable analytic expression for the

A general decay result of a viscoelastic equation with past history and boundary feedback

NASA Astrophysics Data System (ADS)

Messaoudi, Salim A.; Al-Gharabli, Mohammad M.

2015-08-01

In this paper, we consider a viscoelastic equation with a nonlinear feedback localized on a part of the boundary and in the presence of infinite memory term. In the domain as well as on a part of the boundary, we use the multiplier method and some properties of the convex functions to prove an explicit and general decay result.

Comparison of adaptive critic-based and classical wide-area controllers for power systems.

PubMed

Ray, Swakshar; Venayagamoorthy, Ganesh Kumar; Chaudhuri, Balarko; Majumder, Rajat

2008-08-01

An adaptive critic design (ACD)-based damping controller is developed for a thyristor-controlled series capacitor (TCSC) installed in a power system with multiple poorly damped interarea modes. The performance of this ACD computational intelligence-based method is compared with two classical techniques, which are observer-based state-feedback (SF) control and linear matrix inequality LMI-H(infinity) robust control. Remote measurements are used as feedback signals to the wide-area damping controller for modulating the compensation of the TCSC. The classical methods use a linearized model of the system whereas the ACD method is purely measurement-based, leading to a nonlinear controller with fixed parameters. A comparative analysis of the controllers' performances is carried out under different disturbance scenarios. The ACD-based design has shown promising performance with very little knowledge of the system compared to classical model-based controllers. This paper also discusses the advantages and disadvantages of ACDs, SF, and LMI-H(infinity).

Canonical formalism for modelling and control of rigid body dynamics.

PubMed

Gurfil, P

2005-12-01

This paper develops a new paradigm for stabilization of rigid-body dynamics. The state-space model is formulated using canonical elements, known as the Serret-Andoyer (SA) variables, thus far scarcely used for engineering applications. The main feature of the SA formalism is the reduction of the dynamics via the underlying symmetry stemming from conservation of angular momentum and rotational kinetic energy. The controllability of the system model is examined using the notion of accessibility, and is shown to be accessible from all points. Based on the accessibility proof, two nonlinear asymptotic feedback stabilizers are developed: a damping feedback is designed based on the Jurdjevic-Quinn method, and a Hamiltonian controller is derived by using the Hamiltonian as a natural Lyapunov function for the closed-loop dynamics. It is shown that the Hamiltonian control is both passive and inverse optimal with respect to a meaningful performance index. The performance of the new controllers is examined and compared using simulations of realistic scenarios from the satellite attitude dynamics field.

Physics-model-based nonlinear actuator trajectory optimization and safety factor profile feedback control for advanced scenario development in DIII-D

DOE PAGES

Barton, Justin E.; Boyer, Mark D.; Shi, Wenyu; ...

2015-07-30

DIII-D experimental results are reported to demonstrate the potential of physics-model-based safety factor profile control for robust and reproducible sustainment of advanced scenarios. In the absence of feedback control, variability in wall conditions and plasma impurities, as well as drifts due to external disturbances, can limit the reproducibility of discharges with simple pre-programmed scenario trajectories. The control architecture utilized is a feedforward + feedback scheme where the feedforward commands are computed off-line and the feedback commands are computed on-line. In this work, firstly a first-principles-driven (FPD), physics-based model of the q profile and normalized beta (β N) dynamics is embeddedmore » into a numerical optimization algorithm to design feedforward actuator trajectories that sheer the plasma through the tokamak operating space to reach a desired stationary target state that is characterized by the achieved q profile and β N. Good agreement between experimental results and simulations demonstrates the accuracy of the models employed for physics-model-based control design. Secondly, a feedback algorithm for q profile control is designed following a FPD approach, and the ability of the controller to achieve and maintain a target q profile evolution is tested in DIII-D high confinement (H-mode) experiments. The controller is shown to be able to effectively control the q profile when β N is relatively close to the target, indicating the need for integrated q profile and β N control to further enhance the ability to achieve robust scenario execution. Furthermore, the ability of an integrated q profile + β N feedback controller to track a desired target is demonstrated through simulation.« less

Reconfigurable Flight Control Using Nonlinear Dynamic Inversion with a Special Accelerometer Implementation

NASA Technical Reports Server (NTRS)

Bacon, Barton J.; Ostroff, Aaron J.

2000-01-01

This paper presents an approach to on-line control design for aircraft that have suffered either actuator failure, missing effector surfaces, surface damage, or any combination. The approach is based on a modified version of nonlinear dynamic inversion. The approach does not require a model of the baseline vehicle (effectors at zero deflection), but does require feedback of accelerations and effector positions. Implementation issues are addressed and the method is demonstrated on an advanced tailless aircraft. An experimental simulation analysis tool is used to directly evaluate the nonlinear system's stability robustness.

Nonlinear Interactions between Climate and Atmospheric Carbon Dioxide Drivers of Terrestrial and Marine Carbon Cycle Changes

NASA Astrophysics Data System (ADS)

Hoffman, F. M.; Randerson, J. T.; Moore, J. K.; Goulden, M.; Fu, W.; Koven, C.; Swann, A. L. S.; Mahowald, N. M.; Lindsay, K. T.; Munoz, E.

2017-12-01

Quantifying interactions between global biogeochemical cycles and the Earth system is important for predicting future atmospheric composition and informing energy policy. We applied a feedback analysis framework to three sets of Historical (1850-2005), Representative Concentration Pathway 8.5 (2006-2100), and its extension (2101-2300) simulations from the Community Earth System Model version 1.0 (CESM1(BGC)) to quantify drivers of terrestrial and ocean responses of carbon uptake. In the biogeochemically coupled simulation (BGC), the effects of CO2 fertilization and nitrogen deposition influenced marine and terrestrial carbon cycling. In the radiatively coupled simulation (RAD), the effects of rising temperature and circulation changes due to radiative forcing from CO2, other greenhouse gases, and aerosols were the sole drivers of carbon cycle changes. In the third, fully coupled simulation (FC), both the biogeochemical and radiative coupling effects acted simultaneously. We found that climate-carbon sensitivities derived from RAD simulations produced a net ocean carbon storage climate sensitivity that was weaker and a net land carbon storage climate sensitivity that was stronger than those diagnosed from the FC and BGC simulations. For the ocean, this nonlinearity was associated with warming-induced weakening of ocean circulation and mixing that limited exchange of dissolved inorganic carbon between surface and deeper water masses. For the land, this nonlinearity was associated with strong gains in gross primary production in the FC simulation, driven by enhancements in the hydrological cycle and increased nutrient availability. We developed and applied a nonlinearity metric to rank model responses and driver variables. The climate-carbon cycle feedback gain at 2300 was 42% higher when estimated from climate-carbon sensitivities derived from the difference between FC and BGC than when derived from RAD. We re-analyzed other CMIP5 model results to quantify the effects of such nonlinearities on their projected climate-carbon cycle feedback gains.

Nonlinear zero-sum differential game analysis by singular perturbation methods

NASA Technical Reports Server (NTRS)

Sinar, J.; Farber, N.

1982-01-01

A class of nonlinear, zero-sum differential games, exhibiting time-scale separation properties, can be analyzed by singular-perturbation techniques. The merits of such an analysis, leading to an approximate game solution, as well as the 'well-posedness' of the formulation, are discussed. This approach is shown to be attractive for investigating pursuit-evasion problems; the original multidimensional differential game is decomposed to a 'simple pursuit' (free-stream) game and two independent (boundary-layer) optimal-control problems. Using multiple time-scale boundary-layer models results in a pair of uniformly valid zero-order composite feedback strategies. The dependence of suboptimal strategies on relative geometry and own-state measurements is demonstrated by a three dimensional, constant-speed example. For game analysis with realistic vehicle dynamics, the technique of forced singular perturbations and a variable modeling approach is proposed. Accuracy of the analysis is evaluated by comparison with the numerical solution of a time-optimal, variable-speed 'game of two cars' in the horizontal plane.

Simulating closed- and open-loop voluntary movement: a nonlinear control-systems approach.

PubMed

Davidson, Paul R; Jones, Richard D; Andreae, John H; Sirisena, Harsha R

2002-11-01

In many recent human motor control models, including feedback-error learning and adaptive model theory (AMT), feedback control is used to correct errors while an inverse model is simultaneously tuned to provide accurate feedforward control. This popular and appealing hypothesis, based on a combination of psychophysical observations and engineering considerations, predicts that once the tuning of the inverse model is complete the role of feedback control is limited to the correction of disturbances. This hypothesis was tested by looking at the open-loop behavior of the human motor system during adaptation. An experiment was carried out involving 20 normal adult subjects who learned a novel visuomotor relationship on a pursuit tracking task with a steering wheel for input. During learning, the response cursor was periodically blanked, removing all feedback about the external system (i.e., about the relationship between hand motion and response cursor motion). Open-loop behavior was not consistent with a progressive transfer from closed- to open-loop control. Our recently developed computational model of the brain--a novel nonlinear implementation of AMT--was able to reproduce the observed closed- and open-loop results. In contrast, other control-systems models exhibited only minimal feedback control following adaptation, leading to incorrect open-loop behavior. This is because our model continues to use feedback to control slow movements after adaptation is complete. This behavior enhances the internal stability of the inverse model. In summary, our computational model is currently the only motor control model able to accurately simulate the closed- and open-loop characteristics of the experimental response trajectories.

Adaptive nonlinear polynomial neural networks for control of boundary layer/structural interaction

NASA Technical Reports Server (NTRS)

Parker, B. Eugene, Jr.; Cellucci, Richard L.; Abbott, Dean W.; Barron, Roger L.; Jordan, Paul R., III; Poor, H. Vincent

1993-01-01

The acoustic pressures developed in a boundary layer can interact with an aircraft panel to induce significant vibration in the panel. Such vibration is undesirable due to the aerodynamic drag and structure-borne cabin noises that result. The overall objective of this work is to develop effective and practical feedback control strategies for actively reducing this flow-induced structural vibration. This report describes the results of initial evaluations using polynomial, neural network-based, feedback control to reduce flow induced vibration in aircraft panels due to turbulent boundary layer/structural interaction. Computer simulations are used to develop and analyze feedback control strategies to reduce vibration in a beam as a first step. The key differences between this work and that going on elsewhere are as follows: that turbulent and transitional boundary layers represent broadband excitation and thus present a more complex stochastic control scenario than that of narrow band (e.g., laminar boundary layer) excitation; and secondly, that the proposed controller structures are adaptive nonlinear infinite impulse response (IIR) polynomial neural network, as opposed to the traditional adaptive linear finite impulse response (FIR) filters used in most studies to date. The controllers implemented in this study achieved vibration attenuation of 27 to 60 dB depending on the type of boundary layer established by laminar, turbulent, and intermittent laminar-to-turbulent transitional flows. Application of multi-input, multi-output, adaptive, nonlinear feedback control of vibration in aircraft panels based on polynomial neural networks appears to be feasible today. Plans are outlined for Phase 2 of this study, which will include extending the theoretical investigation conducted in Phase 2 and verifying the results in a series of laboratory experiments involving both bum and plate models.

Transient dynamics of NbOx threshold switches explained by Poole-Frenkel based thermal feedback mechanism

NASA Astrophysics Data System (ADS)

Wang, Ziwen; Kumar, Suhas; Nishi, Yoshio; Wong, H.-S. Philip

2018-05-01

Niobium oxide (NbOx) two-terminal threshold switches are potential candidates as selector devices in crossbar memory arrays and as building blocks for neuromorphic systems. However, the physical mechanism of NbOx threshold switches is still under debate. In this paper, we show that a thermal feedback mechanism based on Poole-Frenkel conduction can explain both the quasi-static and the transient electrical characteristics that are experimentally observed for NbOx threshold switches, providing strong support for the validity of this mechanism. Furthermore, a clear picture of the transient dynamics during the thermal-feedback-induced threshold switching is presented, providing useful insights required to model nonlinear devices where thermal feedback is important.

Output transformations and separation results for feedback linearisable delay systems

NASA Astrophysics Data System (ADS)

Cacace, F.; Conte, F.; Germani, A.

2018-04-01

The class of strict-feedback systems enjoys special properties that make it similar to linear systems. This paper proves that such a class is equivalent, under a change of coordinates, to the wider class of feedback linearisable systems with multiplicative input, when the multiplicative terms are functions of the measured variables only. We apply this result to the control problem of feedback linearisable nonlinear MIMO systems with input and/or output delays. In this way, we provide sufficient conditions under which a separation result holds for output feedback control and moreover a predictor-based controller exists. When these conditions are satisfied, we obtain that the existence of stabilising controllers for arbitrarily large delays in the input and/or the output can be proved for a wider class of systems than previously known.

Synchronization of a Class of Switched Neural Networks with Time-Varying Delays via Nonlinear Feedback Control.

PubMed

Wang, Leimin; Shen, Yi; Zhang, Guodong

2016-10-01

This paper is concerned with the synchronization problem for a class of switched neural networks (SNNs) with time-varying delays. First, a new crucial lemma which includes and extends the classical exponential stability theorem is constructed. Then by using the lemma, new algebraic criteria of ψ -type synchronization (synchronization with general decay rate) for SNNs are established via the designed nonlinear feedback control. The ψ -type synchronization which is in a general framework is obtained by introducing a ψ -type function. It contains exponential synchronization, polynomial synchronization, and other synchronization as its special cases. The results of this paper are general, and they also complement and extend some previous results. Finally, numerical simulations are carried out to demonstrate the effectiveness of the obtained results.

Helicity coherence in binary neutron star mergers and nonlinear feedback

NASA Astrophysics Data System (ADS)

Chatelain, Amélie; Volpe, Cristina

2017-02-01

Neutrino flavor conversion studies based on astrophysical environments usually implement neutrino mixings, neutrino interactions with matter, and neutrino self-interactions. In anisotropic media, the most general mean-field treatment includes neutrino mass contributions as well, which introduce a coupling between neutrinos and antineutrinos termed helicity or spin coherence. We discuss resonance conditions for helicity coherence for Dirac and Majorana neutrinos. We explore the role of these mean-field contributions on flavor evolution in the context of a binary neutron star merger remnant. We find that resonance conditions can be satisfied in neutron star merger scenarios while adiabaticity is not sufficient for efficient flavor conversion. We analyze our numerical findings by discussing general conditions to have multiple Mikheyev-Smirnov-Wolfenstein-like resonances, in the presence of nonlinear feedback, in astrophysical environments.

Somatosensory cortex functional connectivity abnormalities in autism show opposite trends, depending on direction and spatial scale

PubMed Central

Khan, Sheraz; Michmizos, Konstantinos; Tommerdahl, Mark; Ganesan, Santosh; Kitzbichler, Manfred G.; Zetino, Manuel; Garel, Keri-Lee A.; Herbert, Martha R.; Hämäläinen, Matti S.

2015-01-01

Functional connectivity is abnormal in autism, but the nature of these abnormalities remains elusive. Different studies, mostly using functional magnetic resonance imaging, have found increased, decreased, or even mixed pattern functional connectivity abnormalities in autism, but no unifying framework has emerged to date. We measured functional connectivity in individuals with autism and in controls using magnetoencephalography, which allowed us to resolve both the directionality (feedforward versus feedback) and spatial scale (local or long-range) of functional connectivity. Specifically, we measured the cortical response and functional connectivity during a passive 25-Hz vibrotactile stimulation in the somatosensory cortex of 20 typically developing individuals and 15 individuals with autism, all males and right-handed, aged 8–18, and the mu-rhythm during resting state in a subset of these participants (12 per group, same age range). Two major significant group differences emerged in the response to the vibrotactile stimulus. First, the 50-Hz phase locking component of the cortical response, generated locally in the primary (S1) and secondary (S2) somatosensory cortex, was reduced in the autism group (P < 0.003, corrected). Second, feedforward functional connectivity between S1 and S2 was increased in the autism group (P < 0.004, corrected). During resting state, there was no group difference in the mu-α rhythm. In contrast, the mu-β rhythm, which has been associated with feedback connectivity, was significantly reduced in the autism group (P < 0.04, corrected). Furthermore, the strength of the mu-β was correlated to the relative strength of 50 Hz component of the response to the vibrotactile stimulus (r = 0.78, P < 0.00005), indicating a shared aetiology for these seemingly unrelated abnormalities. These magnetoencephalography-derived measures were correlated with two different behavioural sensory processing scores (P < 0.01 and P < 0.02 for the autism group, P < 0.01 and P < 0.0001 for the typical group), with autism severity (P < 0.03), and with diagnosis (89% accuracy). A biophysically realistic computational model using data driven feedforward and feedback parameters replicated the magnetoencephalography data faithfully. The direct observation of both abnormally increased and abnormally decreased functional connectivity in autism occurring simultaneously in different functional connectivity streams, offers a potential unifying framework for the unexplained discrepancies in current findings. Given that cortical feedback, whether local or long-range, is intrinsically non-linear, while cortical feedforward is generally linear relative to the stimulus, the present results suggest decreased non-linearity alongside an increased veridical component of the cortical response in autism. PMID:25765326

Nonlinear Control Systems

DTIC Science & Technology

2009-11-18

J.M. Schumacher, Finite -dimensional regulators for a class of infinite dimensional systems . Systems and Control Letters, 3 (1983), 7-12. [39J J.M...for the control of certain examples or system classes us- ing particular feedback design methods ([20, 21, 16, 17, 19, 18]). Still, the control of...long time existence and asymptotic behavior for certain examples or system classes using particular feedback design methods (see, e.g., [20, 21, 16, 17

Nonlinear adaptive optics: aberration correction in three photon fluorescence microscopy for mouse brain imaging

NASA Astrophysics Data System (ADS)

Sinefeld, David; Paudel, Hari P.; Wang, Tianyu; Wang, Mengran; Ouzounov, Dimitre G.; Bifano, Thomas G.; Xu, Chris

2017-02-01

Multiphoton fluorescence microscopy is a well-established technique for deep-tissue imaging with subcellular resolution. Three-photon microscopy (3PM) when combined with long wavelength excitation was shown to allow deeper imaging than two-photon microscopy (2PM) in biological tissues, such as mouse brain, because out-of-focus background light can be further reduced due to the higher order nonlinear excitation. As was demonstrated in 2PM systems, imaging depth and resolution can be improved by aberration correction using adaptive optics (AO) techniques which are based on shaping the scanning beam using a spatial light modulator (SLM). In this way, it is possible to compensate for tissue low order aberration and to some extent, to compensate for tissue scattering. Here, we present a 3PM AO microscopy system for brain imaging. Soliton self-frequency shift is used to create a femtosecond source at 1675 nm and a microelectromechanical (MEMS) SLM serves as the wavefront shaping device. We perturb the 1020 segment SLM using a modified nonlinear version of three-point phase shifting interferometry. The nonlinearity of the fluorescence signal used for feedback ensures that the signal is increasing when the spot size decreases, allowing compensation of phase errors in an iterative optimization process without direct phase measurement. We compare the performance for different orders of nonlinear feedback, showing an exponential growth in signal improvement as the nonlinear order increases. We demonstrate the impact of the method by applying the 3PM AO system for in-vivo mouse brain imaging, showing improvement in signal at 1-mm depth inside the brain.

Feedback control of combustion instabilities from within limit cycle oscillations using H∞ loop-shaping and the ν-gap metric

PubMed Central

Morgans, Aimee S.

2016-01-01

Combustion instabilities arise owing to a two-way coupling between acoustic waves and unsteady heat release. Oscillation amplitudes successively grow, until nonlinear effects cause saturation into limit cycle oscillations. Feedback control, in which an actuator modifies some combustor input in response to a sensor measurement, can suppress combustion instabilities. Linear feedback controllers are typically designed, using linear combustor models. However, when activated from within limit cycle, the linear model is invalid, and such controllers are not guaranteed to stabilize. This work develops a feedback control strategy guaranteed to stabilize from within limit cycle oscillations. A low-order model of a simple combustor, exhibiting the essential features of more complex systems, is presented. Linear plane acoustic wave modelling is combined with a weakly nonlinear describing function for the flame. The latter is determined numerically using a level set approach. Its implication is that the open-loop transfer function (OLTF) needed for controller design varies with oscillation level. The difference between the mean and the rest of the OLTFs is characterized using the ν-gap metric, providing the minimum required ‘robustness margin’ for an H∞ loop-shaping controller. Such controllers are designed and achieve stability both for linear fluctuations and from within limit cycle oscillations. PMID:27493558

Feedback Linearization in a Six Degree-of-Freedom MAG-LEV Stage

NASA Technical Reports Server (NTRS)

Ludwick, Stephen J.; Trumper, David L.; Holmes, Michael L.

1996-01-01

A six degree-of-freedom electromagnetically suspended motion control stage (the Angstrom Stage) has been designed and constructed for use in short-travel, high-resolution motion control applications. It achieves better than 0.5 nm resolution over a 100 micron range of travel. The stage consists of a single moving element (the platen) floating in an oil filled chamber. The oil is crucial to the stage's operation since it forms squeeze film dampers between the platen and the frame. Twelve electromagnetic actuators provide the forces necessary to suspend and servo the platen, and six capacitance probes measure its position relative to the frame. The system is controlled using a digital signal processing board residing in a '486 based PC. This digital controller implements a feedback linearization algorithm in real-time to account for nonlinearities in both the magnetic actuators and the fluid film dampers. The feedback linearization technique reduces a highly nonlinear plant with coupling between the degrees of freedom into one that is linear, decoupled, and setpoint independent. The key to this procedure is a detailed plant model. The operation of the feedback linearization procedure is transparent to the outer loop of the controller, and so a proportional controller is sufficient for normal operation. We envision applications of this stage in scanned probe microscopy and for integrated circuit measurement.

Pulse width modulation-based temperature tracking for feedback control of a shape memory alloy actuator.

PubMed

Ayvali, Elif; Desai, Jaydev P

2014-04-01

This work presents a temperature-feedback approach to control the radius of curvature of an arc-shaped shape memory alloy (SMA) wire. The nonlinear properties of the SMA such as phase transformation and its dependence on temperature and stress make SMA actuators difficult to control. Tracking a desired trajectory is more challenging than controlling just the position of the SMA actuator since the desired path is continuously changing. Consequently, tracking the desired strain directly or tracking the parameters such as temperature and electrical resistance that are related to strain with a model is a challenging task. Temperature-feedback is an attractive approach when direct measurement of strain is not practical. Pulse width modulation (PWM) is an effective method for SMA actuation and it can be used along with a compensator to control the temperature of the SMA. Using the constitutive model of the SMA, the desired temperature profile can be obtained for a given strain trajectory. A PWM-based nonlinear PID controller with a feed-forward heat transfer model is proposed to use temperature-feedback for tracking a desired temperature trajectory. The proposed controller is used during the heating phase of the SMA actuator. The controller proves to be effective in tracking step-wise and continuous trajectories.

Ocean Carbon Cycle Feedbacks Under Negative Emissions

NASA Astrophysics Data System (ADS)

Schwinger, Jörg; Tjiputra, Jerry

2018-05-01

Negative emissions will most likely be needed to achieve ambitious climate targets, such as limiting global warming to 1.5°. Here we analyze the ocean carbon-concentration and carbon-climate feedback in an Earth system model under an idealized strong CO2 peak and decline scenario. We find that the ocean carbon-climate feedback is not reversible by means of negative emissions on decadal to centennial timescales. When preindustrial surface climate is restored, the oceans, due to the carbon-climate feedback, still contain about 110 Pg less carbon compared to a simulation without climate change. This result is unsurprising but highlights an issue with a widely used carbon cycle feedback metric. We show that this metric can be greatly improved by using ocean potential temperature as a proxy for climate change. The nonlinearity (nonadditivity) of climate and CO2-driven feedbacks continues to grow after the atmospheric CO2 peak.

Experimental Chaos - Proceedings of the 3rd Conference

NASA Astrophysics Data System (ADS)

Harrison, Robert G.; Lu, Weiping; Ditto, William; Pecora, Lou; Spano, Mark; Vohra, Sandeep

1996-10-01

The Table of Contents for the full book PDF is as follows: * Preface * Spatiotemporal Chaos and Patterns * Scale Segregation via Formation of Domains in a Nonlinear Optical System * Laser Dynamics as Hydrodynamics * Spatiotemporal Dynamics of Human Epileptic Seizures * Experimental Transition to Chaos in a Quasi 1D Chain of Oscillators * Measuring Coupling in Spatiotemporal Dynamical Systems * Chaos in Vortex Breakdown * Dynamical Analysis * Radial Basis Function Modelling and Prediction of Time Series * Nonlinear Phenomena in Polyrhythmic Hand Movements * Using Models to Diagnose, Test and Control Chaotic Systems * New Real-Time Analysis of Time Series Data with Physical Wavelets * Control and Synchronization * Measuring and Controlling Chaotic Dynamics in a Slugging Fluidized Bed * Control of Chaos in a Laser with Feedback * Synchronization and Chaotic Diode Resonators * Control of Chaos by Continuous-time Feedback with Delay * A Framework for Communication using Chaos Sychronization * Control of Chaos in Switching Circuits * Astrophysics, Meteorology and Oceanography * Solar-Wind-Magnetospheric Dynamics via Satellite Data * Nonlinear Dynamics of the Solar Atmosphere * Fractal Dimension of Scalar and Vector Variables from Turbulence Measurements in the Atmospheric Surface Layer * Mechanics * Escape and Overturning: Subtle Transient Behavior in Nonlinear Mechanical Models * Organising Centres in the Dynamics of Parametrically Excited Double Pendulums * Intermittent Behaviour in a Heating System Driven by Phase Transitions * Hydrodynamics * Size Segregation in Couette Flow of Granular Material * Routes to Chaos in Rotational Taylor-Couette Flow * Experimental Study of the Laminar-Turbulent Transition in an Open Flow System * Chemistry * Order and Chaos in Excitable Media under External Forcing * A Chemical Wave Propagation with Accelerating Speed Accompanied by Hydrodynamic Flow * Optics * Instabilities in Semiconductor Lasers with Optical Injection * Spatio-Temporal Dynamics of a Bimode CO2 Laser with Saturable Absorber * Chaotic Homoclinic Phenomena in Opto-Thermal Devices * Observation and Characterisation of Low-Frequency Chaos in Semiconductor Lasers with External Feedback * Condensed Matter * The Application of Nonlinear Dynamics in the Study of Ferroelectric Materials * Cellular Convection in a Small Aspect Ratio Liquid Crystal Device * Driven Spin-Wave Dynamics in YIG Films * Quantum Chaology in Quartz * Small Signal Amplification Caused by Nonlinear Properties of Ferroelectrics * Composite Materials Evolved from Chaos * Electronics and Circuits * Controlling a Chaotic Array of Pulse-Coupled Fitzhugh-Nagumo Circuits * Experimental Observation of On-Off Intermittency * Phase Lock-In of Chaotic Relaxation Oscillators * Biology and Medicine * Singular Value Decomposition and Circuit Structure in Invertebrate Ganglia * Nonlinear Forecasting of Spike Trains from Neurons of a Mollusc * Ultradian Rhythm in the Sensitive Plants: Chaos or Coloured Noise? * Chaos and the Crayfish Sixth Ganglion * Hardware Coupled Nonlinear Oscillators as a Model of Retina

Nonlinearity measure and internal model control based linearization in anti-windup design

DOE Office of Scientific and Technical Information (OSTI.GOV)

Perev, Kamen

2013-12-18

This paper considers the problem of internal model control based linearization in anti-windup design. The nonlinearity measure concept is used for quantifying the control system degree of nonlinearity. The linearizing effect of a modified internal model control structure is presented by comparing the nonlinearity measures of the open-loop and closed-loop systems. It is shown that the linearization properties are improved by increasing the control system local feedback gain. However, it is emphasized that at the same time the stability of the system deteriorates. The conflicting goals of stability and linearization are resolved by solving the design problem in different frequencymore » ranges.« less

Dynamics and control for Constrained Multibody Systems modeled with Maggi's equation: Application to Differential Mobile Robots Partll

NASA Astrophysics Data System (ADS)

Amengonu, Yawo H.; Kakad, Yogendra P.

2014-07-01

Quasivelocity techniques were applied to derive the dynamics of a Differential Wheeled Mobile Robot (DWMR) in the companion paper. The present paper formulates a control system design for trajectory tracking of this class of robots. The method develops a feedback linearization technique for the nonlinear system using dynamic extension algorithm. The effectiveness of the nonlinear controller is illustrated with simulation example.

Nonlinear and Dissipation Characteristics of Ocean Surface Waves in Estuarine Environments

DTIC Science & Technology

2014-09-30

transformation and evolution . In addition these modules would allow for feedback between the surface wave and the energy dissipating feature. OBJECTIVES...dissipation on wave processes. 3) Develop and test low-dimension, reduced representations of estuarine effects for inclusion into operational wave models...Sheremet (PI), Miao Tian and Cihan Sahin (Ph.D. students) who are working on modeling nonlinear wave evolution in dissipative environments (mud), and

Time-optimal aircraft pursuit-evasion with a weapon envelope constraint

NASA Technical Reports Server (NTRS)

Menon, P. K. A.; Duke, E. L.

1990-01-01

The optimal pursuit-evasion problem between two aircraft, including nonlinear point-mass vehicle models and a realistic weapon envelope, is analyzed. Using a linear combination of flight time and the square of the vehicle acceleration as the performance index, a closed-form solution is obtained in nonlinear feedback form. Due to its modest computational requirements, this guidance law can be used for onboard real-time implementation.

Chaos crisis and bistability of self-pulsing dynamics in a laser diode with phase-conjugate feedback

DOE Office of Scientific and Technical Information (OSTI.GOV)

Virte, Martin; Karsaklian Dal Bosco, Andreas; Wolfersberger, Delphine

2011-10-15

A laser diode subject to a phase-conjugate optical feedback can exhibit rich nonlinear dynamics and chaos. We report here on two bifurcation mechanisms that appear when increasing the amount of light being fed back to the laser. First, we report on a full suppression of chaos from a crisis induced by a saddle-node bifurcation on self-pulsing, so-called external-cavity-mode solutions (ECMs). Second, the feedback-dependent torus and saddle-node bifurcations on ECMs may be responsible for large regions of bistability between ECMs of different and high (beyond gigahertz) frequencies.

A new lattice hydrodynamic model based on control method considering the flux change rate and delay feedback signal

NASA Astrophysics Data System (ADS)

Qin, Shunda; Ge, Hongxia; Cheng, Rongjun

2018-02-01

In this paper, a new lattice hydrodynamic model is proposed by taking delay feedback and flux change rate effect into account in a single lane. The linear stability condition of the new model is derived by control theory. By using the nonlinear analysis method, the mKDV equation near the critical point is deduced to describe the traffic congestion. Numerical simulations are carried out to demonstrate the advantage of the new model in suppressing traffic jam with the consideration of flux change rate effect in delay feedback model.

Stabilizing detached Bridgman melt crystal growth: Model-based nonlinear feedback control

NASA Astrophysics Data System (ADS)

Yeckel, Andrew; Daoutidis, Prodromos; Derby, Jeffrey J.

2012-12-01

The dynamics and operability limits of a nonlinear-proportional-integral controller designed to stabilize detached vertical Bridgman crystal growth are studied. The manipulated variable is the pressure difference between upper and lower vapor spaces, and the controlled variable is the gap width at the triple-phase line. The controller consists of a model-based nonlinear component coupled with a standard proportional-integral controller. The nonlinear component is based on a capillary model of shape stability. Perturbations to gap width, pressure difference, wetting angle, and growth angle are studied under both shape stable and shape unstable conditions. The nonlinear-PI controller allows a wider operating range of gain than a standard PI controller used alone, is easier to tune, and eliminates solution multiplicity from closed-loop operation.

Nonlinear Waves in the Terrestrial Quasiparallel Foreshock.

PubMed

Hnat, B; Kolotkov, D Y; O'Connell, D; Nakariakov, V M; Rowlands, G

2016-12-02

We provide strongly conclusive evidence that the cubic nonlinearity plays an important part in the evolution of the large amplitude magnetic structures in the terrestrial foreshock. Large amplitude nonlinear wave trains at frequencies above the proton cyclotron frequency are identified after nonharmonic slow variations are filtered out by applying the empirical mode decomposition. Numerical solutions of the derivative nonlinear Schrödinger equation, predicted analytically by the use of a pseudopotential approach, are found to be consistent with the observed wave forms. The approximate phase speed of these nonlinear waves, indicated by the parameters of numerical solutions, is of the order of the local Alfvén speed. We suggest that the feedback of the large amplitude fluctuations on background plasma is reflected in the evolution of the pseudopotential.

Neural Approximation-Based Adaptive Control for a Class of Nonlinear Nonstrict Feedback Discrete-Time Systems.

PubMed

Yan-Jun Liu; Shu Li; Shaocheng Tong; Chen, C L Philip

2017-07-01

In this paper, an adaptive control approach-based neural approximation is developed for a class of uncertain nonlinear discrete-time (DT) systems. The main characteristic of the considered systems is that they can be viewed as a class of multi-input multioutput systems in the nonstrict feedback structure. The similar control problem of this class of systems has been addressed in the past, but it focused on the continuous-time systems. Due to the complicacies of the system structure, it will become more difficult for the controller design and the stability analysis. To stabilize this class of systems, a new recursive procedure is developed, and the effect caused by the noncausal problem in the nonstrict feedback DT structure can be solved using a semirecurrent neural approximation. Based on the Lyapunov difference approach, it is proved that all the signals of the closed-loop system are semiglobal, ultimately uniformly bounded, and a good tracking performance can be guaranteed. The feasibility of the proposed controllers can be validated by setting a simulation example.

Time skewing and amplitude nonlinearity mitigation by feedback equalization for 56 Gbps VCSEL-based PAM-4 links

NASA Astrophysics Data System (ADS)

You, Yue; Zhang, Wenjia; Sun, Lin; Du, Jiangbing; Liang, Chenyu; Yang, Fan; He, Zuyuan

2018-03-01

The vertical cavity surface emitting laser (VCSEL)-based multimode optical transceivers enabled by pulse amplitude modulation (PAM)-4 will be commercialized in near future to meet the 400-Gbps standard short reach optical interconnects. It is still challenging to achieve over 56/112-Gbps with the multilevel signaling as the multimode property of the device and link would introduce the nonlinear temporal response for the different levels. In this work, we scrutinize the distortions that relates to the multilevel feature of PAM-4 modulation, and propose an effective feedback equalization scheme for 56-Gbps VCSEL-based PAM-4 optical interconnects system to mitigate the distortions caused by eye timing-skew and nonlinear power-dependent noise. Level redistribution at Tx side is theoretically modeled and constructed to achieve equivalent symbol error ratios (SERs) of four levels and improved BER performance. The cause of the eye skewing and the mitigation approach are also simulated at 100-Gbps and experimentally investigated at 56-Gbps. The results indicate more than 2-dB power penalty improvement has been achieved by using such a distortion aware equalizer.

Non-normal dynamics and positive feedback between motion and sensation boosts run-and-tumble navigation.

NASA Astrophysics Data System (ADS)

Long, Junjiajia; Zucker, Steven W.; Emonet, Thierry

The capability to navigate environmental gradients is of critical importance for survival. Countless organisms (microbes, human cells, worms, larvae, and insects) as well as human-made robots use a run-and-tumble strategy to do so. The classical drawback of this approach is that runs in the wrong direction are wasteful. We show analytically that organisms can overcome this fundamental limitation by exploiting the non-normal dynamics and intrinsic nonlinearities inherent to the positive feedback between motion and sensation. Most importantly, this nonlinear amplification is asymmetric, elongating runs in favorable directions and abbreviating others. The result is a ``ratchet-like'' gradient climbing behavior with drift speeds that can approach half the maximum run speed of the organism. By extending the theoretical study of run-and-tumble navigation into the non-mean-field, nonlinear, and non-normal domains, our results provide a new level of understanding about this basic strategy. We thank Yale HPC, NIGMS 1R01GM106189, and the Allen Distinguished Investigator Program through The Paul G. Allen Frontiers Group for support.

Quasi-minimal active disturbance rejection control of MIMO perturbed linear systems based on differential neural networks and the attractive ellipsoid method.

PubMed

Salgado, Iván; Mera-Hernández, Manuel; Chairez, Isaac

2017-11-01

This study addresses the problem of designing an output-based controller to stabilize multi-input multi-output (MIMO) systems in the presence of parametric disturbances as well as uncertainties in the state model and output noise measurements. The controller design includes a linear state transformation which separates uncertainties matched to the control input and the unmatched ones. A differential neural network (DNN) observer produces a nonlinear approximation of the matched perturbation and the unknown states simultaneously in the transformed coordinates. This study proposes the use of the Attractive Ellipsoid Method (AEM) to optimize the gains of the controller and the gain observer in the DNN structure. As a consequence, the obtained control input minimizes the convergence zone for the estimation error. Moreover, the control design uses the estimated disturbance provided by the DNN to obtain a better performance in the stabilization task in comparison with a quasi-minimal output feedback controller based on a Luenberger observer and a sliding mode controller. Numerical results pointed out the advantages obtained by the nonlinear control based on the DNN observer. The first example deals with the stabilization of an academic linear MIMO perturbed system and the second example stabilizes the trajectories of a DC-motor into a predefined operation point. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Topological solitons as addressable phase bits in a driven laser

NASA Astrophysics Data System (ADS)

Garbin, Bruno; Javaloyes, Julien; Tissoni, Giovanna; Barland, Stéphane

2015-01-01

Optical localized states are usually defined as self-localized bistable packets of light, which exist as independently controllable optical intensity pulses either in the longitudinal or transverse dimension of nonlinear optical systems. Here we demonstrate experimentally and analytically the existence of longitudinal localized states that exist fundamentally in the phase of laser light. These robust and versatile phase bits can be individually nucleated and canceled in an injection-locked semiconductor laser operated in a neuron-like excitable regime and submitted to delayed feedback. The demonstration of their control opens the way to their use as phase information units in next-generation coherent communication systems. We analyse our observations in terms of a generic model, which confirms the topological nature of the phase bits and discloses their formal but profound analogy with Sine-Gordon solitons.

Toward experimental validation of a model for human sensorimotor learning and control in teleoperation

NASA Astrophysics Data System (ADS)

Roth, Eatai; Howell, Darrin; Beckwith, Cydney; Burden, Samuel A.

2017-05-01

Humans, interacting with cyber-physical systems (CPS), formulate beliefs about the system's dynamics. It is natural to expect that human operators, tasked with teleoperation, use these beliefs to control the remote robot. For tracking tasks in the resulting human-cyber-physical system (HCPS), theory suggests that human operators can achieve exponential tracking (in stable systems) without state estimation provided they possess an accurate model of the system's dynamics. This internalized inverse model, however, renders a portion of the system state unobservable to the human operator—the zero dynamics. Prior work shows humans can track through observable linear dynamics, thus we focus on nonlinear dynamics rendered unobservable through tracking control. We propose experiments to assess the human operator's ability to learn and invert such models, and distinguish this behavior from that achieved by pure feedback control.

Optimal linear-quadratic control of coupled parabolic-hyperbolic PDEs

NASA Astrophysics Data System (ADS)

Aksikas, I.; Moghadam, A. Alizadeh; Forbes, J. F.

2017-10-01

This paper focuses on the optimal control design for a system of coupled parabolic-hypebolic partial differential equations by using the infinite-dimensional state-space description and the corresponding operator Riccati equation. Some dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the linear-quadratic (LQ)-optimal control problem. A state LQ-feedback operator is computed by solving the operator Riccati equation, which is converted into a set of algebraic and differential Riccati equations, thanks to the eigenvalues and the eigenvectors of the parabolic operator. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ-optimal controller designed in the early portion of the paper is implemented for the original nonlinear model. Numerical simulations are performed to show the controller performances.

Terahertz generation in mid-infrared quantum cascade lasers with a dual-upper-state active region

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fujita, Kazuue, E-mail: kfujita@crl.hpk.co.jp; Hitaka, Masahiro; Ito, Akio

2015-06-22

We report the performance of room temperature terahertz sources based on intracavity difference-frequency generation in mid-infrared quantum cascade lasers with a dual-upper-state (DAU) active region. DAU active region design is theoretically expected to produce larger optical nonlinearity for terahertz difference-frequency generation, compared to the active region designs of the bound-to-continuum type used previously. Fabricated buried heterostructure devices with a two-section buried distributed feedback grating and the waveguide designed for Cherenkov difference-frequency phase-matching scheme operate in two single-mode mid-infrared wavelengths at 10.7 μm and 9.7 μm and produce terahertz output at 2.9 THz with mid-infrared to terahertz conversion efficiency of 0.8 mW/W{sup 2}more » at room temperature.« less

Lyapunov-based control of limit cycle oscillations in uncertain aircraft systems

NASA Astrophysics Data System (ADS)

Bialy, Brendan

Store-induced limit cycle oscillations (LCO) affect several fighter aircraft and is expected to remain an issue for next generation fighters. LCO arises from the interaction of aerodynamic and structural forces, however the primary contributor to the phenomenon is still unclear. The practical concerns regarding this phenomenon include whether or not ordnance can be safely released and the ability of the aircrew to perform mission-related tasks while in an LCO condition. The focus of this dissertation is the development of control strategies to suppress LCO in aircraft systems. The first contribution of this work (Chapter 2) is the development of a controller consisting of a continuous Robust Integral of the Sign of the Error (RISE) feedback term with a neural network (NN) feedforward term to suppress LCO behavior in an uncertain airfoil system. The second contribution of this work (Chapter 3) is the extension of the development in Chapter 2 to include actuator saturation. Suppression of LCO behavior is achieved through the implementation of an auxiliary error system that features hyperbolic functions and a saturated RISE feedback control structure. Due to the lack of clarity regarding the driving mechanism behind LCO, common practice in literature and in Chapters 2 and 3 is to replicate the symptoms of LCO by including nonlinearities in the wing structure, typically a nonlinear torsional stiffness. To improve the accuracy of the system model a partial differential equation (PDE) model of a flexible wing is derived (see Appendix F) using Hamilton's principle. Chapters 4 and 5 are focused on developing boundary control strategies for regulating the bending and twisting deformations of the derived model. The contribution of Chapter 4 is the construction of a backstepping-based boundary control strategy for a linear PDE model of an aircraft wing. The backstepping-based strategy transforms the original system to a exponentially stable system. A Lyapunov-based stability analysis is then used to show boundedness of the wing bending dynamics. A Lyapunov-based boundary control strategy for an uncertain nonlinear PDE model of an aircraft wing is developed in Chapter 5. In this chapter, a proportional feedback term is coupled with an gradient-based adaptive update law to ensure asymptotic regulation of the flexible states.

High angle of attack control law development for a free-flight wind tunnel model using direct eigenstructure assignment

NASA Technical Reports Server (NTRS)

Wendel, Thomas R.; Boland, Joseph R.; Hahne, David E.

1991-01-01

Flight-control laws are developed for a wind-tunnel aircraft model flying at a high angle of attack by using a synthesis technique called direct eigenstructure assignment. The method employs flight guidelines and control-power constraints to develop the control laws, and gain schedules and nonlinear feedback compensation provide a framework for considering the nonlinear nature of the attack angle. Linear and nonlinear evaluations show that the control laws are effective, a conclusion that is further confirmed by a scale model used for free-flight testing.

Synchronization and Cardio-pulmonary feedback in Sleep Apnea

NASA Astrophysics Data System (ADS)

Xu, Limei; Ivanov, Plamen Ch.; Chen, Zhi; Hu, Kun; Paydarfar, David; Stanley, H. Eugene

2004-03-01

Findings indicate a dynamical coupling between respiratory and cardiac function. However, the nature of this nonlinear interaction remains not well understood. We investigate transient patterns in the cardio-pulmonary interaction under healthy conditions by means of cross-correlation and nonlinear synchronization techniques, and we compare how these patterns change under pathologic conditions such as obstructive sleep apnea --- a periodic cessation of breathing during sleep. We find that during apnea episodes the nonlinear features of cardio-pulmonary interaction change intermittently, and can exhibit variations characterized by different time delays in the phase synchronization between breathing and heartbeat dynamics.

Neural-Based Compensation of Nonlinearities in an Airplane Longitudinal Model with Dynamic-Inversion Control

PubMed Central

Li, YuHui; Jin, FeiTeng

2017-01-01

The inversion design approach is a very useful tool for the complex multiple-input-multiple-output nonlinear systems to implement the decoupling control goal, such as the airplane model and spacecraft model. In this work, the flight control law is proposed using the neural-based inversion design method associated with the nonlinear compensation for a general longitudinal model of the airplane. First, the nonlinear mathematic model is converted to the equivalent linear model based on the feedback linearization theory. Then, the flight control law integrated with this inversion model is developed to stabilize the nonlinear system and relieve the coupling effect. Afterwards, the inversion control combined with the neural network and nonlinear portion is presented to improve the transient performance and attenuate the uncertain effects on both external disturbances and model errors. Finally, the simulation results demonstrate the effectiveness of this controller. PMID:29410680

Digital control of a direct current converter for a hybrid vehicle

NASA Astrophysics Data System (ADS)

Hernandez, Juan Manuel

The nonlinear feedback loops permitting the large signal control of pulse width modulators in direct current converters are discussed. A digital feedback loop on a converter controlling the coupling of a direct current machine is described. It is used in the propulsion of a hybrid vehicle (thermal-electric) with regenerative braking. The protection of the power switches is also studied. An active protection of the MOST bipolar transistor association is proposed.

Multiwavelength generation in a random distributed feedback fiber laser using an all fiber Lyot filter.

PubMed

Sugavanam, S; Yan, Z; Kamynin, V; Kurkov, A S; Zhang, L; Churkin, D V

2014-02-10

Multiwavelength lasing in the random distributed feedback fiber laser is demonstrated by employing an all fiber Lyot filter. Stable multiwavelength generation is obtained, with each line exhibiting sub-nanometer line-widths. A flat power distribution over multiple lines is obtained, which indicates that the power between lines is redistributed in nonlinear mixing processes. The multiwavelength generation is observed both in first and second Stokes waves.

Feasibility of a feedback control of atomic self-organization in an optical cavity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ivanov, D. A., E-mail: ivanov-den@yandex.ru; Ivanova, T. Yu.

Many interesting nonlinear effects are based on the strong interaction of motional degrees of freedom of atoms with an optical cavity field. Among them is the spatial self-organization of atoms in a pattern where the atoms group in either odd or even sites of the cavity-induced optical potential. An experimental observation of this effect can be simplified by using, along with the original cavity-induced feedback, an additional electronic feedback based on the detection of light leaking the cavity and the control of the optical potential for the atoms. Following our previous study, we show that this approach is more efficientmore » from the laser power perspective than the original scheme without the electronic feedback.« less

An accurate halo model for fitting non-linear cosmological power spectra and baryonic feedback models

NASA Astrophysics Data System (ADS)

Mead, A. J.; Peacock, J. A.; Heymans, C.; Joudaki, S.; Heavens, A. F.

2015-12-01

We present an optimized variant of the halo model, designed to produce accurate matter power spectra well into the non-linear regime for a wide range of cosmological models. To do this, we introduce physically motivated free parameters into the halo-model formalism and fit these to data from high-resolution N-body simulations. For a variety of Λ cold dark matter (ΛCDM) and wCDM models, the halo-model power is accurate to ≃ 5 per cent for k ≤ 10h Mpc-1 and z ≤ 2. An advantage of our new halo model is that it can be adapted to account for the effects of baryonic feedback on the power spectrum. We demonstrate this by fitting the halo model to power spectra from the OWLS (OverWhelmingly Large Simulations) hydrodynamical simulation suite via parameters that govern halo internal structure. We are able to fit all feedback models investigated at the 5 per cent level using only two free parameters, and we place limits on the range of these halo parameters for feedback models investigated by the OWLS simulations. Accurate predictions to high k are vital for weak-lensing surveys, and these halo parameters could be considered nuisance parameters to marginalize over in future analyses to mitigate uncertainty regarding the details of feedback. Finally, we investigate how lensing observables predicted by our model compare to those from simulations and from HALOFIT for a range of k-cuts and feedback models and quantify the angular scales at which these effects become important. Code to calculate power spectra from the model presented in this paper can be found at https://github.com/alexander-mead/hmcode.

Preliminary demonstration of a robust controller design method

NASA Technical Reports Server (NTRS)

Anderson, L. R.

1980-01-01

Alternative computational procedures for obtaining a feedback control law which yields a control signal based on measurable quantitites are evaluated. The three methods evaluated are: (1) the standard linear quadratic regulator design model; (2) minimization of the norm of the feedback matrix, k via nonlinear programming subject to the constraint that the closed loop eigenvalues be in a specified domain in the complex plane; and (3) maximize the angles between the closed loop eigenvectors in combination with minimizing the norm of K also via the constrained nonlinear programming. The third or robust design method was chosen to yield a closed loop system whose eigenvalues are insensitive to small changes in the A and B matrices. The relationship between orthogonality of closed loop eigenvectors and the sensitivity of closed loop eigenvalues is described. Computer programs are described.

Automatic Adaptation to Fast Input Changes in a Time-Invariant Neural Circuit

PubMed Central

Bharioke, Arjun; Chklovskii, Dmitri B.

2015-01-01

Neurons must faithfully encode signals that can vary over many orders of magnitude despite having only limited dynamic ranges. For a correlated signal, this dynamic range constraint can be relieved by subtracting away components of the signal that can be predicted from the past, a strategy known as predictive coding, that relies on learning the input statistics. However, the statistics of input natural signals can also vary over very short time scales e.g., following saccades across a visual scene. To maintain a reduced transmission cost to signals with rapidly varying statistics, neuronal circuits implementing predictive coding must also rapidly adapt their properties. Experimentally, in different sensory modalities, sensory neurons have shown such adaptations within 100 ms of an input change. Here, we show first that linear neurons connected in a feedback inhibitory circuit can implement predictive coding. We then show that adding a rectification nonlinearity to such a feedback inhibitory circuit allows it to automatically adapt and approximate the performance of an optimal linear predictive coding network, over a wide range of inputs, while keeping its underlying temporal and synaptic properties unchanged. We demonstrate that the resulting changes to the linearized temporal filters of this nonlinear network match the fast adaptations observed experimentally in different sensory modalities, in different vertebrate species. Therefore, the nonlinear feedback inhibitory network can provide automatic adaptation to fast varying signals, maintaining the dynamic range necessary for accurate neuronal transmission of natural inputs. PMID:26247884

Active disturbance rejection control based robust output feedback autopilot design for airbreathing hypersonic vehicles.

PubMed

Tian, Jiayi; Zhang, Shifeng; Zhang, Yinhui; Li, Tong

2018-03-01

Since motion control plant (y (n) =f(⋅)+d) was repeatedly used to exemplify how active disturbance rejection control (ADRC) works when it was proposed, the integral chain system subject to matched disturbances is always regarded as a canonical form and even misconstrued as the only form that ADRC is applicable to. In this paper, a systematic approach is first presented to apply ADRC to a generic nonlinear uncertain system with mismatched disturbances and a robust output feedback autopilot for an airbreathing hypersonic vehicle (AHV) is devised based on that. The key idea is to employ the feedback linearization (FL) and equivalent input disturbance (EID) technique to decouple nonlinear uncertain system into several subsystems in canonical form, thus it would be much easy to directly design classical/improved linear/nonlinear ADRC controller for each subsystem. It is noticed that all disturbances are taken into account when implementing FL rather than just omitting that in previous research, which greatly enhances controllers' robustness against external disturbances. For autopilot design, ADRC strategy enables precise tracking for velocity and altitude reference command in the presence of severe parametric perturbations and atmospheric disturbances only using measurable output information. Bounded-input-bounded-output (BIBO) stable is analyzed for closed-loop system. To illustrate the feasibility and superiority of this novel design, a series of comparative simulations with some prominent and representative methods are carried out on a benchmark longitudinal AHV model. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Hybrid associative memory using an incoherent correlation system

NASA Astrophysics Data System (ADS)

Taniguchi, Masaki; Ichioka, Yoshiki; Matsuoka, Katsunori

1990-10-01

A hybrid heteroassociative memory is presented that uses an incoherent system in which two correlators and a nonlinear element form a nonlinear feedback system. This system can recall any pattern from an input pattern without cross-talk or ghosts by properly designing a pair of filters installed in the correlators. Experiments on a simple hybrid system were performed to ensure the operation of the system and to demonstrate the usefulness of this proposed system.

Modelling and properties of a nonlinear autonomous switching system in fed-batch culture of glycerol

NASA Astrophysics Data System (ADS)

Wang, Juan; Sun, Qingying; Feng, Enmin

2012-11-01

A nonlinear autonomous switching system is proposed to describe the coupled fed-batch fermentation with the pH as the feedback parameter. We prove the non-Zeno behaviors of the switching system and some basic properties of its solution, including the existence, uniqueness, boundedness and regularity. Numerical simulation is also carried out, which reveals that the proposed system can describe the factual fermentation process properly.

Non-equilibrium phase transition in mesoscopic biochemical systems: from stochastic to nonlinear dynamics and beyond

PubMed Central

Ge, Hao; Qian, Hong

2011-01-01

A theory for an non-equilibrium phase transition in a driven biochemical network is presented. The theory is based on the chemical master equation (CME) formulation of mesoscopic biochemical reactions and the mathematical method of large deviations. The large deviations theory provides an analytical tool connecting the macroscopic multi-stability of an open chemical system with the multi-scale dynamics of its mesoscopic counterpart. It shows a corresponding non-equilibrium phase transition among multiple stochastic attractors. As an example, in the canonical phosphorylation–dephosphorylation system with feedback that exhibits bistability, we show that the non-equilibrium steady-state (NESS) phase transition has all the characteristics of classic equilibrium phase transition: Maxwell construction, a discontinuous first-derivative of the ‘free energy function’, Lee–Yang's zero for a generating function and a critical point that matches the cusp in nonlinear bifurcation theory. To the biochemical system, the mathematical analysis suggests three distinct timescales and needed levels of description. They are (i) molecular signalling, (ii) biochemical network nonlinear dynamics, and (iii) cellular evolution. For finite mesoscopic systems such as a cell, motions associated with (i) and (iii) are stochastic while that with (ii) is deterministic. Both (ii) and (iii) are emergent properties of a dynamic biochemical network. PMID:20466813

Guidance and Control strategies for aerospace vehicles

NASA Technical Reports Server (NTRS)

Hibey, J. L.; Naidu, D. S.; Charalambous, C. D.

1989-01-01

A neighboring optimal guidance scheme was devised for a nonlinear dynamic system with stochastic inputs and perfect measurements as applicable to fuel optimal control of an aeroassisted orbital transfer vehicle. For the deterministic nonlinear dynamic system describing the atmospheric maneuver, a nominal trajectory was determined. Then, a neighboring, optimal guidance scheme was obtained for open loop and closed loop control configurations. Taking modelling uncertainties into account, a linear, stochastic, neighboring optimal guidance scheme was devised. Finally, the optimal trajectory was approximated as the sum of the deterministic nominal trajectory and the stochastic neighboring optimal solution. Numerical results are presented for a typical vehicle. A fuel-optimal control problem in aeroassisted noncoplanar orbital transfer is also addressed. The equations of motion for the atmospheric maneuver are nonlinear and the optimal (nominal) trajectory and control are obtained. In order to follow the nominal trajectory under actual conditions, a neighboring optimum guidance scheme is designed using linear quadratic regulator theory for onboard real-time implementation. One of the state variables is used as the independent variable in reference to the time. The weighting matrices in the performance index are chosen by a combination of a heuristic method and an optimal modal approach. The necessary feedback control law is obtained in order to minimize the deviations from the nominal conditions.

Diversified pulse generation from frequency shifted feedback Tm-doped fibre lasers.

PubMed

Chen, He; Chen, Sheng-Ping; Jiang, Zong-Fu; Hou, Jing

2016-05-19

Pulsed fibre lasers operating in the eye-safe 2 μm spectral region have numerous potential applications in areas such as remote sensing, medicine, mid-infrared frequency conversion, and free-space communication. Here, for the first time, we demonstrate versatile 2 μm ps-ns pulses generation from Tm-based fibre lasers based on frequency shifted feedback and provide a comprehensive report of their special behaviors. The lasers are featured with elegant construction and the unparalleled capacity of generating versatile pulses. The self-starting mode-locking is initiated by an intra-cavity acousto-optical frequency shifter. Diversified mode-locked pulse dynamics were observed by altering the pump power, intra-cavity polarization state and cavity structure, including as short as 8 ps single pulse sequence, pulse bundle state and up to 12 nJ, 3 ns nanosecond rectangular pulse. A reflective nonlinear optical loop mirror was introduced to successfully shorten the pulses from 24 ps to 8 ps. Beside the mode-locking operation, flexible Q-switching and Q-switched mode-locking operation can also be readily achieved in the same cavity. Up to 78 μJ high energy nanosecond pulse can be generated in this regime. Several intriguing pulse dynamics are characterized and discussed.

Complex metabolic oscillations in plants forced by harmonic irradiance.

PubMed Central

Nedbal, Ladislav; Brezina, Vítezslav

2002-01-01

Plants exposed to harmonically modulated irradiance, approximately 1 + cos(omegat), exhibit a complex periodic pattern of chlorophyll fluorescence emission that can be deconvoluted into a steady-state component, a component that is modulated with the frequency of the irradiance (omega), and into at least two upper harmonic components (2omega and 3omega). A model is proposed that accounts for the upper harmonics in fluorescence emission by nonlinear negative feedback regulation of photosynthesis. In contrast to simpler linear models, the model predicts that the steady-state fluorescence component will depend on the frequency of light modulation, and that amplitudes of all fluorescence components will exhibit resonance peak(s) when the irradiance frequency is tuned to an internal frequency of a regulatory component. The experiments confirmed that the upper harmonic components appear and exhibit distinct resonant peaks. The frequency of autonomous oscillations observed earlier upon an abrupt increase in CO(2) concentration corresponds to the sharpest of the resonant peaks of the forced oscillations. We propose that the underlying principles are general for a wide spectrum of negative-feedback regulatory mechanisms. The analysis by forced harmonic oscillations will enable us to examine internal dynamics of regulatory processes that have not been accessible to noninvasive fluorescence monitoring to date. PMID:12324435

The Generation of Harmonic Distortion and Distortion Products in a Computational Model of the Cochlea

NASA Astrophysics Data System (ADS)

Meaud, Julien; Li, Yizeng; Grosh, Karl

2011-11-01

It is generally agreed that the nonlinear response of the cochlea is due to the forward transduction of the outer hair cell (OHC) hair bundle (HB) and subsequent alteration of the active force applied to the cochlear structures, including the basilar membrane (BM). A mechanical-acoustical-electrical model of the cochlea with three-dimensional fluid representation, and feedback from OHC somatic motility coupled to nonlinear HB mechanotransduction is used to predict nonlinear distortion of the BM response to acoustic stimulus. An efficient alternating frequency time scheme is implemented to solve for the nonlinear stationary dynamics of the cochlea. The model is used to predict the location of maximum generation of nonlinear distortion during pure tone and two-tone stimulation as well as the propagation of the distortion components on the BM.

Gain optimization with non-linear controls

NASA Technical Reports Server (NTRS)

Slater, G. L.; Kandadai, R. D.

1984-01-01

An algorithm has been developed for the analysis and design of controls for non-linear systems. The technical approach is to use statistical linearization to model the non-linear dynamics of a system by a quasi-Gaussian model. A covariance analysis is performed to determine the behavior of the dynamical system and a quadratic cost function. Expressions for the cost function and its derivatives are determined so that numerical optimization techniques can be applied to determine optimal feedback laws. The primary application for this paper is centered about the design of controls for nominally linear systems but where the controls are saturated or limited by fixed constraints. The analysis is general, however, and numerical computation requires only that the specific non-linearity be considered in the analysis.

Adaptive nonlinear control for autonomous ground vehicles

NASA Astrophysics Data System (ADS)

Black, William S.

We present the background and motivation for ground vehicle autonomy, and focus on uses for space-exploration. Using a simple design example of an autonomous ground vehicle we derive the equations of motion. After providing the mathematical background for nonlinear systems and control we present two common methods for exactly linearizing nonlinear systems, feedback linearization and backstepping. We use these in combination with three adaptive control methods: model reference adaptive control, adaptive sliding mode control, and extremum-seeking model reference adaptive control. We show the performances of each combination through several simulation results. We then consider disturbances in the system, and design nonlinear disturbance observers for both single-input-single-output and multi-input-multi-output systems. Finally, we show the performance of these observers with simulation results.

Anti-sway control of tethered satellite systems using attitude control of the main satellite

NASA Astrophysics Data System (ADS)

Yousefian, Peyman; Salarieh, Hassan

2015-06-01

In this study a new method is introduced to suppress libration of a tethered satellite system (TSS). It benefits from coupling between satellites and tether libration dynamics. The control concept uses the main satellite attitude maneuvers to suppress librational motion of the tether, and the main satellite's actuators for attitude control are used as the only actuation in the system. The study considers planar motion of a two body TSS system in a circular orbit and it is assumed that the tether's motion will not change it. Governing dynamic equations of motion are derived using the extended Lagrange method. Controllability of the system around the equilibrium state is studied and a linear LQG controller is designed to regulate libration of the system. Tether tension and satellite attitude are assumed as only measurable outputs of the system. The Extended Kalman Filter (EKF) is used to estimate states of the system to be used as feedback to the controller. The designed controller and observer are implemented to the nonlinear plant and simulations demonstrate that the controller lead to reduction of the tether libration propoerly. By the way, because the controller is linear, it is applicable only at low amplitudes in the vicinity of equilibrium point. To reach global stability, a nonlinear controller is demanded.

Data-driven robust approximate optimal tracking control for unknown general nonlinear systems using adaptive dynamic programming method.

PubMed

Zhang, Huaguang; Cui, Lili; Zhang, Xin; Luo, Yanhong

2011-12-01

In this paper, a novel data-driven robust approximate optimal tracking control scheme is proposed for unknown general nonlinear systems by using the adaptive dynamic programming (ADP) method. In the design of the controller, only available input-output data is required instead of known system dynamics. A data-driven model is established by a recurrent neural network (NN) to reconstruct the unknown system dynamics using available input-output data. By adding a novel adjustable term related to the modeling error, the resultant modeling error is first guaranteed to converge to zero. Then, based on the obtained data-driven model, the ADP method is utilized to design the approximate optimal tracking controller, which consists of the steady-state controller and the optimal feedback controller. Further, a robustifying term is developed to compensate for the NN approximation errors introduced by implementing the ADP method. Based on Lyapunov approach, stability analysis of the closed-loop system is performed to show that the proposed controller guarantees the system state asymptotically tracking the desired trajectory. Additionally, the obtained control input is proven to be close to the optimal control input within a small bound. Finally, two numerical examples are used to demonstrate the effectiveness of the proposed control scheme.

A nonlinear optimal control approach to stabilization of a macroeconomic development model

NASA Astrophysics Data System (ADS)

Rigatos, G.; Siano, P.; Ghosh, T.; Sarno, D.

2017-11-01

A nonlinear optimal (H-infinity) control approach is proposed for the problem of stabilization of the dynamics of a macroeconomic development model that is known as the Grossman-Helpman model of endogenous product cycles. The dynamics of the macroeconomic development model is divided in two parts. The first one describes economic activities in a developed country and the second part describes variation of economic activities in a country under development which tries to modify its production so as to serve the needs of the developed country. The article shows that through control of the macroeconomic model of the developed country, one can finally control the dynamics of the economy in the country under development. The control method through which this is achieved is the nonlinear H-infinity control. The macroeconomic model for the country under development undergoes approximate linearization round a temporary operating point. This is defined at each time instant by the present value of the system's state vector and the last value of the control input vector that was exerted on it. The linearization is based on Taylor series expansion and the computation of the associated Jacobian matrices. For the linearized model an H-infinity feedback controller is computed. The controller's gain is calculated by solving an algebraic Riccati equation at each iteration of the control method. The asymptotic stability of the control approach is proven through Lyapunov analysis. This assures that the state variables of the macroeconomic model of the country under development will finally converge to the designated reference values.

Modeling heart rate variability by stochastic feedback

NASA Technical Reports Server (NTRS)

Amaral, L. A.; Goldberger, A. L.; Stanley, H. E.

1999-01-01

We consider the question of how the cardiac rhythm spontaneously self-regulates and propose a new mechanism as a possible answer. We model the neuroautonomic regulation of the heart rate as a stochastic feedback system and find that the model successfully accounts for key characteristics of cardiac variability, including the 1/f power spectrum, the functional form and scaling of the distribution of variations of the interbeat intervals, and the correlations in the Fourier phases which indicate nonlinear dynamics.