Nonlinear filter based decision feedback equalizer for optical communication systems.
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.
Nonlinear system identification and control based on modular neural networks.
Puscasu, Gheorghe; Codres, Bogdan
2011-08-01
A new approach for nonlinear system identification and control based on modular neural networks (MNN) is proposed in this paper. The computational complexity of neural identification can be greatly reduced if the whole system is decomposed into several subsystems. This is obtained using a partitioning algorithm. Each local nonlinear model is associated with a nonlinear controller. These are also implemented by neural networks. The switching between the neural controllers is done by a dynamical switcher, also implemented by neural networks, that tracks the different operating points. The proposed multiple modelling and control strategy has been successfully tested on simulated laboratory scale liquid-level system.
Observer Based Compensators for Nonlinear Systems
1989-03-31
Automation, vol. 4, no. 1, 1988. [42] Poincare, H., Oeuvres, Tome 1, Gauthier- Villars , Paris, 1928. [43] Su, R., "On the linear equivalents of nonlinear...Control Theory, M. Fliess and M. Hazewinkel (eds.). D. Reidel, Dordrehct, to appear. [161 H. Poincare, Oeuvres, Tome 1 (Gauthier- Villars , Paris 1928). 117...one can choose a metric G on N .M G [ Gil 0 (49 def ffL (2)_ i(2) +() 2 G 0 (49) QP(x,u)dxdu (42) 2 and find a solution to 7(2) min I 1 (50) We want to
Nonlinear system identification based on internal recurrent neural networks.
Puscasu, Gheorghe; Codres, Bogdan; Stancu, Alexandru; Murariu, Gabriel
2009-04-01
A novel approach for nonlinear complex system identification based on internal recurrent neural networks (IRNN) is proposed in this paper. The computational complexity of neural identification can be greatly reduced if the whole system is decomposed into several subsystems. This approach employs internal state estimation when no measurements coming from the sensors are available for the system states. A modified backpropagation algorithm is introduced in order to train the IRNN for nonlinear system identification. The performance of the proposed design approach is proven on a car simulator case study.
Adaptive Neural Network Based Control of Noncanonical Nonlinear Systems.
Zhang, Yanjun; Tao, Gang; Chen, Mou
2016-09-01
This paper presents a new study on the adaptive neural network-based control of a class of noncanonical nonlinear systems with large parametric uncertainties. Unlike commonly studied canonical form nonlinear systems whose neural network approximation system models have explicit relative degree structures, which can directly be used to derive parameterized controllers for adaptation, noncanonical form nonlinear systems usually do not have explicit relative degrees, and thus their approximation system models are also in noncanonical forms. It is well-known that the adaptive control of noncanonical form nonlinear systems involves the parameterization of system dynamics. As demonstrated in this paper, it is also the case for noncanonical neural network approximation system models. Effective control of such systems is an open research problem, especially in the presence of uncertain parameters. This paper shows that it is necessary to reparameterize such neural network system models for adaptive control design, and that such reparameterization can be realized using a relative degree formulation, a concept yet to be studied for general neural network system models. This paper then derives the parameterized controllers that guarantee closed-loop stability and asymptotic output tracking for noncanonical form neural network system models. An illustrative example is presented with the simulation results to demonstrate the control design procedure, and to verify the effectiveness of such a new design method.
Nonlinear control structures based on embedded neural system models.
Lightbody, G; Irwin, G W
1997-01-01
This paper investigates in detail the possible application of neural networks to the modeling and adaptive control of nonlinear systems. Nonlinear neural-network-based plant modeling is first discussed, based on the approximation capabilities of the multilayer perceptron. A structure is then proposed to utilize feedforward networks within a direct model reference adaptive control strategy. The difficulties involved in training this network, embedded within the closed-loop are discussed and a novel neural-network-based sensitivity modeling approach proposed to allow for the backpropagation of errors through the plant to the neural controller. Finally, a novel nonlinear internal model control (IMC) strategy is suggested, that utilizes a nonlinear neural model of the plant to generate parameter estimates over the nonlinear operating region for an adaptive linear internal model, without the problems associated with recursive parameter identification algorithms. Unlike other neural IMC approaches the linear control law can then be readily designed. A continuous stirred tank reactor was chosen as a realistic nonlinear case study for the techniques discussed in the paper.
Ding, Bo; Fang, Huajing
2017-03-31
This paper is concerned with the fault prediction for the nonlinear stochastic system with incipient faults. Based on the particle filter and the reasonable assumption about the incipient faults, the modified fault estimation algorithm is proposed, and the system state is estimated simultaneously. According to the modified fault estimation, an intuitive fault detection strategy is introduced. Once each of the incipient fault is detected, the parameters of which are identified by a nonlinear regression method. Then, based on the estimated parameters, the future fault signal can be predicted. Finally, the effectiveness of the proposed method is verified by the simulations of the Three-tank system.
Seismic analysis of series isolation system based on geometry nonlinearity
NASA Astrophysics Data System (ADS)
Lin, Z. D.; Shi, H.; Xue, L.
2017-08-01
According to the system of rubber bearing serially connected with column, the mathematical model of serially isolated system based on geometric nonlinear is investigated by using Hamilton’s principle. The effects of axial pressure and difference column size to the series isolation system in seismic response is discussed. The series isolation system dynamics model based on geometric nonlinear is established considering the cross section rotated and the influence of the shear deformation and axial pressure. The differential quadrature element method is employed for discrete processing on governing equations and boundary conditions. Seismic response of series isolation system subjected to the far-field ground motions is solved numerically. Results show that: the slenderness ratio of cantilever column will significantly affect the seismic response of the isolation system under far-field ground motions, and it is particularly to response of the cantilever column.
Observer-based controller for nonlinear analytical systems
NASA Astrophysics Data System (ADS)
Elloumi, S.; Belhouane, M. M.; Benhadj Braiek, N.
2016-06-01
In this paper, we propose to design a polynomial observer-based control for nonlinear systems and to determine sufficient linear matrix inequality (LMI) global stabilisation conditions of the polynomial controlled system augmented by its observer. The design of the observer-based control leverages some notations from the Kronecker product and the power of matrices properties for the state space description of polynomial systems. The stability study of the polynomial controlled system augmented by its observer is based on the Lyapunov stability direct method. Intensive simulations are performed to illustrate the validity and the effectiveness of the polynomial approach used to design the control.
NASA Astrophysics Data System (ADS)
Deng, Mingcong; Bi, Shuhui
2010-09-01
In this article, operator-based robust nonlinear control system design for multi-input multi-output (MIMO) plants with unknown coupling effects is considered. That is, by using operator-based robust nonlinear control design, coupling effects existing in the MIMO nonlinear plants can be decoupled based on a feedback design and robust right coprime factorisation approach, the coupling effects caused by controllers and plant outputs can be stabilised by using definition of Lipschitz operator and contraction mapping theorem, and output tracking performance can be realised by a tracking design scheme. Finally, a simulation example about temperature control process of 3-input/3-output aluminum plate is given to support the theoretical analysis.
Optimum Damping in a Non-Linear Base Isolation System
NASA Astrophysics Data System (ADS)
Jangid, R. S.
1996-02-01
Optimum isolation damping for minimum acceleration of a base-isolated structure subjected to earthquake ground excitation is investigated. The stochastic model of the El-Centro1940 earthquake, which preserves the non-stationary evolution of amplitude and frequency content of ground motion, is used as an earthquake excitation. The base isolated structure consists of a linear flexible shear type multi-storey building supported on a base isolation system. The resilient-friction base isolator (R-FBI) is considered as an isolation system. The non-stationary stochastic response of the system is obtained by the time dependent equivalent linearization technique as the force-deformation of the R-FBI system is non-linear. The optimum damping of the R-FBI system is obtained under important parametric variations; i.e., the coefficient of friction of the R-FBI system, the period and damping of the superstructure; the effective period of base isolation. The criterion selected for optimality is the minimization of the top floor root mean square (r.m.s.) acceleration. It is shown that the above parameters have significant effects on optimum isolation damping.
Network-Based Practical Consensus of Heterogeneous Nonlinear Multiagent Systems.
Ding, Lei; Zheng, Wei Xing
2016-09-07
This paper studies network-based practical leader-following consensus problem of heterogeneous multiagent systems with Lipschitz nonlinear dynamics under both fixed and switching topologies. Considering the effect of network-induced delay, a network-based leader-following consensus protocol with heterogeneous gain matrix is proposed for each follower agent. By employing Lyapunov-Krasovskii method, a sufficient condition for designing the network-based consensus controller gain is derived such that the leader-following consensus error exponentially converges to a bounded region under a fixed topology. Correspondingly, the proposed design approach is then extended to the case of switching topology. Two numerical examples with networked Chua's circuits are given to show the efficiency of the design method proposed in this paper.
General purpose nonlinear system solver based on Newton-Krylov method.
2013-12-01
KINSOL is part of a software family called SUNDIALS: SUite of Nonlinear and Differential/Algebraic equation Solvers [1]. KINSOL is a general-purpose nonlinear system solver based on Newton-Krylov and fixed-point solver technologies [2].
Fuzzy model-based servo and model following control for nonlinear systems.
Ohtake, Hiroshi; Tanaka, Kazuo; Wang, Hua O
2009-12-01
This correspondence presents servo and nonlinear model following controls for a class of nonlinear systems using the Takagi-Sugeno fuzzy model-based control approach. First, the construction method of the augmented fuzzy system for continuous-time nonlinear systems is proposed by differentiating the original nonlinear system. Second, the dynamic fuzzy servo controller and the dynamic fuzzy model following controller, which can make outputs of the nonlinear system converge to target points and to outputs of the reference system, respectively, are introduced. Finally, the servo and model following controller design conditions are given in terms of linear matrix inequalities. Design examples illustrate the utility of this approach.
ERIC Educational Resources Information Center
Seider, Warren D.; Ungar, Lyle H.
1987-01-01
Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…
ERIC Educational Resources Information Center
Seider, Warren D.; Ungar, Lyle H.
1987-01-01
Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…
NASA Astrophysics Data System (ADS)
Komatsu, Kazuo; Takata, Hitoshi
2012-11-01
In this paper, we consider an observer design by using a formal linearization based on Fourier expansion for nonlinear dynamic and measurement systems. A non-linear dynamic system is given by a nonlinear ordinary differential equation, and a measurement sysetm is done by a nonlinear equation. Defining a linearization function which consists of the trigonometric functions considered up to the higher-order, a nonlinear dynamic system is transformed into an augmented linear one with respect to this linearization function by using Fourier expansion. Introducing an augmented measurement vector which consists of polynomials of measurement data, a measurement equation is transformed into an augmented linear one with respect to the linearization function in the same way. To these augmented linearized systems, a linear estimation theory is applied to design a new non-linear observer.
2007-03-01
Nonlinear Time-Variant Response in an Avalanche Photodiode Array Based Laser Detection and Ranging System THESIS Michael D. Seal, Captain, USAF AFIT...DISTRIBUTION UNLIMITED. AFIT/GEO/ENG/07-03 Nonlinear Time-Variant Response in an Avalanche Photodiode Array Based Laser Detection and Ranging System...time-variant behavior exhibited by an avalanche photodiode (APD) array based laser ranging and detec- tion (LADAR) system. This examination was
Nonlinear systems in medicine.
Higgins, John P.
2002-01-01
Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states. PMID:14580107
Strong vibration nonlinearity in semiconductor-based nanomechanical systems
NASA Astrophysics Data System (ADS)
Moskovtsev, Kirill; Dykman, M. I.
2017-02-01
We study the effect of the electron-phonon coupling on vibrational eigenmodes of nano- and micromechanical systems made of semiconductors with equivalent energy valleys. We show that the coupling can lead to a strong mode nonlinearity. The mechanism is the lifting of the valley degeneracy by the strain. The redistribution of the electrons between the valleys is controlled by a large ratio of the electron-phonon coupling constant to the electron chemical potential or temperature. We find the quartic in the strain terms in the electron free energy, which determine the amplitude dependence of the mode frequencies. This dependence is calculated for silicon microsystems. It is significantly different for different modes and the crystal orientation, and can vary nonmonotonously with the electron density and temperature.
NASA Astrophysics Data System (ADS)
Yang, Jun; Li, Shihua; Chen, Wen-Hua
2012-08-01
For a multi-input multi-output (MIMO) nonlinear system, the existing disturbance observer-based control (DOBC) only provides solutions to those whose disturbance relative degree (DRD) is higher than or equal to its input relative degree. By designing a novel disturbance compensation gain matrix, a generalised nonlinear DOBC method is proposed in this article to solve the disturbance attenuation problem of the MIMO nonlinear system with arbitrary DRD. It is shown that the disturbances are able to be removed from the output channels by the proposed method with appropriately chosen control parameters. The property of nominal performance recovery, which is the major merit of the DOBCs, is retained with the proposed method. The feasibility and effectiveness of the proposed method are demonstrated by simulation studies of both the numerical and application examples.
Zhang, Yajun; Chai, Tianyou; Wang, Hong
2011-11-01
This paper presents a novel nonlinear control strategy for a class of uncertain single-input and single-output discrete-time nonlinear systems with unstable zero-dynamics. The proposed method combines adaptive-network-based fuzzy inference system (ANFIS) with multiple models, where a linear robust controller, an ANFIS-based nonlinear controller and a switching mechanism are integrated using multiple models technique. It has been shown that the linear controller can ensure the boundedness of the input and output signals and the nonlinear controller can improve the dynamic performance of the closed loop system. Moreover, it has also been shown that the use of the switching mechanism can simultaneously guarantee the closed loop stability and improve its performance. As a result, the controller has the following three outstanding features compared with existing control strategies. First, this method relaxes the assumption of commonly-used uniform boundedness on the unmodeled dynamics and thus enhances its applicability. Second, since ANFIS is used to estimate and compensate the effect caused by the unmodeled dynamics, the convergence rate of neural network learning has been increased. Third, a "one-to-one mapping" technique is adapted to guarantee the universal approximation property of ANFIS. The proposed controller is applied to a numerical example and a pulverizing process of an alumina sintering system, respectively, where its effectiveness has been justified.
Command Filtering-Based Fuzzy Control for Nonlinear Systems With Saturation Input.
Yu, Jinpeng; Shi, Peng; Dong, Wenjie; Lin, Chong
2017-09-01
In this paper, command filtering-based fuzzy control is designed for uncertain multi-input multioutput (MIMO) nonlinear systems with saturation nonlinearity input. First, the command filtering method is employed to deal with the explosion of complexity caused by the derivative of virtual controllers. Then, fuzzy logic systems are utilized to approximate the nonlinear functions of MIMO systems. Furthermore, error compensation mechanism is introduced to overcome the drawback of the dynamics surface approach. The developed method will guarantee all signals of the systems are bounded. The effectiveness and advantages of the theoretic result are obtained by a simulation example.
Filtering by nonlinear systems.
Campos Cantón, E; González Salas, J S; Urías, J
2008-12-01
Synchronization of nonlinear systems forced by external signals is formalized as the response of a nonlinear filter. Sufficient conditions for a nonlinear system to behave as a filter are given. Some examples of generalized chaos synchronization are shown to actually be special cases of nonlinear filtering.
Observer-based robust control of one-sided Lipschitz nonlinear systems.
Ahmad, Sohaira; Rehan, Muhammad; Hong, Keum-Shik
2016-11-01
This paper presents an observer-based controller design for the class of nonlinear systems with time-varying parametric uncertainties and norm-bounded disturbances. The design methodology, for the less conservative one-sided Lipschitz nonlinear systems, involves astute utilization of Young's inequality and several matrix decompositions. A sufficient condition for simultaneous extraction of observer and controller gains is stipulated by a numerically tractable set of convex optimization conditions. The constraints are handled by a nonlinear iterative cone-complementary linearization method in obtaining gain matrices. Further, an observer-based control technique for one-sided Lipschitz nonlinear systems, robust against L2-norm-bounded perturbations, is contrived. The proposed methodology ensures robustness against parametric uncertainties and external perturbations. Simulation examples demonstrating the effectiveness of the proposed methodologies are presented.
Lyapunov based nonlinear control of electrical and mechanical systems
NASA Astrophysics Data System (ADS)
Behal, Aman
fusing a filtered tracking error transformation with the dynamic oscillator design presented in [20]. The proposed tracking controller yields a GUUB result for the regulation problem also. In the final chapter, a nonlinear controller is designed for the kinematic model of an underactuated rigid spacecraft that ensures uniform, ultimately bounded (UUB) tracking provided the initial errors are selected sufficiently small. The result is achieved via a judicious formulation of the spacecraft kinematics and the novel design of a Lyapunov-based controller. It is also demonstrated how standard backstepping control techniques can be fused with the kinematic controller to solve the full-order regulation problem for an axisymmetric spacecraft. Simulation results are included to demonstrate the efficacy of the proposed algorithm. 1It is to be noted that the controller presented in [16] was originally designed to obtain exponential rotor position /rotor flux tracking for the full-order induction motor model (i.e., stator current dynamics are included).
Estimating nonlinear interdependences in dynamical systems using cellular nonlinear networks
NASA Astrophysics Data System (ADS)
Krug, Dieter; Osterhage, Hannes; Elger, Christian E.; Lehnertz, Klaus
2007-10-01
We propose a method for estimating nonlinear interdependences between time series using cellular nonlinear networks. Our approach is based on the nonlinear dynamics of interacting nonlinear elements. We apply it to time series of coupled nonlinear model systems and to electroencephalographic time series from an epilepsy patient, and we show that an accurate approximation of symmetric and asymmetric realizations of a nonlinear interdependence measure can be achieved, thus allowing one to detect the strength and direction of couplings.
Robust Model-Based Sensor Fault Monitoring System for Nonlinear Systems in Sensor Networks
Wang, Dejun; Song, Shiyao
2014-01-01
A new model-based sensor fault diagnosis (FD) scheme, using an equivalent model, is developed for a kind of Multiple Inputs Multiple Outputs (MIMO) nonlinear system which fulfills the Lipschitz condition. The equivalent model, which is a bank of one-dimensional linear state equations with the bounded model uncertainty, can take the place of a plant's exact nonlinear model in the case of sensor FD. This scheme shows a new perspective whereby, by using the equivalent model, it doesn't have to study the nonlinear internal structure character or get the exact model. The influence of the model uncertainty on the residuals is explained in this paper. A method, called pretreatment, is utilized to minimize the model uncertainty. The eigenstructure assignment method with assistant state is employed to solve the problem of perfect decoupling against the model uncertainty, disturbance, system faults, the relevant actuator faults, or even the case of no input from the relevant actuator. The realization of the proposed scheme is given by an algorithm according to a single sensor FD, and verified by a simulation example. Depending on the above, a sensor fault monitoring system is established by the sensor network and diagnosis logic, then the effectiveness is testified by a simulation. PMID:25320904
Dynamic neural network-based robust observers for uncertain nonlinear systems.
Dinh, H T; Kamalapurkar, R; Bhasin, S; Dixon, W E
2014-12-01
A dynamic neural network (DNN) based robust observer for uncertain nonlinear systems is developed. The observer structure consists of a DNN to estimate the system dynamics on-line, a dynamic filter to estimate the unmeasurable state and a sliding mode feedback term to account for modeling errors and exogenous disturbances. The observed states are proven to asymptotically converge to the system states of high-order uncertain nonlinear systems through Lyapunov-based analysis. Simulations and experiments on a two-link robot manipulator are performed to show the effectiveness of the proposed method in comparison to several other state estimation methods.
NASA Astrophysics Data System (ADS)
Royston, T. J.; Singh, R.
1996-07-01
While significant non-linear behavior has been observed in many vibration mounting applications, most design studies are typically based on the concept of linear system theory in terms of force or motion transmissibility. In this paper, an improved analytical strategy is presented for the design optimization of complex, active of passive, non-linear mounting systems. This strategy is built upon the computational Galerkin method of weighted residuals, and incorporates order reduction and numerical continuation in an iterative optimization scheme. The overall dynamic characteristics of the mounting system are considered and vibratory power transmission is minimized via adjustment of mount parameters by using both passive and active means. The method is first applied through a computational example case to the optimization of basic passive and active, non-linear isolation configurations. It is found that either active control or intentionally introduced non-linearity can improve the mount's performance; but a combination of both produces the greatest benefit. Next, a novel experimental, active, non-linear isolation system is studied. The effect of non-linearity on vibratory power transmission and active control are assessed via experimental measurements and the enhanced Galerkin method. Results show how harmonic excitation can result in multiharmonic vibratory power transmission. The proposed optimization strategy offers designers some flexibility in utilizing both passive and active means in combination with linear and non-linear components for improved vibration mounts.
Adhesive nonlinearity in Lamb-wave-based structural health monitoring systems
NASA Astrophysics Data System (ADS)
Shan, Shengbo; Cheng, Li; Li, Peng
2017-02-01
Structural health monitoring (SHM) techniques with nonlinear Lamb waves have gained wide popularity due to their high sensitivity to microstructural changes for the detection of damage precursors. Despite the significant progress made, various unavoidable nonlinear sources in a practical SHM system, as well as their impact on the detection, have not been fully assessed and understood. For the real-time and online monitoring, transducers are usually permanently bonded on the structure under inspection. In this case, the inherent material nonlinear properties of the bonding layer, referred to as adhesive nonlinearity (AN), may create undesired interference to the SHM system, or even jeopardize the damage diagnosis if they become serious. In this paper, a nonlinear theoretical framework is developed, covering the process of wave generation, propagation and sensing, with the aim of investigating the mechanism and characteristics of AN-induced Lamb waves in plates, which potentially allows for further system optimization to minimize the influence of AN. The model shows that an equivalent nonlinear normal stress is generated in the bonding layer due to its nonlinear material behavior, which, through its coupling with the system, is responsible for the generation of second harmonic Lamb waves in the plate, subsequently resulting in the nonlinear responses in the captured signals. With the aid of the finite element (FE) modeling and a superposition method for nonlinear feature extraction, the theoretical model is validated in terms of generation mechanism of the AN-induced wave components as well as their propagating characteristics. Meanwhile, the influence of the AN is evaluated by comparing the AN-induced nonlinear responses with those caused by the material nonlinearity of the plate, showing that AN should be considered as a non-negligible nonlinear source in a typical nonlinear Lamb-wave-based SHM system. In addition, the theoretical model is also experimentally
NASA Astrophysics Data System (ADS)
Skwara, B.; Loboda, O.; Avramopoulos, A.; Luis, J.-M.; Reis, H.; Papadopoulos, M. G.
2012-12-01
Recent studies of the linear and nonlinear electric properties of various fullerene-based subsystems are reviewed. The electric properties of derivatives of C60 fullerene with carbazole, benzothiazole, benzothiazole-triphenyloamine and free-base porphyrin substituents at different levels of theory are summarized. In addition, the electronic and vibrational electric properties of endohedral Sc2@C72 system are reported.
H∞ consensus and synchronization of nonlinear systems based on a novel fuzzy model.
Zhao, Yan; Li, Bing; Qin, Jiahu; Gao, Huijun; Karimi, Hamid Reza
2013-12-01
This paper investigates the H∞ consensus control problem of nonlinear multiagent systems under an arbitrary topological structure. A novel Takagi-Sukeno (T-S) fuzzy modeling method is proposed to describe the problem of nonlinear follower agents approaching a time-varying leader, i.e., the error dynamics between the follower agents and the leader, whose dynamics is evolving according to an isolated unforced nonlinear agent model, is described as a set of T-S fuzzy models. Based on the model, a leader-following consensus algorithm is designed so that, under an arbitrary network topology, all the follower agents reach consensus with the leader subject to external disturbances, preserving a guaranteed H(∞) performance level. In addition, we obtain a sufficient condition for choosing the pinned nodes to make the entire multiagent network reach consensus. Moreover, the fuzzy modeling method is extended to solve the synchronization problem of nonlinear systems, and a fuzzy H(∞) controller is designed so that two nonlinear systems reach synchronization with a prescribed H(∞) performance level. The controller design procedure is greatly simplified by utilization of the proposed fuzzy modeling method. Finally, numerical simulations on chaotic systems and arbitrary nonlinear functions are provided to illustrate the effectiveness of the obtained theoretical results.
Hamedi, H R; Gharamaleki, Ali Hamrah; Sahrai, Mostafa
2016-08-01
The paper is aimed at modeling the enhanced Kerr nonlinearity in a five-level double-ladder-type atomic system based on electromagnetically induced transparency (EIT) by using the semi-classical density matrix method. We present an analytical model to explain the origin of Kerr nonlinearity enhancement. The scheme also results in a several orders of magnitude increase in the Kerr nonlinearity in comparison with the well-known four- and three-level atomic systems. In addition to the steady-state case, the time-dependent Kerr nonlinearity and the switching feature of EIT-based colossal Kerr nonlinearity is investigated for the proposed system.
Detection of micro-cracks using nonlinear lamb waves based on the Duffing-Holmes system
NASA Astrophysics Data System (ADS)
Liu, Xiaofeng; Bo, Lin; Liu, Yaolu; Zhao, Youxuan; Zhang, Jun; Hu, Ning; Fu, Shaoyun; Deng, Mingxi
2017-09-01
To solve the problem that weak nonlinear Lamb waves caused by micro-cracks are often buried in background noises, a Duffing-Holmes system was used to enhance the weak nonlinear Lamb waves and the crack size was quantitatively characterized using Lyapunov exponent(LE). The frequency and amplitude critical threshold of the external driving force were determined according to the center frequency of excitation signal and the Poincaré map of the Duffing-Holmes oscillator, respectively. After periodic extending and filtering, the Lamb waves were input to the Duffing-Holmes system, and then the nonlinear second harmonic was identified according to the phase trajectory and Poincaré map. Based on the phase space reconstruction of Duffing system output, the maximal LE was calculated to characterize the magnitude of the second harmonic. Based on S0 Lamb wave mode, the simulations on models with different micro-crack sizes showed that the Duffing-Holmes system could accurately identify the structural micro-cracks under strong noise interference. Compared with the traditional acoustic nonlinearity parameter β‧, the damage index defined here had a better linear relationship with the crack size, and the micro-cracks could be accurately quantified. The proposed method has obvious advantages for the detection of micro-crack defects under noise interference, and can greatly improve the sensitivity of nonlinear Lamb waves detection.
Quasi-ARX wavelet network for SVR based nonlinear system identification
NASA Astrophysics Data System (ADS)
Cheng, Yu; Wang, Lan; Hu, Jinglu
In this paper, quasi-ARX wavelet network (Q-ARX-WN) is proposed for nonlinear system identification. There are mainly two contributions are clarified. Firstly, compared with conventional wavelet networks (WNs), it is equipped with a linear structure, where WN is incorporated to interpret parameters of the linear ARX structure, thus Q-ARX-WN prediction model could be constructed and it is easy-to-use in nonlinear control. Secondly, guidelines for network construction are well considered due to the introduction of WNs, and Q-ARX-WN could be represented in a linear-in-parameter way. Therefore, linear support vector regression (SVR) based identification scheme may be introduced for the robust performance. Moreover, in adaptive control procedure, only linear parameters are needed to be adjusted when sudden changes have happened on the nonlinear system, thus the controller can track reference signal quickly. The effectiveness and robustness of the proposed nonlinear system identification method are validated by applying it to identify a real data system and a mathematical example, and an example of nonlinear system control is given to show usefulness of the proposed model.
NASA Technical Reports Server (NTRS)
Babcock, P. S., IV
1986-01-01
Nonlinear system controller design based on the domain of attraction is presented. This is particularly suited to investigating Closed Ecological Life Support Systems (CELSS) models. In particular, the dynamic consequences of changes in the waste storage capacity and system mass, and how information is used for control in CELSS models are examined. The models' high dimensionality and nonlinear state equations make them difficult to analyze by any other technique. The domain of attraction is the region in initial conditions that tend toward an attractor and it is delineated by randomly selecting initial conditions from the region of state space being investigated. Error analysis is done by repeating the domain simulations with independent samples. A refinement of this region is the domain of performance which is the region of initial conditions meeting a performance criteria. In nonlinear systems, local stability does not insure stability over a larger region. The domain of attraction marks out this stability region; hence, it can be considered a measure of a nonlinear system's ability to recovery from state perturbations. Considering random perturbations, the minimum radius of the domain is a measure of the magnitude of perturbations for which recovery is guaranteed. Design of both linear and nonlinear controllers are shown. Three CELSS models, with 9 to 30 state variable, are presented. Measures of the domain of attraction are used to show the global behavior of these models under a variety of design and controller scenarios.
NASA Astrophysics Data System (ADS)
Rigatos, Gerasimos
2016-07-01
The Derivative-free nonlinear Kalman Filter is used for developing a communication system that is based on a chaotic modulator such as the Duffing system. In the transmitter's side, the source of information undergoes modulation (encryption) in which a chaotic signal generated by the Duffing system is the carrier. The modulated signal is transmitted through a communication channel and at the receiver's side demodulation takes place, after exploiting the estimation provided about the state vector of the chaotic oscillator by the Derivative-free nonlinear Kalman Filter. Evaluation tests confirm that the proposed filtering method has improved performance over the Extended Kalman Filter and reduces significantly the rate of transmission errors. Moreover, it is shown that the proposed Derivative-free nonlinear Kalman Filter can work within a dual Kalman Filtering scheme, for performing simultaneously transmitter-receiver synchronisation and estimation of unknown coefficients of the communication channel.
Finite time control for MIMO nonlinear system based on higher-order sliding mode.
Liu, Xiangjie; Han, Yaozhen
2014-11-01
Considering a class of MIMO uncertain nonlinear system, a novel finite time stable control algorithm is proposed based on higher-order sliding mode concept. The higher-order sliding mode control problem of MIMO nonlinear system is firstly transformed into finite time stability problem of multivariable system. Then continuous control law, which can guarantee finite time stabilization of nominal integral chain system, is employed. The second-order sliding mode is used to overcome the system uncertainties. High frequency chattering phenomenon of sliding mode is greatly weakened, and the arbitrarily fast convergence is reached. The finite time stability is proved based on the quadratic form Lyapunov function. Examples concerning the triple integral chain system with uncertainty and the hovercraft trajectory tracking are simulated respectively to verify the effectiveness and the robustness of the proposed algorithm.
Control and synchronizing nonlinear systems with delay based on a special matrix structure
NASA Astrophysics Data System (ADS)
Hu, Jianbing; Zhao, Lingdong; Xie, Zhenguang
2014-04-01
This work presents a direct approach to design stabilizing controller for nonlinear systems with delay based on a special matrix structure and proves the validity of the approach according to Lyapunov-Krasovskii stable theorem and Linear Matrix Inequality—LMI. Control Lorenz system and synchronizing Rössler system with delay are taken as examples to explain the approach. Numerical simulations confirm the effectiveness of the approach proposed.
Nonlinear optical security system based on a joint transform correlator in the Fresnel domain.
Vilardy, Juan M; Millán, María S; Pérez-Cabré, Elisabet
2014-03-10
A new optical security system for image encryption based on a nonlinear joint transform correlator (JTC) in the Fresnel domain (FrD) is proposed. The proposal of the encryption process is a lensless optical system that produces a real encrypted image and is a simplified version of some previous JTC-based encryption systems. We use a random complex mask as the key in the nonlinear system for the purpose of increasing the security of the encrypted image. In order to retrieve the primary image in the decryption process, a nonlinear operation has to be introduced in the encrypted function. The optical decryption process is implemented through the Fresnel transform and the fractional Fourier transform. The security system proposed in this paper preserves the shift-invariance property of the JTC-based encryption system in the Fourier domain, with respect to the lateral displacement of the key random mask in the decryption process. This system shows an improved resistance to chosen-plaintext and known-plaintext attacks, as they have been proposed in the cryptanalysis of the JTC encrypting system. Numerical simulations show the validity of this new optical security system.
Adaptive-Fourier-neural-network-based control for a class of uncertain nonlinear systems.
Zuo, Wei; Cai, Lilong
2008-10-01
An adaptive Fourier neural network (AFNN) control scheme is presented in this paper for the control of a class of uncertain nonlinear systems. Based on Fourier analysis and neural network (NN) theory, AFNN employs orthogonal complex Fourier exponentials as the activation functions. Due to the clear physical meaning of the neurons, the determination of the AFNN structure as well as the parameters of the activation functions becomes convenient. One salient feature of the proposed AFNN approach is that all the nonlinearities and uncertainties of the dynamical system are lumped together and compensated online by AFNN. It can, therefore, be applied to uncertain nonlinear systems without any a priori knowledge about the system dynamics. Derived from Lyapunov theory, a novel learning algorithm is proposed, which is essentially a frequency domain method and can guarantee asymptotic stability of the closed-loop system. The simulation results of a multiple-input-multiple-output (MIMO) nonlinear system and the experimental results of an X - Y positioning table are presented to show the effectiveness of the proposed AFNN controller.
Position control of nonlinear hydraulic system using an improved PSO based PID controller
NASA Astrophysics Data System (ADS)
Ye, Yi; Yin, Chen-Bo; Gong, Yue; Zhou, Jun-jing
2017-01-01
This paper addresses the position control of valve-controlled cylinder system employed in hydraulic excavator. Nonlinearities such as dead zone, saturation, discharge coefficient and friction existed in the system are highlighted during the mathematical modeling. On this basis, simulation model is established and then validated against experiments. Aim for achieving excellent position control performances, an improved particle swarm optimization (PSO) algorithm is presented to search for the optimal proportional-integral-derivative (PID) controller gains for the nonlinear hydraulic system. The proposed algorithm is a hybrid based on the standard PSO algorithm but with the addition of selection and crossover operators from genetic algorithm in order to enhance the searching efficiency. Furthermore, a nonlinear decreasing scheme for the inertia weight of the improved PSO algorithm is adopted to balance global exploration and local exploration abilities of particles. Then a co-simulation platform combining the simulation model with the improved PSO tuning based PID controller is developed. Comparisons of the improved PSO, standard PSO and Phase Margin (PM) tuning methods are carried out with three position references as step signal, ramp signal and sinusoidal wave using the co-simulation platform. The results demonstrated that the improved PSO algorithm can perform well in PID control for positioning of nonlinear hydraulic system.
Image-Based Visual Servoing for Robotic Systems: A Nonlinear Lyapunov-Based Control Approach
Dixon, Warren
2004-06-01
There is significant motivation to provide robotic systems with improved autonomy as a means to significantly accelerate deactivation and decommissioning (D&D) operations while also reducing the associated costs, removing human operators from hazardous environments, and reducing the required burden and skill of human operators. To achieve improved autonomy, this project focused on the basic science challenges leading to the development of visual servo controllers. The challenge in developing these controllers is that a camera provides 2-dimensional image information about the 3-dimensional Euclidean-space through a perspective (range dependent) projection that can be corrupted by uncertainty in the camera calibration matrix and by disturbances such as nonlinear radial distortion. Disturbances in this relationship (i.e., corruption in the sensor information) propagate erroneous information to the feedback controller of the robot, leading to potentially unpredictable task execution. This research project focused on the development of a visual servo control methodology that targets compensating for disturbances in the camera model (i.e., camera calibration and the recovery of range information) as a means to achieve predictable response by the robotic system operating in unstructured environments. The fundamental idea is to use nonlinear Lyapunov-based techniques along with photogrammetry methods to overcome the complex control issues and alleviate many of the restrictive assumptions that impact current robotic applications. The outcome of this control methodology is a plug-and-play visual servoing control module that can be utilized in conjunction with current technology such as feature recognition and extraction to enable robotic systems with the capabilities of increased accuracy, autonomy, and robustness, with a larger field of view (and hence a larger workspace). The developed methodology has been reported in numerous peer-reviewed publications and the
Computational analysis of nonlinearities within dynamics of cable-based driving systems
NASA Astrophysics Data System (ADS)
Anghelache, G. D.; Nastac, S.
2017-08-01
This paper deals with computational nonlinear dynamics of mechanical systems containing some flexural parts within the actuating scheme, and, especially, the situations of the cable-based driving systems were treated. It was supposed both functional nonlinearities and the real characteristic of the power supply, in order to obtain a realistically computer simulation model being able to provide very feasible results regarding the system dynamics. It was taken into account the transitory and stable regimes during a regular exploitation cycle. The authors present a particular case of a lift system, supposed to be representatively for the objective of this study. The simulations were made based on the values of the essential parameters acquired from the experimental tests and/or the regular practice in the field. The results analysis and the final discussions reveal the correlated dynamic aspects within the mechanical parts, the driving system, and the power supply, whole of these supplying potential sources of particular resonances, within some transitory phases of the working cycle, and which can affect structural and functional dynamics. In addition, it was underlines the influences of computational hypotheses on the both quantitative and qualitative behaviour of the system. Obviously, the most significant consequence of this theoretical and computational research consist by developing an unitary and feasible model, useful to dignify the nonlinear dynamic effects into the systems with cable-based driving scheme, and hereby to help an optimization of the exploitation regime including a dynamics control measures.
A general U-block model-based design procedure for nonlinear polynomial control systems
NASA Astrophysics Data System (ADS)
Zhu, Q. M.; Zhao, D. Y.; Zhang, Jianhua
2016-10-01
The proposition of U-model concept (in terms of 'providing concise and applicable solutions for complex problems') and a corresponding basic U-control design algorithm was originated in the first author's PhD thesis. The term of U-model appeared (not rigorously defined) for the first time in the first author's other journal paper, which established a framework for using linear polynomial control system design approaches to design nonlinear polynomial control systems (in brief, linear polynomial approaches → nonlinear polynomial plants). This paper represents the next milestone work - using linear state-space approaches to design nonlinear polynomial control systems (in brief, linear state-space approaches → nonlinear polynomial plants). The overall aim of the study is to establish a framework, defined as the U-block model, which provides a generic prototype for using linear state-space-based approaches to design the control systems with smooth nonlinear plants/processes described by polynomial models. For analysing the feasibility and effectiveness, sliding mode control design approach is selected as an exemplary case study. Numerical simulation studies provide a user-friendly step-by-step procedure for the readers/users with interest in their ad hoc applications. In formality, this is the first paper to present the U-model-oriented control system design in a formal way and to study the associated properties and theorems. The previous publications, in the main, have been algorithm-based studies and simulation demonstrations. In some sense, this paper can be treated as a landmark for the U-model-based research from intuitive/heuristic stage to rigour/formal/comprehensive studies.
Wu, Huai-Ning; Li, Han-Xiong
2008-05-01
This paper presents a Galerkin/neural-network- based guaranteed cost control (GCC) design for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities. A parabolic PDE system typically involves a spatial differential operator with eigenspectrum that can be partitioned into a finite-dimensional slow one and an infinite-dimensional stable fast complement. Motivated by this, in the proposed control scheme, Galerkin method is initially applied to the PDE system to derive an ordinary differential equation (ODE) system with unknown nonlinearities, which accurately describes the dynamics of the dominant (slow) modes of the PDE system. The resulting nonlinear ODE system is subsequently parameterized by a multilayer neural network (MNN) with one-hidden layer and zero bias terms. Then, based on the neural model and a Lure-type Lyapunov function, a linear modal feedback controller is developed to stabilize the closed-loop PDE system and provide an upper bound for the quadratic cost function associated with the finite-dimensional slow system for all admissible approximation errors of the network. The outcome of the GCC problem is formulated as a linear matrix inequality (LMI) problem. Moreover, by using the existing LMI optimization technique, a suboptimal guaranteed cost controller in the sense of minimizing the cost bound is obtained. Finally, the proposed design method is applied to the control of the temperature profile of a catalytic rod.
Data based identification and prediction of nonlinear and complex dynamical systems
NASA Astrophysics Data System (ADS)
Wang, Wen-Xu; Lai, Ying-Cheng; Grebogi, Celso
2016-07-01
systems theories with tools from statistical physics, optimization, engineering control, applied mathematics, and scientific computing enables the development of a number of paradigms to address the problem of nonlinear and complex systems reconstruction. In this Review, we describe the recent advances in this forefront and rapidly evolving field, with a focus on compressive sensing based methods. In particular, compressive sensing is a paradigm developed in recent years in applied mathematics, electrical engineering, and nonlinear physics to reconstruct sparse signals using only limited data. It has broad applications ranging from image compression/reconstruction to the analysis of large-scale sensor networks, and it has become a powerful technique to obtain high-fidelity signals for applications where sufficient observations are not available. We will describe in detail how compressive sensing can be exploited to address a diverse array of problems in data based reconstruction of nonlinear and complex networked systems. The problems include identification of chaotic systems and prediction of catastrophic bifurcations, forecasting future attractors of time-varying nonlinear systems, reconstruction of complex networks with oscillatory and evolutionary game dynamics, detection of hidden nodes, identification of chaotic elements in neuronal networks, reconstruction of complex geospatial networks and nodal positioning, and reconstruction of complex spreading networks with binary data.. A number of alternative methods, such as those based on system response to external driving, synchronization, and noise-induced dynamical correlation, will also be discussed. Due to the high relevance of network reconstruction to biological sciences, a special section is devoted to a brief survey of the current methods to infer biological networks. Finally, a number of open problems including control and controllability of complex nonlinear dynamical networks are discussed. The methods
Nonlinear control for systems containing input uncertainty via a Lyapunov-based approach
NASA Astrophysics Data System (ADS)
Mackunis, William
Controllers are often designed based on the assumption that a control actuation can be directly applied to the system. This assumption may not be valid, however, for systems containing parametric input uncertainty or unmodeled actuator dynamics. In this dissertation, a tracking control methodology is proposed for aircaft and aerospace systems for which the corresponding dynamic models contain uncertainty in the control actuation. The dissertation will focus on five problems of interest: (1) adaptive CMG-actuated satellite attitude control in the presence of inertia uncertainty and uncertain CMG gimbal friction; (2) adaptive neural network (NN)-based satellite attitude control for CMG-actuated small-sats in the presence of uncertain satellite inertia, nonlinear disturbance torques, uncertain CMG gimbal friction, and nonlinear electromechanical CMG actuator disturbances; (3) dynamic inversion (DI) control for aircraft systems containing parametric input uncertainty and additive, nonlinearly parameterizable (non-LP) disturbances; (4) adaptive dynamic inversion (ADI) control for aircraft systems as described in (3); and (5) adaptive output feedback control for aircraft systems as described in (3) and (4).
Gottlieb, O.; Feldman, M.
1996-12-31
The authors combine an averaging procedure with a Hilbert transform based algorithm for parameter estimation of a nonlinear ocean system roll model. System backbone curves obtained from data are compared to those obtained analytically and are found to be accurate. Sensitivity of the results is tested by introducing random noise to a nonlinear model describing roll response of a small boat. An example field calibration test of a small semisubmersible exhibiting nonlinear damping is also considered.
GA and Lyapunov theory-based hybrid adaptive fuzzy controller for non-linear systems
NASA Astrophysics Data System (ADS)
Roy, Ananya; Das Sharma, Kaushik
2015-02-01
In this present article, a new hybrid methodology for designing stable adaptive fuzzy logic controllers (AFLCs) for a class of non-linear system is proposed. The proposed design strategy exploits the features of genetic algorithm (GA)-based stochastic evolutionary global search technique and Lyapunov theory-based local adaptation scheme. The objective is to develop a methodology for designing AFLCs with optimised free parameters and guaranteed closed-loop stability. Simultaneously, the proposed method introduces automation in the design process. The stand-alone Lyapunov theory-based design, GA-based design and proposed hybrid GA-Lyapunov design methodologies are implemented for two benchmark non-linear plants in simulation case studies with different reference signals and one experimental case study. The results demonstrate that the hybrid design methodology outperforms the other control strategies on the whole.
Runge-Kutta model-based nonlinear observer for synchronization and control of chaotic systems.
Beyhan, Selami
2013-07-01
This paper proposes a novel nonlinear gradient-based observer for synchronization and observer-based control of chaotic systems. The model is based on a Runge-Kutta model of the chaotic system where the evolution of the states or parameters is derived based on the error-square minimization. The stability and convergence conditions of observer and control methods are analyzed using a Lyapunov stability approach. In numerical simulations, the proposed observer and well-known sliding-mode observer are compared for the synchronization of a Lü chaotic system and observer-based stabilization of a Chen chaotic system. The noisy case for synchronization and parameter uncertainty case for stabilization are also considered for both observer-based methods. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.
NASA Astrophysics Data System (ADS)
Zhang, Wentao; Liu, Yang
2016-01-01
In this paper, observer-based distributed consensus for general nonlinear multi-agent systems with interval control inputs under strongly connected balanced topology is encountered when the relative states of agents are unavailable or undesirable. Theoretical analysis method is further extended to the case of general nonlinear multi-agent systems under switching setting. Moreover, tracking problem on the leader-follower scenario is also explicitly investigated under a mutual assumption that the communication graph, which represents the interaction among agents, contains a directed spanning tree with the leader as its root. It is shown that the consensus for underlying considered multi-agent systems can be desirable as long as the data missing rate does not exceed a certain threshold. Finally, simulation examples are presented to effectively corroborate the analytical findings.
Stable neural-network-based adaptive control for sampled-data nonlinear systems.
Sun, F; Sun, Z; Woo, P Y
1998-01-01
For a class of multiinput-multioutput (MIMO) sampled-data nonlinear systems with unknown dynamic nonlinearities, a stable neural-network (NN)-based adaptive control approach which is an integration of an NN approach and the adaptive implementation of the variable structure control with a sector, is developed. The sampled-data nonlinear system is assumed to be controllable and its state vector is available for measurement. The variable structure control with a sector serves two purposes. One is to force the system state to be within the state region in which the NN's are used when the system goes out of neural control; and the other is to provide an additional control until the system tracking error metric is controlled inside the sector within the network approximation region. The proof of a complete stability and a tracking error convergence is given and the setting of the sector and the NN parameters is discussed. It is demonstrated that the asymptotic error of the system can be made dependent only on inherent network approximation errors and the frequency range of unmodeled dynamics. Simulation studies of a two-link manipulator show the effectiveness of the proposed control approach.
Nonlinear contrast imaging with an array-based micro-ultrasound system.
Needles, A; Arditi, M; Rognin, N G; Mehi, J; Coulthard, T; Bilan-Tracey, C; Gaud, E; Frinking, P; Hirson, D; Foster, F S
2010-12-01
The main goal of this study was to determine the optimal strategy for a real-time nonlinear contrast mode for small-animal imaging at high frequencies, on a new array-based micro-ultrasound system. Previously reported contrast imaging at frequencies above 15 MHz has primarily relied on subtraction schemes involving B-mode image data. These approaches provide insufficient contrast to tissue ratios under many imaging conditions. In this work, pulse inversion, amplitude modulation and combinations of these were systematically investigated for the detection of nonlinear fundamental and subharmonic signal components to maximize contrast-to-tissue ratio (CTR) in the 18-24 MHz range. From in vitro and in vivo measurements, nonlinear fundamental detection with amplitude modulation provided optimal results, allowing an improvement in CTR of 13 dB compared with fundamental imaging. Based on this detection scheme, in vivo parametric images of murine kidneys were generated using sequences of nonlinear contrast images after intravenous bolus injections of microbubble suspensions. Initial parametric images of peak enhancement (PE), wash-in rate (WiR) and rise time (RT) are presented. The parametric images are indicative of blood perfusion kinetics, which, in the context of preclinical imaging with small animals, are anticipated to provide valuable insights into the progression of human disease models, where blood perfusion plays a critical role in either the diagnosis or treatment of the disease. Copyright © 2010 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.
NASA Astrophysics Data System (ADS)
Wei, Xile; Lu, Meili; Wang, Jiang; Tsang, K. M.; Deng, Bin; Che, Yanqiu
2010-05-01
We consider the assumption of existence of the general nonlinear internal model that is introduced in the design of robust output regulators for a class of minimum-phase nonlinear systems with rth degree (r ≥ 2). The robust output regulation problem can be converted into a robust stabilisation problem of an augmented system consisting of the given plant and a high-gain nonlinear internal model, perfectly reproducing the bounded including not only periodic but also nonperiodic exogenous signal from a nonlinear system, which satisfies some general immersion assumption. The state feedback controller is designed to guarantee the asymptotic convergence of system errors to zero manifold. Furthermore, the proposed scheme makes use of output feedback dynamic controller that only processes information from the regulated output error by using high-gain observer to robustly estimate the derivatives of the regulated output error. The stabilisation analysis of the resulting closed-loop systems leads to regional as well as semi-global robust output regulation achieved for some appointed initial condition in the state space, for all possible values of the uncertain parameter vector and the exogenous signal, ranging over an arbitrary compact set.
NASA Astrophysics Data System (ADS)
Zhu, Zhiliang; Meng, Zhiqiang; Cao, Tingting; Zhang, Zhengjiang; Dai, Yuxing
2017-06-01
State and parameter estimation (SPE) plays an important role in process monitoring, online optimization, and process control. The estimation of states and parameters is generally solved simultaneously in the SPE problem, where the parameters to be estimated are specified as augmented states. When state and/or measurement equations are highly nonlinear and the posterior probability of the state is non-Gaussian, particle filter (PF) is commonly used for SPE. However, when the parameters switch with the operating conditions, the change of parameters cannot be detected and tracked by the conventional SPE method. This paper proposes a PF-based robust SPE method for a nonlinear process system with variable parameters. The measurement test criterion based on observation error is introduced to indirectly identify whether the parameters are changed. Based on the result of identification, the variances of the particles are modified adaptively for the tracking of the changed parameters. Finally, reliable SPE can be derived through iterative particles. The proposed PF-based robust SPE method is applied to two nonlinear process systems. The results demonstrate the effectiveness and robustness of the proposed method.
Image-Based Visual Servoing for Robotic Systems: A Nonlinear Lyapunov-Based Control Approach
Dixon, Warren
2003-06-01
The objective of this project is to enable current and future EM robots with an increased ability to perceive and interact with unstructured and unknown environments through the use of camera-based visual servo controllers. The scientific goals of this research are to develop a new visual servo control methodology that: (1) adapts for the unknown camera calibration parameters (e.g., focal length, scaling factors, camera position, and orientation) and the physical parameters of the robotic system (e.g., mass, inertia, friction), (2) compensates for unknown depth information (extract 3D information from the 2D image), and (3) enables multi-uncalibrated cameras to be used as a means to provide a larger field-of-view. Nonlinear Lyapunov-based techniques in conjunction with results from projective geometry are being used to overcome the complex control issues and alleviate many of the restrictive assumptions that impact current visual servo controlled robotic systems. The potential relevance of this control methodology will be a plug-and-play visual servoing control module that can be utilized in conjunction with current technology such as feature extraction and recognition, to enable current EM robotic systems with the capabilities of increased accuracy, autonomy, and robustness, with a larger field of view (and hence a larger workspace). These capabilities will enable EM robots to significantly accelerate D&D operations by providing for improved robot autonomy and increased worker productivity, while also reducing the associated costs, removing the human operator from the hazardous environments, and reducing the burden and skill of the human operators.
Image-Based Visual Servoing for Robotic Systems: A Nonlinear Lyapunov-Based Control Approach
Dixon, Warren
2002-06-01
The objective of this project is to enable current and future EM robots with an increased ability to perceive and interact with unstructured and unknown environments through the use of camera-based visual servo controlled robots. The scientific goals of this research are to develop a new visual servo control methodology that: (1) adapts for the unknown camera calibration parameters (e.g., focal length, scaling factors, camera position and orientation) and the physical parameters of the robotic system (e.g., mass, inertia, friction), (2) compensates for unknown depth information (extract 3D information from the 2D image), and (3) enables multi-uncalibrated cameras to be used as a means to provide a larger field-of-view. Nonlinear Lyapunov-based techniques are being used to overcome the complex control issues and alleviate many of the restrictive assumptions that impact current visual servo controlled robotic systems. The potential relevance of this control methodology will be a plug-and-play visual servoing control module that can be utilized in conjunction with current technology such as feature extraction and recognition, to enable current EM robotic systems with the capabilities of increased accuracy, autonomy, and robustness, with a larger field of view (and hence a larger workspace). These capabilities will enable EM robots to significantly accelerate D&D operations by providing for improved robot autonomy and increased worker productivity, while also reducing the associated costs, removing the human operator from the hazardous environments, and reducing the burden and skill of the human operators.
Li, Xingfeng; Coyle, Damien; Maguire, Liam; McGinnity, Thomas M; Benali, Habib
2011-07-01
In this paper a model selection algorithm for a nonlinear system identification method is proposed to study functional magnetic resonance imaging (fMRI) effective connectivity. Unlike most other methods, this method does not need a pre-defined structure/model for effective connectivity analysis. Instead, it relies on selecting significant nonlinear or linear covariates for the differential equations to describe the mapping relationship between brain output (fMRI response) and input (experiment design). These covariates, as well as their coefficients, are estimated based on a least angle regression (LARS) method. In the implementation of the LARS method, Akaike's information criterion corrected (AICc) algorithm and the leave-one-out (LOO) cross-validation method were employed and compared for model selection. Simulation comparison between the dynamic causal model (DCM), nonlinear identification method, and model selection method for modelling the single-input-single-output (SISO) and multiple-input multiple-output (MIMO) systems were conducted. Results show that the LARS model selection method is faster than DCM and achieves a compact and economic nonlinear model simultaneously. To verify the efficacy of the proposed approach, an analysis of the dorsal and ventral visual pathway networks was carried out based on three real datasets. The results show that LARS can be used for model selection in an fMRI effective connectivity study with phase-encoded, standard block, and random block designs. It is also shown that the LOO cross-validation method for nonlinear model selection has less residual sum squares than the AICc algorithm for the study.
Identification of nonlinear system using extreme learning machine based Hammerstein model
NASA Astrophysics Data System (ADS)
Tang, Yinggan; Li, Zhonghui; Guan, Xinping
2014-09-01
In this paper, a new method for nonlinear system identification via extreme learning machine neural network based Hammerstein model (ELM-Hammerstein) is proposed. The ELM-Hammerstein model consists of static ELM neural network followed by a linear dynamic subsystem. The identification of nonlinear system is achieved by determining the structure of ELM-Hammerstein model and estimating its parameters. Lipschitz quotient criterion is adopted to determine the structure of ELM-Hammerstein model from input-output data. A generalized ELM algorithm is proposed to estimate the parameters of ELM-Hammerstein model, where the parameters of linear dynamic part and the output weights of ELM neural network are estimated simultaneously. The proposed method can obtain more accurate identification results with less computation complexity. Three simulation examples demonstrate its effectiveness.
Nonlinear dynamic modeling of a simple flexible rotor system subjected to time-variable base motions
NASA Astrophysics Data System (ADS)
Chen, Liqiang; Wang, Jianjun; Han, Qinkai; Chu, Fulei
2017-09-01
Rotor systems carried in transportation system or under seismic excitations are considered to have a moving base. To study the dynamic behavior of flexible rotor systems subjected to time-variable base motions, a general model is developed based on finite element method and Lagrange's equation. Two groups of Euler angles are defined to describe the rotation of the rotor with respect to the base and that of the base with respect to the ground. It is found that the base rotations would cause nonlinearities in the model. To verify the proposed model, a novel test rig which could simulate the base angular-movement is designed. Dynamic experiments on a flexible rotor-bearing system with base angular motions are carried out. Based upon these, numerical simulations are conducted to further study the dynamic response of the flexible rotor under harmonic angular base motions. The effects of base angular amplitude, rotating speed and base frequency on response behaviors are discussed by means of FFT, waterfall, frequency response curve and orbits of the rotor. The FFT and waterfall plots of the disk horizontal and vertical vibrations are marked with multiplications of the base frequency and sum and difference tones of the rotating frequency and the base frequency. Their amplitudes will increase remarkably when they meet the whirling frequencies of the rotor system.
Neural Network-Based Event-Triggered State Feedback Control of Nonlinear Continuous-Time Systems.
Sahoo, Avimanyu; Xu, Hao; Jagannathan, Sarangapani
2016-03-01
This paper presents a novel approximation-based event-triggered control of multi-input multi-output uncertain nonlinear continuous-time systems in affine form. The controller is approximated using a linearly parameterized neural network (NN) in the context of event-based sampling. After revisiting the NN approximation property in the context of event-based sampling, an event-triggered condition is proposed using the Lyapunov technique to reduce the network resource utilization and to generate the required number of events for the NN approximation. In addition, a novel weight update law for aperiodic tuning of the NN weights at triggered instants is proposed to relax the knowledge of complete system dynamics and to reduce the computation when compared with the traditional NN-based control. Nonetheless, a nonzero positive lower bound for the inter-event times is guaranteed to avoid the accumulation of events or Zeno behavior. For analyzing the stability, the event-triggered system is modeled as a nonlinear impulsive dynamical system and the Lyapunov technique is used to show local ultimate boundedness of all signals. Furthermore, in order to overcome the unnecessary triggered events when the system states are inside the ultimate bound, a dead-zone operator is used to reset the event-trigger errors to zero. Finally, the analytical design is substantiated with numerical results.
Ohtake, Hiroshi; Tanaka, Kazuo; Wang, Hua O
2006-02-01
This paper presents a switching fuzzy controller design for a class of nonlinear systems. A switching fuzzy model is employed to represent the dynamics of a nonlinear system. In our previous papers, we proposed the switching fuzzy model and a switching Lyapunov function and derived stability conditions for open-loop systems. In this paper, we design a switching fuzzy controller. We firstly show that switching fuzzy controller design conditions based on the switching Lyapunov function are given in terms of bilinear matrix inequalities, which is difficult to design the controller numerically. Then, we propose a new controller design approach utilizing an augmented system. By introducing the augmented system which consists of the switching fuzzy model and a stable linear system, the controller design conditions based on the switching Lyapunov function are given in terms of linear matrix inequalities (LMIs). Therefore, we can effectively design the switching fuzzy controller via LMI-based approach. A design example illustrates the utility of this approach. Moreover, we show that the approach proposed in this paper is available in the research area of piecewise linear control.
a Frequency Domain Based NUMERIC-ANALYTICAL Method for Non-Linear Dynamical Systems
NASA Astrophysics Data System (ADS)
Narayanan, S.; Sekar, P.
1998-04-01
In this paper a multiharmonic balancing technique is used to develop certain algorithms to determine periodic orbits of non-liner dynamical systems with external, parametric and self excitations. Essentially, in this method the non-linear differential equations are transformed into a set of non-linear algebraic equations in terms of the Fourier coefficients of the periodic solutions which are solved by using the Newton-Raphson technique. The method is developed such that both fast Fourier transform and discrete Fourier transform algorithms can be used. It is capable of treating all types of non-linearities and higher dimensional systems. The stability of periodic orbits is investigated by obtaining the monodromy matrix. A path following algorithm based on the predictor-corrector method is also presented to enable the bifurcation analysis. The prediction is done with a cubic extrapolation technique with an arc length incrementation while the correction is done with the use of the least square minimisation technique. The under determined system of equations is solved by singular value decomposition. The suitability of the method is demonstrated by obtaining the bifurcational behaviour of rolling contact vibrations modelled by Hertz contact law.
Shape Distributions of Nonlinear Dynamical Systems for Video-Based Inference.
Venkataraman, Vinay; Turaga, Pavan
2016-12-01
This paper presents a shape-theoretic framework for dynamical analysis of nonlinear dynamical systems which appear frequently in several video-based inference tasks. Traditional approaches to dynamical modeling have included linear and nonlinear methods with their respective drawbacks. A novel approach we propose is the use of descriptors of the shape of the dynamical attractor as a feature representation of nature of dynamics. The proposed framework has two main advantages over traditional approaches: a) representation of the dynamical system is derived directly from the observational data, without any inherent assumptions, and b) the proposed features show stability under different time-series lengths where traditional dynamical invariants fail. We illustrate our idea using nonlinear dynamical models such as Lorenz and Rossler systems, where our feature representations (shape distribution) support our hypothesis that the local shape of the reconstructed phase space can be used as a discriminative feature. Our experimental analyses on these models also indicate that the proposed framework show stability for different time-series lengths, which is useful when the available number of samples are small/variable. The specific applications of interest in this paper are: 1) activity recognition using motion capture and RGBD sensors, 2) activity quality assessment for applications in stroke rehabilitation, and 3) dynamical scene classification. We provide experimental validation through action and gesture recognition experiments on motion capture and Kinect datasets. In all these scenarios, we show experimental evidence of the favorable properties of the proposed representation.
Shape Descriptions of Nonlinear Dynamical Systems for Video-based Inference.
Venkataraman, Vinay; Turaga, Pavan
2016-02-23
This paper presents a shape-theoretic framework for dynamical analysis of nonlinear dynamical systems which appear frequently in several video-based inference tasks. Traditional approaches to dynamical modeling have included linear and nonlinear methods with their respective drawbacks. A novel approach we propose is the use of descriptors of the shape of the dynamical attractor as a feature representation of nature of dynamics. The proposed framework has two main advantages over traditional approaches: a) representation of the dynamical system is derived directly from the observational data, without any inherent assumptions, and b) the proposed features show stability under different time-series lengths where traditional dynamical invariants fail. We illustrate our idea using nonlinear dynamical models such as Lorenz and Rossler systems, where our feature representations (shape distribution) support our hypothesis that the local shape of the reconstructed phase space can be used as a discriminative feature. Our experimental analyses on these models also indicate that the proposed framework show stability for different time-series lengths, which is useful when the available number of samples are small/variable. The specific applications of interest in this paper are: 1) activity recognition using motion capture and RGBD sensors, 2) activity quality assessment for applications in stroke rehabilitation, and 3) dynamical scene classification.We provide experimental validation through action and gesture recognition experiments on motion capture and Kinect datasets. In all these scenarios, we show experimental evidence of the favorable properties of the proposed representation.
Abbaspour, Alireza; Aboutalebi, Payam; Yen, Kang K; Sargolzaei, Arman
2017-03-01
A new online detection strategy is developed to detect faults in sensors and actuators of unmanned aerial vehicle (UAV) systems. In this design, the weighting parameters of the Neural Network (NN) are updated by using the Extended Kalman Filter (EKF). Online adaptation of these weighting parameters helps to detect abrupt, intermittent, and incipient faults accurately. We apply the proposed fault detection system to a nonlinear dynamic model of the WVU YF-22 unmanned aircraft for its evaluation. The simulation results show that the new method has better performance in comparison with conventional recurrent neural network-based fault detection strategies. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.
Intelligent control of non-linear dynamical system based on the adaptive neurocontroller
NASA Astrophysics Data System (ADS)
Engel, E.; Kovalev, I. V.; Kobezhicov, V.
2015-10-01
This paper presents an adaptive neuro-controller for intelligent control of non-linear dynamical system. The formed as the fuzzy selective neural net the adaptive neuro-controller on the base of system's state, creates the effective control signal under random perturbations. The validity and advantages of the proposed adaptive neuro-controller are demonstrated by numerical simulations. The simulation results show that the proposed controller scheme achieves real-time control speed and the competitive performance, as compared to PID, fuzzy logic controllers.
Volterra series based blind equalization for nonlinear distortions in short reach optical CAP system
NASA Astrophysics Data System (ADS)
Tao, Li; Tan, Hui; Fang, Chonghua; Chi, Nan
2016-12-01
In this paper, we propose a blind Volterra series based nonlinear equalization (VNLE) with low complexity for the nonlinear distortion mitigation in short reach optical carrierless amplitude and phase (CAP) modulation system. The principle of the blind VNLE is presented and the performance of its blind adaptive algorithms including the modified cascaded multi-mode algorithm (MCMMA) and direct detection LMS (DD-LMS) are investigated experimentally. Compared to the conventional VNLE using training symbols before demodulation, it is performed after matched filtering and downsampling, so shorter memory length is required but similar performance improvement is observed. About 1 dB improvement is observed at BER of 3.8×10-3 for 40 Gb/s CAP32 signal over 40 km standard single mode fiber.
Neural Network-Based DOBC for a Class of Nonlinear Systems With Unmatched Disturbances.
Sun, Haibin; Guo, Lei
2017-02-01
In this brief, the problem of composite anti-disturbance tracking control for a class of strict-feedback systems with unmatched unknown nonlinear functions and external disturbances is investigated. A disturbance-observer-based control (DOBC) in combination with a neural network scheme and back-stepping method is developed to achieve a composite anti-disturbance controller design that provides guaranteed performance. In the proposed method, a conventional disturbance observer and a radial basis function neural network (RBFNN) are combined into a new disturbance observer to estimate the unmatched disturbances. As compared with conventional DOBC methods, the primary merit of the proposed method is that the unknown nonlinear functions are approximated using the RBFNN technique, and not regarded as part of the disturbances or estimated by a conventional disturbance observer. Hence, the proposed method can obtain higher control accuracy than the conventional DOBC methods. This advantage is validated by simulation studies.
Dong, Lu; Zhong, Xiangnan; Sun, Changyin; He, Haibo
2016-04-08
This paper presents the design of a novel adaptive event-triggered control method based on the heuristic dynamic programming (HDP) technique for nonlinear discrete-time systems with unknown system dynamics. In the proposed method, the control law is only updated when the event-triggered condition is violated. Compared with the periodic updates in the traditional adaptive dynamic programming (ADP) control, the proposed method can reduce the computation and transmission cost. An actor-critic framework is used to learn the optimal event-triggered control law and the value function. Furthermore, a model network is designed to estimate the system state vector. The main contribution of this paper is to design a new trigger threshold for discrete-time systems. A detailed Lyapunov stability analysis shows that our proposed event-triggered controller can asymptotically stabilize the discrete-time systems. Finally, we test our method on two different discrete-time systems, and the simulation results are included.
Implementation of nonlinear registration of brain atlas based on piecewise grid system
NASA Astrophysics Data System (ADS)
Liu, Rong; Gu, Lixu; Xu, Jianrong
2007-12-01
In this paper, a multi-step registration method of brain atlas and clinical Magnetic Resonance Imaging (MRI) data based on Thin-Plate Splines (TPS) and Piecewise Grid System (PGS) is presented. The method can help doctors to determine the corresponding anatomical structure between patient image and the brain atlas by piecewise nonlinear registration. Since doctors mostly pay attention to particular Region of Interest (ROI), and a global nonlinear registration is quite time-consuming which is not suitable for real-time clinical application, we propose a novel method to conduct linear registration in global area before nonlinear registration is performed in selected ROI. The homogenous feature points are defined to calculate the transform matrix between patient data and the brain atlas to conclude the mapping function. Finally, we integrate the proposed approach into an application of neurosurgical planning and guidance system which lends great efficiency in both neuro-anatomical education and guiding of neurosurgical operations. The experimental results reveal that the proposed approach can keep an average registration error of 0.25mm in near real-time manner.
Data-based fault-tolerant control for affine nonlinear systems with actuator faults.
Xie, Chun-Hua; Yang, Guang-Hong
2016-09-01
This paper investigates the fault-tolerant control (FTC) problem for unknown nonlinear systems with actuator faults including stuck, outage, bias and loss of effectiveness. The upper bounds of stuck faults, bias faults and loss of effectiveness faults are unknown. A new data-based FTC scheme is proposed. It consists of the online estimations of the bounds and a state-dependent function. The estimations are adjusted online to compensate automatically the actuator faults. The state-dependent function solved by using real system data helps to stabilize the system. Furthermore, all signals in the resulting closed-loop system are uniformly bounded and the states converge asymptotically to zero. Compared with the existing results, the proposed approach is data-based. Finally, two simulation examples are provided to show the effectiveness of the proposed approach.
Chen, Ziting; Li, Zhijun; Chen, C L Philip
2016-03-16
We develop a novel disturbance observer-based adaptive fuzzy control approach in this paper for a class of uncertain multi-input-multi-output mechanical systems possessing unknown input nonlinearities, i.e., deadzone and saturation and time-varying external disturbance. It is shown that the input nonlinearities can be represented by a nominal part and a nonlinear disturbance term. High-dimensional integral-type Lyapunov function is used to construct the controller. Fuzzy logic system is employed to cancel model uncertainties, and disturbance observer is also integrated into control design to compensate the fuzzy approximation error, external disturbance, and nonlinear disturbance caused by the unknown input nonlinearities. Semiglobally uniformly ultimately boundness of the closed-loop control system is guaranteed with tracking errors keeping bounded. Experimental studies on a robotic exoskeleton using the proposed control demonstrate the effectiveness of the approach.
Li, Hongyi; Wu, Chengwei; Shi, Peng; Gao, Yabin
2015-11-01
In this paper, the problem of fuzzy control for nonlinear networked control systems with packet dropouts and parameter uncertainties is studied based on the interval type-2 fuzzy-model-based approach. In the control design, the intermittent data loss existing in the closed-loop system is taken into account. The parameter uncertainties can be represented and captured effectively via the membership functions described by lower and upper membership functions and relative weighting functions. A novel fuzzy state-feedback controller is designed to guarantee the resulting closed-loop system to be stochastically stable with an optimal performance. Furthermore, to make the controller design more flexible, the designed controller does not need to share membership functions and amount of fuzzy rules with the model. Some simulation results are provided to demonstrate the effectiveness of the proposed results.
Decentralized neural identifier and control for nonlinear systems based on extended Kalman filter.
Castañeda, Carlos E; Esquivel, P
2012-07-01
A time-varying learning algorithm for recurrent high order neural network in order to identify and control nonlinear systems which integrates the use of a statistical framework is proposed. The learning algorithm is based in the extended Kalman filter, where the associated state and measurement noises covariance matrices are composed by the coupled variance between the plant states. The formulation allows identification of interactions associate between plant state and the neural convergence. Furthermore, a sliding window-based method for dynamical modeling of nonstationary systems is presented to improve the neural identification in the proposed methodology. The efficiency and accuracy of the proposed method is assessed to a five degree of freedom (DOF) robot manipulator where based on the time-varying neural identifier model, the decentralized discrete-time block control and sliding mode techniques are used to design independent controllers and develop the trajectory tracking for each DOF.
Actor-critic-based optimal tracking for partially unknown nonlinear discrete-time systems.
Kiumarsi, Bahare; Lewis, Frank L
2015-01-01
This paper presents a partially model-free adaptive optimal control solution to the deterministic nonlinear discrete-time (DT) tracking control problem in the presence of input constraints. The tracking error dynamics and reference trajectory dynamics are first combined to form an augmented system. Then, a new discounted performance function based on the augmented system is presented for the optimal nonlinear tracking problem. In contrast to the standard solution, which finds the feedforward and feedback terms of the control input separately, the minimization of the proposed discounted performance function gives both feedback and feedforward parts of the control input simultaneously. This enables us to encode the input constraints into the optimization problem using a nonquadratic performance function. The DT tracking Bellman equation and tracking Hamilton-Jacobi-Bellman (HJB) are derived. An actor-critic-based reinforcement learning algorithm is used to learn the solution to the tracking HJB equation online without requiring knowledge of the system drift dynamics. That is, two neural networks (NNs), namely, actor NN and critic NN, are tuned online and simultaneously to generate the optimal bounded control policy. A simulation example is given to show the effectiveness of the proposed method.
1980-02-26
6-7 C. Minimum Energy Regulators for Commutative Bilinear Systems .................... ........ 8-9 D. Control Law.s for Certain Aerospace...class of nonlinear systems (3,10]. (c) Minimum energy regulators for commutative bilinear systems [3,10]. (D) Control laws for certain aerospace...With Delay in Control," IEEE Trans. on Auto Contr., Vol. AC-20, pp. 702-704, 1975, and [3].) - !. 8 C. Minimum Energy Regulators for Commutative Bilinear
NASA Astrophysics Data System (ADS)
Errami, Y.; Obbadi, A.; Sahnoun, S.; Benhmida, M.; Ouassaid, M.; Maaroufi, M.
2016-07-01
This paper presents nonlinear backstepping control for Wind Power Generation System (WPGS) based Permanent Magnet Synchronous Generator (PMSG) and connected to utility grid. The block diagram of the WPGS with PMSG and the grid side back-to-back converter is established with the dq frame of axes. This control scheme emphasises the regulation of the dc-link voltage and the control of the power factor at changing wind speed. Besides, in the proposed control strategy of WPGS, Maximum Power Point Tracking (MPPT) technique and pitch control are provided. The stability of the regulators is assured by employing Lyapunov analysis. The proposed control strategy for the system has been validated by MATLAB simulations under varying wind velocity and the grid fault condition. In addition, a comparison of simulation results based on the proposed Backstepping strategy and conventional Vector Control is provided.
Indirect adaptive control of nonlinear systems based on bilinear neuro-fuzzy approximation.
Boutalis, Yiannis; Christodoulou, Manolis; Theodoridis, Dimitrios
2013-10-01
In this paper, we investigate the indirect adaptive regulation problem of unknown affine in the control nonlinear systems. The proposed approach consists of choosing an appropriate system approximation model and a proper control law, which will regulate the system under the certainty equivalence principle. The main difference from other relevant works of the literature lies in the proposal of a potent approximation model that is bilinear with respect to the tunable parameters. To deploy the bilinear model, the components of the nonlinear plant are initially approximated by Fuzzy subsystems. Then, using appropriately defined fuzzy rule indicator functions, the initial dynamical fuzzy system is translated to a dynamical neuro-fuzzy model, where the indicator functions are replaced by High Order Neural Networks (HONNS), trained by sampled system data. The fuzzy output partitions of the initial fuzzy components are also estimated based on sampled data. This way, the parameters to be estimated are the weights of the HONNs and the centers of the output partitions, both arranged in matrices of appropriate dimensions and leading to a matrix to matrix bilinear parametric model. Based on the bilinear parametric model and the design of appropriate control law we use a Lyapunov stability analysis to obtain parameter adaptation laws and to regulate the states of the system. The weight updating laws guarantee that both the identification error and the system states reach zero exponentially fast, while keeping all signals in the closed loop bounded. Moreover, introducing a method of "concurrent" parameter hopping, the updating laws are modified so that the existence of the control signal is always assured. The main characteristic of the proposed approach is that the a priori experts information required by the identification scheme is extremely low, limited to the knowledge of the signs of the centers of the fuzzy output partitions. Therefore, the proposed scheme is not
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.
Event-Based Robust Control for Uncertain Nonlinear Systems Using Adaptive Dynamic Programming.
Zhang, Qichao; Zhao, Dongbin; Wang, Ding
2016-10-18
In this paper, the robust control problem for a class of continuous-time nonlinear system with unmatched uncertainties is investigated using an event-based control method. First, the robust control problem is transformed into a corresponding optimal control problem with an augmented control and an appropriate cost function. Under the event-based mechanism, we prove that the solution of the optimal control problem can asymptotically stabilize the uncertain system with an adaptive triggering condition. That is, the designed event-based controller is robust to the original uncertain system. Note that the event-based controller is updated only when the triggering condition is satisfied, which can save the communication resources between the plant and the controller. Then, a single network adaptive dynamic programming structure with experience replay technique is constructed to approach the optimal control policies. The stability of the closed-loop system with the event-based control policy and the augmented control policy is analyzed using the Lyapunov approach. Furthermore, we prove that the minimal intersample time is bounded by a nonzero positive constant, which excludes Zeno behavior during the learning process. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed control scheme.
Nam, Kyung-Tae; Lee, Seung-Joon; Kuc, Tae-Yong; Kim, Hyungjong
2015-12-31
In this paper, we consider the state estimation problem for flexible joint manipulators that involve nonlinear characteristics in their stiffness. The two key ideas of our design are that (a) an accelerometer is used in order that the estimation error dynamics do not depend on nonlinearities at the link part of the manipulators and (b) the model of the nonlinear stiffness is indeed a Lipschitz function. Based on the measured acceleration, we propose a nonlinear observer under the Lipschitz condition of the nonlinear stiffness. In addition, in order to effectively compensate for the estimation error, the gain of the proposed observer is chosen from the ARE (algebraic Riccati equations) which depend on the Lipschitz constant. Comparative experimental results verify the effectiveness of the proposed method.
Nam, Kyung-Tae; Lee, Seung-Joon; Kuc, Tae-Yong; Kim, Hyungjong
2015-01-01
In this paper, we consider the state estimation problem for flexible joint manipulators that involve nonlinear characteristics in their stiffness. The two key ideas of our design are that (a) an accelerometer is used in order that the estimation error dynamics do not depend on nonlinearities at the link part of the manipulators and (b) the model of the nonlinear stiffness is indeed a Lipschitz function. Based on the measured acceleration, we propose a nonlinear observer under the Lipschitz condition of the nonlinear stiffness. In addition, in order to effectively compensate for the estimation error, the gain of the proposed observer is chosen from the ARE (algebraic Riccati equations) which depend on the Lipschitz constant. Comparative experimental results verify the effectiveness of the proposed method. PMID:26729125
Zhang, Xian-Xia; Jiang, Ye; Li, Han-Xiong; Li, Shao-Yuan
2013-10-01
A data-driven 3-D fuzzy-logic controller (3-D FLC) design methodology based on support vector regression (SVR) learning is developed for nonlinear spatially distributed dynamic systems. Initially, the spatial information expression and processing as well as the fuzzy linguistic expression and rule inference of a 3-D FLC are integrated into spatial fuzzy basis functions (SFBFs), and then the 3-D FLC can be depicted by a three-layer network structure. By relating SFBFs of the 3-D FLC directly to spatial kernel functions of an SVR, an equivalence relationship of the 3-D FLC and the SVR is established, which means that the 3-D FLC can be designed with the help of the SVR learning. Subsequently, for an easy implementation, a systematic SVR learning-based 3-D FLC design scheme is formulated. In addition, the universal approximation capability of the proposed 3-D FLC is presented. Finally, the control of a nonlinear catalytic packed-bed reactor is considered as an application to demonstrate the effectiveness of the proposed 3-D FLC.
Yang, Yuan; Solis-Escalante, Teodoro; Yao, Jun; Daffertshofer, Andreas; Schouten, Alfred C; van der Helm, Frans C T
2016-02-01
Interaction between distant neuronal populations is essential for communication within the nervous system and can occur as a highly nonlinear process. To better understand the functional role of neural interactions, it is important to quantify the nonlinear connectivity in the nervous system. We introduce a general approach to measure nonlinear connectivity through phase coupling: the multi-spectral phase coherence (MSPC). Using simulated data, we compare MSPC with existing phase coupling measures, namely n : m synchronization index and bi-phase locking value. MSPC provides a system description, including (i) the order of the nonlinearity, (ii) the direction of interaction, (iii) the time delay in the system, and both (iv) harmonic and (v) intermodulation coupling beyond the second order; which are only partly revealed by other methods. We apply MSPC to analyze data from a motor control experiment, where subjects performed isotonic wrist flexions while receiving movement perturbations. MSPC between the perturbation, EEG and EMG was calculated. Our results reveal directional nonlinear connectivity in the afferent and efferent pathways, as well as the time delay (43 ± 8 ms) between the perturbation and the brain response. In conclusion, MSPC is a novel approach capable to assess high-order nonlinear interaction and timing in the nervous system.
Disturbance observer based sliding mode control of nonlinear mismatched uncertain systems
NASA Astrophysics Data System (ADS)
Ginoya, Divyesh; Shendge, P. D.; Phadke, S. B.
2015-09-01
This paper presents a new design of multiple-surface sliding mode control for a class of nonlinear uncertain systems with mismatched uncertainties and disturbances. In the method of multiple-surface sliding mode control, it is required to compensate for the derivatives of the virtual inputs which gives rise to the so-called problem of 'explosion of terms'. In this paper a disturbance observer based multiple-surface sliding mode control is proposed to estimate the uncertainties as well as the derivative of the virtual inputs to overcome this problem. The practical stability of the overall system is proved. The effectiveness of the proposed control strategy is illustrated via simulation of a benchmark problem and comparison with other control strategies. The proposed scheme is validated by implementing it on a serial flexible joint manipulator in the laboratory.
Chen, Mou; Ge, Shuzhi Sam
2013-08-01
In this paper, the direct adaptive neural control is proposed for a class of uncertain nonaffine nonlinear systems with unknown nonsymmetric input saturation. Based on the implicit function theorem and mean value theorem, both state feedback and output feedback direct adaptive controls are developed using neural networks (NNs) and a disturbance observer. A compounded disturbance is defined to take into account of the effect of the unknown external disturbance, the unknown nonsymmetric input saturation, and the approximation error of NN. Then, a disturbance observer is developed to estimate the unknown compounded disturbance, and it is established that the estimate error converges to a compact set if appropriate observer design parameters are chosen. Both state feedback and output feedback direct adaptive controls can guarantee semiglobal uniform boundedness of the closed-loop system signals as rigorously proved by Lyapunov analysis. Numerical simulation results are presented to illustrate the effectiveness of the proposed direct adaptive neural control techniques.
NASA Astrophysics Data System (ADS)
Yang, Hongjiu; You, Xiu; Liu, Zhixin; Sun, Fuchun
2015-10-01
This paper studies the problem of synchronisation to a desired trajectory for non-linear multi-agent systems. By introducing extended state observer approach, decentralised adaptive controllers are designed for distributed systems which have non-identical unknown non-linear dynamics. The non-identical unknown non-linear dynamics allows for a tracked command dynamics which is also non-linear and unknown. State variables of agents can be obtained only in the case where leader agent and the network communication topology for multi-agent systems is strongly connected digraph network structures. A Lyapunov-function-based approach is given to show that the tracking error is ultimately bounded. Some simulation results are given to demonstrate the effectiveness of the developed techniques in this paper.
NASA Astrophysics Data System (ADS)
Kun, David William
Unmanned aircraft systems (UASs) are gaining popularity in civil and commercial applications as their lightweight on-board computers become more powerful and affordable, their power storage devices improve, and the Federal Aviation Administration addresses the legal and safety concerns of integrating UASs in the national airspace. Consequently, many researchers are pursuing novel methods to control UASs in order to improve their capabilities, dependability, and safety assurance. The nonlinear control approach is a common choice as it offers several benefits for these highly nonlinear aerospace systems (e.g., the quadrotor). First, the controller design is physically intuitive and is derived from well known dynamic equations. Second, the final control law is valid in a larger region of operation, including far from the equilibrium states. And third, the procedure is largely methodical, requiring less expertise with gain tuning, which can be arduous for a novice engineer. Considering these facts, this thesis proposes a nonlinear controller design method that combines the advantages of adaptive robust control (ARC) with the powerful design tools of linear matrix inequalities (LMI). The ARC-LMI controller is designed with a discontinuous projection-based adaptation law, and guarantees a prescribed transient and steady state tracking performance for uncertain systems in the presence of matched disturbances. The norm of the tracking error is bounded by a known function that depends on the controller design parameters in a known form. Furthermore, the LMI-based part of the controller ensures the stability of the system while overcoming polytopic uncertainties, and minimizes the control effort. This can reduce the number of parameters that require adaptation, and helps to avoid control input saturation. These desirable characteristics make the ARC-LMI control algorithm well suited for the quadrotor UAS, which may have unknown parameters and may encounter external
Observed-Based Adaptive Fuzzy Tracking Control for Switched Nonlinear Systems With Dead-Zone.
Tong, Shaocheng; Sui, Shuai; Li, Yongming
2015-12-01
In this paper, the problem of adaptive fuzzy output-feedback control is investigated for a class of uncertain switched nonlinear systems in strict-feedback form. The considered switched systems contain unknown nonlinearities, dead-zone, and immeasurable states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, a switched fuzzy state observer is designed and thus the immeasurable states are obtained by it. By applying the adaptive backstepping design principle and the average dwell time method, an adaptive fuzzy output-feedback tracking control approach is developed. It is proved that the proposed control approach can guarantee that all the variables in the closed-loop system are bounded under a class of switching signals with average dwell time, and also that the system output can track a given reference signal as closely as possible. The simulation results are given to check the effectiveness of the proposed approach.
Coupled nonlinear dynamical systems
NASA Astrophysics Data System (ADS)
Sun, Hongyan
In this dissertation, we study coupled nonlinear dynamical systems that exhibit new types of complex behavior. We numerically and analytically examine a variety of dynamical models, ranging from systems of ordinary differential equations (ODE) with novel elements of feedback to systems of partial differential equations (PDE) that model chemical pattern formation. Chaos, dynamical uncertainty, synchronization, and spatiotemporal pattern formation constitute the primary topics of the dissertation. Following the introduction in Chapter 1, we study chaos and dynamical uncertainty in Chapter 2 with coupled Lorenz systems and demonstrate the existence of extreme complexity in high-dimensional ODE systems. In Chapter 3, we demonstrate that chaos synchronization can be achieved by mutual and multiplicative coupling of dynamical systems. Chapter 4 and 5 focus on pattern formation in reaction-diffusion systems, and we investigate segregation and integration behavior of populations in competitive and cooperative environments, respectively.
Identification and control of nonlinear system based on Laguerre-ELM Wiener model
NASA Astrophysics Data System (ADS)
Tang, Yinggan; Han, Zhenzhen; Liu, Fucai; Guan, Xinping
2016-09-01
In this paper, a new Wiener model is presented for identification and control of single-input single-output (SISO) nonlinear systems. The proposed Wiener model consists of a linear Laguerre filter in cascaded with an extreme learning machine (ELM) neural network (called Laguerre-ELM Wiener model). Laguerre filter can approximate a stable linear system to any degree of accuracy with a small number of Laguerre filters, which provides a parsimony structure and high level accuracy simultaneously. To determine the appropriated number of Laguerre filters in Laguerre-ELM Wiener model, Lipschitz quotient criterion is adapted to determine the order of linear part. A generalized ELM algorithm is proposed to estimate the parameters of Laguerre-ELM Wiener model. Once the unknown nonlinear system is identified using Laguerre-ELM Wiener model, a generalized predictive control (GPC) algorithm is designed for control of nonlinear system. The advantage of the proposed control method is that it transfers a nonlinear control problem to a linear one by inserting the inverse of static nonlinear section. Simulation results demonstrate the effectiveness of the proposed identification and control algorithms.
Niu, Ben; Li, Lu
2017-04-17
This brief proposes a new neural-network (NN)-based adaptive output tracking control scheme for a class of disturbed multiple-input multiple-output uncertain nonlinear switched systems with input delays. By combining the universal approximation ability of radial basis function NNs and adaptive backstepping recursive design with an improved multiple Lyapunov function (MLF) scheme, a novel adaptive neural output tracking controller design method is presented for the switched system. The feature of the developed design is that different coordinate transformations are adopted to overcome the conservativeness caused by adopting a common coordinate transformation for all subsystems. It is shown that all the variables of the resulting closed-loop system are semiglobally uniformly ultimately bounded under a class of switching signals in the presence of MLF and that the system output can follow the desired reference signal. To demonstrate the practicability of the obtained result, an adaptive neural output tracking controller is designed for a mass-spring-damper system.
Han, Honggui; Wu, Xiao-Long; Qiao, Jun-Fei
2014-04-01
In this paper, a self-organizing fuzzy-neural-network with adaptive computation algorithm (SOFNN-ACA) is proposed for modeling a class of nonlinear systems. This SOFNN-ACA is constructed online via simultaneous structure and parameter learning processes. In structure learning, a set of fuzzy rules can be self-designed using an information-theoretic methodology. The fuzzy rules with high spiking intensities (SI) are divided into new ones. And the fuzzy rules with a small relative mutual information (RMI) value will be pruned in order to simplify the FNN structure. In parameter learning, the consequent part parameters are learned through the use of an ACA that incorporates an adaptive learning rate strategy into the learning process to accelerate the convergence speed. Then, the convergence of SOFNN-ACA is analyzed. Finally, the proposed SOFNN-ACA is used to model nonlinear systems. The modeling results demonstrate that this proposed SOFNN-ACA can model nonlinear systems effectively.
Iterative nonlinear ISI cancellation in optical tilted filter-based Nyquist 4-PAM system
NASA Astrophysics Data System (ADS)
Ju, Cheng; Liu, Na
2016-09-01
The conventional double sideband (DSB) modulation and direct detection scheme suffers from severer power fading, linear and nonlinear inter-symbol interference (ISI) caused by fiber dispersion and square-law direct detection. The system's frequency response deteriorates at high frequencies owing to the limited device bandwidth. Moreover, the linear and nonlinear ISI is enhanced induced by the bandwidth limited effect. In this paper, an optical tilted filter is used to mitigate the effect of power fading, and improve the high frequency response of bandwidth limited device in Nyquist 4-ary pulse amplitude modulation (4-PAM) system. Furtherly, iterative technique is introduced to mitigate the nonlinear ISI caused by the combined effects of electrical Nyquist filter, limited device bandwidth, optical tilted filter, dispersion, and square-law photo-detection. Thus, the system's frequency response is greatly improved and the delivery distance can be extended.
NASA Astrophysics Data System (ADS)
Aitouche, A.; Yang, Q.; Ould Bouamama, B.
2011-05-01
This paper presents a procedure dealing with the issue of fault detection and isolation (FDI) using nonlinear analytical redundancy (NLAR) technique applied in a proton exchange membrane (PEM) fuel cell system based on its mathematic model. The model is proposed and simplified into a five orders state space representation. The transient phenomena captured in the model include the compressor dynamics, the flow characteristics, mass and energy conservation and manifold fluidic mechanics. Nonlinear analytical residuals are generated based on the elimination of the unknown variables of the system by an extended parity space approach to detect and isolate actuator and sensor faults. Finally, numerical simulation results are given corresponding to a faults signature matrix.
Xu, Hao; Jagannathan, Sarangapani
2015-03-01
The stochastic optimal control of nonlinear networked control systems (NNCSs) using neuro-dynamic programming (NDP) over a finite time horizon is a challenging problem due to terminal constraints, system uncertainties, and unknown network imperfections, such as network-induced delays and packet losses. Since the traditional iteration or time-based infinite horizon NDP schemes are unsuitable for NNCS with terminal constraints, a novel time-based NDP scheme is developed to solve finite horizon optimal control of NNCS by mitigating the above-mentioned challenges. First, an online neural network (NN) identifier is introduced to approximate the control coefficient matrix that is subsequently utilized in conjunction with the critic and actor NNs to determine a time-based stochastic optimal control input over finite horizon in a forward-in-time and online manner. Eventually, Lyapunov theory is used to show that all closed-loop signals and NN weights are uniformly ultimately bounded with ultimate bounds being a function of initial conditions and final time. Moreover, the approximated control input converges close to optimal value within finite time. The simulation results are included to show the effectiveness of the proposed scheme.
Linearization of Nonlinear Systems.
1986-11-24
series. IEEE Trans. Circuits Syst., CAS-32(11):1150-1171, November 1985. [BC85b] S. Boyd and L. 0. Chua. Uniqueness of circuits and systems containing...Control and Information Sciences vol. 58, p10 1- 1 19 , June 1983. [BC85c] S. Boyd and L. 0. Chua. Volterra series for nonlinear circuits . In Proc. IEEE...ISCAS, Tokyo, June 1985. [BCD84] S. Boyd, L. 0. Chua, and C. A. Desoer . Analytical foundations of Volterra series. IMA Journal of Mathematical
Nonlinear photocurrents in two-dimensional systems based on graphene and boron nitride
NASA Astrophysics Data System (ADS)
Hipolito, F.; Pedersen, Thomas G.; Pereira, Vitor M.
2016-07-01
The dc photoelectrical currents can be generated purely as a nonlinear effect in uniform media lacking inversion symmetry without the need for a material junction or bias voltages to drive it, in what is termed photogalvanic effect. These currents are strongly dependent on the polarization state of the radiation, as well as on topological properties of the underlying Fermi surface such as its Berry curvature. In order to study the intrinsic photogalvanic response of gapped graphene, biased bilayer graphene (BBG), and hexagonal boron nitride (hBN), we compute the nonlinear current using a perturbative expansion of the density matrix. This allows a microscopic description of the quadratic response to an electromagnetic field in these materials, which we analyze as a function of temperature and electron density. We find that the intrinsic response is robust across these systems and allows for currents in the range of pA cm/W to nA cm/W. At the independent-particle level, the response of hBN-based structures is significant only in the ultraviolet due to their sizable band gap. However, when Coulomb interactions are accounted for by explicit solution of the Bethe-Salpeter equation, we find that the photoconductivity is strongly modified by transitions involving exciton levels in the gap region, whose spectral weight dominates in the overall frequency range. Biased bilayers and gapped monolayers of graphene have a strong photoconductivity in the visible and infrared window, allowing for photocurrent densities of several nA cm/W. We further show that the richer electronic dispersion of BBG at low energies and the ability to change its band gap on demand allows a higher tunability of the photocurrent, including not only its magnitude but also, and significantly, its polarity.
NASA Astrophysics Data System (ADS)
Khouaja, Anis; Garna, Tarek; Ragot, José; Messaoud, Hassani
2015-08-01
This paper proposes a new predictive controller approach for nonlinear process based on a reduced complexity homogeneous, quadratic discrete-time Volterra model called quadratic S-PARAFAC Volterra model. The proposed model is yielded by using the symmetry property of the Volterra kernels and their tensor decomposition using the PARAFAC technique that provides a parametric reduction compared to the conventional Volterra model. This property allows synthesising a new nonlinear-model-based predictive control (NMBPC). We develop the general form of a new predictor, and therefore, we propose an optimisation algorithm formulated as a quadratic programming under linear and nonlinear constraints. The performances of the proposed quadratic S-PARAFAC Volterra model and the developed NMBPC algorithm are illustrated on a numerical simulation and validated on a benchmark as a continuous stirred-tank reactor system. Moreover, the efficiency of the proposed quadratic S-PARAFAC Volterra model and the NMBPC approach are validated on an experimental communicating two-tank system.
Observer-based fault-tolerant control for a class of nonlinear networked control systems
NASA Astrophysics Data System (ADS)
Mahmoud, M. S.; Memon, A. M.; Shi, Peng
2014-08-01
This paper presents a fault-tolerant control (FTC) scheme for nonlinear systems which are connected in a networked control system. The nonlinear system is first transformed into two subsystems such that the unobservable part is affected by a fault and the observable part is unaffected. An observer is then designed which gives state estimates using a Luenberger observer and also estimates unknown parameter of the system; this helps in fault estimation. The FTC is applied in the presence of sampling due to the presence of a network in the loop. The controller gain is obtained using linear-quadratic regulator technique. The methodology is applied on a mechatronic system and the results show satisfactory performance.
Fuzzy neural-based control for nonlinear time-varying delay systems.
Hwang, Chih-Lyang; Chang, Li-Jui
2007-12-01
In this paper, a partially known nonlinear dynamic system with time-varying delays of the input and state is approximated by N fuzzy-based linear subsystems described by a state-space model with average delay. To shape the response of the closed-loop system, a set of fuzzy reference models is established. Similarly, the same fuzzy sets of the system rule are employed to design a fuzzy neural-based control. The proposed control contains a radial-basis function neural network to learn the uncertainties caused by the approximation error of the fuzzy model (e.g., time-varying delays and parameter variations) and the interactions resulting from the other subsystems. As the norm of the switching surface is inside of a defined set, the learning law starts; in this situation, the proposed method is an adaptive control possessing an extra compensation of uncertainties. As it is outside of the other set, which is smaller than the aforementioned set, the learning law stops; under this circumstance, the proposed method becomes a robust control without the compensation of uncertainties. A transition between robust control and adaptive control is also assigned to smooth the possible discontinuity of the control input. No assumption about the upper bound of the time-varying delays for the state and the input is required. However, two time-average delays are needed to simplify the controller design: 1) the stabilized conditions for every transformed delay-free subsystem must be satisfied; and 2) the learning uncertainties must be relatively bounded. The stability of the overall system is verified by Lyapunov stability theory. Simulations as compared with a linear transformed state feedback with integration control are also arranged to consolidate the usefulness of the proposed control.
2009-11-18
in a trim condition is a typical problem of output regulation near an equilibrium setting, tailless or nearly tailless aircraft , such as UCAV’s...control to produce significant nonlinear excursions. Taking advantage of these nonequilibrium nonlinearities in tailless aircraft also promises to...will also have multiple nonlinear axes and a smaller domain of stability than conventional aircraft , involving nonlinear trajectories which cannot be
A frequency up-converting harvester based on internal resonance in 2-DOF nonlinear systems
NASA Astrophysics Data System (ADS)
Wu, Yipeng; Qiu, Jinhao; Ji, Hongli
2016-11-01
This paper reports the design and experimental testing of a novel frequency up- converting piezoelectric energy harvester. The harvester is firstly approximated as a 2-degree- of-freedom cubic nonlinear system instead of the general Duffing systems. A 1:3 internal resonance innovatively applied in the frequency up-conversion approach is thoroughly investigated. Finally, the theoretical dynamic model confirmed by the experimental results clearly shows the effect of the frequency up-conversion.
Shao-Cheng Tong; Yong-Ming Li; Gang Feng; Tie-Shan Li
2011-08-01
In this paper, an adaptive fuzzy backstepping dynamic surface control (DSC) approach is developed for a class of multiple-input-multiple-output nonlinear systems with immeasurable states. Using fuzzy-logic systems to approximate the unknown nonlinear functions, a fuzzy state observer is designed to estimate the immeasurable states. By combining adaptive-backstepping technique and DSC technique, an adaptive fuzzy output-feedback backstepping-control approach is developed. The proposed control method not only overcomes the problem of "explosion of complexity" inherent in the backstepping-design methods but also overcomes the problem of unavailable state measurements. It is proved that all the signals of the closed-loop adaptive-control system are semiglobally uniformly ultimately bounded, and the tracking errors converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approach.
Lai, Guanyu; Liu, Zhi; Zhang, Yun; Philip Chen, C L
2016-06-01
This paper is concentrated on the problem of adaptive fuzzy tracking control for an uncertain nonlinear system whose actuator is encountered by the asymmetric backlash behavior. First, we propose a new smooth inverse model which can approximate the asymmetric actuator backlash arbitrarily. By applying it, two adaptive fuzzy control scenarios, namely, the compensation-based control scheme and nonlinear decomposition-based control scheme, are then developed successively. It is worth noticing that the first fuzzy controller exhibits a better tracking control performance, although it recourses to a known slope ratio of backlash nonlinearity. The second one further removes the restriction, and also gets a desirable control performance. By the strict Lyapunov argument, both adaptive fuzzy controllers guarantee that the output tracking error is convergent to an adjustable region of zero asymptotically, while all the signals remain semiglobally uniformly ultimately bounded. Lastly, two comparative simulations are conducted to verify the effectiveness of the proposed fuzzy controllers.
NASA Technical Reports Server (NTRS)
Turner, L. R.
1960-01-01
The problem of solving systems of nonlinear equations has been relatively neglected in the mathematical literature, especially in the textbooks, in comparison to the corresponding linear problem. Moreover, treatments that have an appearance of generality fail to discuss the nature of the solutions and the possible pitfalls of the methods suggested. Probably it is unrealistic to expect that a unified and comprehensive treatment of the subject will evolve, owing to the great variety of situations possible, especially in the applied field where some requirement of human or mechanical efficiency is always present. Therefore we attempt here simply to pose the problem and to describe and partially appraise the methods of solution currently in favor.
Yang, Qinmin; Vance, Jonathan Blake; Jagannathan, S
2008-08-01
A nonaffine discrete-time system represented by the nonlinear autoregressive moving average with eXogenous input (NARMAX) representation with unknown nonlinear system dynamics is considered. An equivalent affinelike representation in terms of the tracking error dynamics is first obtained from the original nonaffine nonlinear discrete-time system so that reinforcement-learning-based near-optimal neural network (NN) controller can be developed. The control scheme consists of two linearly parameterized NNs. One NN is designated as the critic NN, which approximates a predefined long-term cost function, and an action NN is employed to derive a near-optimal control signal for the system to track a desired trajectory while minimizing the cost function simultaneously. The NN weights are tuned online. By using the standard Lyapunov approach, the stability of the closed-loop system is shown. The net result is a supervised actor-critic NN controller scheme which can be applied to a general nonaffine nonlinear discrete-time system without needing the affinelike representation. Simulation results demonstrate satisfactory performance of the controller.
Cen, Zhaohui; Wei, Jiaolong; Jiang, Rui
2013-12-01
A novel gray-box neural network model (GBNNM), including multi-layer perception (MLP) neural network (NN) and integrators, is proposed for a model identification and fault estimation (MIFE) scheme. With the GBNNM, both the nonlinearity and dynamics of a class of nonlinear dynamic systems can be approximated. Unlike previous NN-based model identification methods, the GBNNM directly inherits system dynamics and separately models system nonlinearities. This model corresponds well with the object system and is easy to build. The GBNNM is embedded online as a normal model reference to obtain the quantitative residual between the object system output and the GBNNM output. This residual can accurately indicate the fault offset value, so it is suitable for differing fault severities. To further estimate the fault parameters (FPs), an improved extended state observer (ESO) using the same NNs (IESONN) from the GBNNM is proposed to avoid requiring the knowledge of ESO nonlinearity. Then, the proposed MIFE scheme is applied for reaction wheels (RW) in a satellite attitude control system (SACS). The scheme using the GBNNM is compared with other NNs in the same fault scenario, and several partial loss of effect (LOE) faults with different severities are considered to validate the effectiveness of the FP estimation and its superiority.
Embedded EMD algorithm within an FPGA-based design to classify nonlinear SDOF systems
NASA Astrophysics Data System (ADS)
Jones, Jonathan D.; Pei, Jin-Song; Wright, Joseph P.; Tull, Monte P.
2010-04-01
Compared with traditional microprocessor-based systems, rapidly advancing field-programmable gate array (FPGA) technology offers a more powerful, efficient and flexible hardware platform. An FPGA and microprocessor (i.e., hardware and software) co-design is developed to classify three types of nonlinearities (including linear, hardening and softening) of a single-degree-of-freedom (SDOF) system subjected to free vibration. This significantly advances the team's previous work on using FPGAs for wireless structural health monitoring. The classification is achieved by embedding two important algorithms - empirical mode decomposition (EMD) and backbone curve analysis. Design considerations to embed EMD in FPGA and microprocessor are discussed. In particular, the implementation of cubic spline fitting and the challenges encountered using both hardware and software environments are discussed. The backbone curve technique is fully implemented within the FPGA hardware and used to extract instantaneous characteristics from the uniformly distributed data sets produced by the EMD algorithm as presented in a previous SPIE conference by the team. An off-the-shelf high-level abstraction tool along with the MATLAB/Simulink environment is utilized to manage the overall FPGA and microprocessor co-design. Given the limited computational resources of an embedded system, we strive for a balance between the maximization of computational efficiency and minimization of resource utilization. The value of this study lies well beyond merely programming existing algorithms in hardware and software. Among others, extensive and intensive judgment is exercised involving experiences and insights with these algorithms, which renders processed instantaneous characteristics of the signals that are well-suited for wireless transmission.
Li, Linlin; Ding, Steven X; Qiu, Jianbin; Yang, Ying
2017-02-01
This paper is concerned with a real-time observer-based fault detection (FD) approach for a general type of nonlinear systems in the presence of external disturbances. To this end, in the first part of this paper, we deal with the definition and the design condition for an L ∞ / L 2 type of nonlinear observer-based FD systems. This analytical framework is fundamental for the development of real-time nonlinear FD systems with the aid of some well-established techniques. In the second part, we address the integrated design of the L ∞ / L 2 observer-based FD systems by applying Takagi-Sugeno (T-S) fuzzy dynamic modeling technique as the solution tool. This fuzzy observer-based FD approach is developed via piecewise Lyapunov functions, and can be applied to the case that the premise variables of the FD system is nonsynchronous with the premise variables of the fuzzy model of the plant. In the end, a case study on the laboratory setup of three-tank system is given to show the efficiency of the proposed results.
NASA Astrophysics Data System (ADS)
Elkoteshy, Yasser; Jiao, L. C.; Chen, Weisheng
2014-05-01
In this work, the adaptive backstepping neural control technique is proposed for a class of uncertain multi-input multi-output nonlinear systems in block-triangular form with the ultimate tracking accuracy assumed to be known a priori. The stability analysis of the closed-loop control system is derived based on Barbalat's Lemma instead of Lyapunov stability theory. Semi-global uniform ultimate boundedness of all the signals in the closed-loop system is achieved and after a sufficiently large interval of time, the outputs of the system are proven to converge to the predefined value. A single hidden layer feed-forward neural network based on the extreme learning machine is used in this work to approximate the unknown nonlinear functions in the control laws. Two simulation examples, including a mathematical one and a practical one, are given to verify the effectiveness of the proposed controller and its superiority over the existing techniques.
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
NASA Astrophysics Data System (ADS)
Yoshimura, Toshio
2016-02-01
This paper presents the design of an adaptive fuzzy sliding mode control (AFSMC) for uncertain discrete-time nonlinear dynamic systems. The dynamic systems are described by a discrete-time state equation with nonlinear uncertainties, and the uncertainties include the modelling errors and the external disturbances to be unknown but nonlinear with the bounded properties. The states are measured by the restriction of measurement sensors and the contamination with independent measurement noises. The nonlinear uncertainties are approximated by using the fuzzy IF-THEN rules based on the universal approximation theorem, and the approximation error is compensated by adding an adaptive complementary term to the proposed AFSMC. The fuzzy inference approach based on the extended single input rule modules is proposed to reduce the number of the fuzzy IF-THEN rules. The estimates for the un-measurable states and the adjustable parameters are obtained by using the weighted least squares estimator and its simplified one. It is proved that under some conditions the estimation errors will remain in the vicinity of zero as time increases, and the states are ultimately bounded subject to the proposed AFSMC. The effectiveness of the proposed method is indicated through the simulation experiment of a simple numerical system.
NASA Astrophysics Data System (ADS)
Zhang, Shao-Jie; Qiu, Xiang-Wei; Jiang, Bin; Liu, Chun-Sheng
2015-03-01
This paper presents a new adaptive compensation control approach for a class of multi-input multi-output (MIMO) nonlinear systems with actuator failures. In order to enlarge the set of compensable actuator failures, an actuators grouping scheme based on multiple model switching and tuning (MMST) is proposed for the nonlinear MIMO minimum-phase systems with multiple actuator failures. Then, an adaptive compensation scheme based on prescribed performance bound (PPB) which characterises the convergence rate and maximum overshoot of the tracking error is designed for the systems to ensure closed-loop signal boundedness and asymptotic output tracking despite unknown actuator failures. Simulation results are given to show the effectiveness of the control design.
Chen, C L Philip; Wen, Guo-Xing; Liu, Yan-Jun; Liu, Zhi
2016-07-01
Combined with backstepping techniques, an observer-based adaptive consensus tracking control strategy is developed for a class of high-order nonlinear multiagent systems, of which each follower agent is modeled in a semi-strict-feedback form. By constructing the neural network-based state observer for each follower, the proposed consensus control method solves the unmeasurable state problem of high-order nonlinear multiagent systems. The control algorithm can guarantee that all signals of the multiagent system are semi-globally uniformly ultimately bounded and all outputs can synchronously track a reference signal to a desired accuracy. A simulation example is carried out to further demonstrate the effectiveness of the proposed consensus control method.
NASA Astrophysics Data System (ADS)
Jeng, Jin-Tsong; Lee, Tsu-Tian
1998-03-01
In this paper, we propose a neural network model with a faster learning speed and a good approximate capability in the function approximation for solving worst-case identification of nonlinear systems H(infinity ) problems. Specifically, via the approximate transformable technique, we develop a Chebyshev Polynomials Based unified model neural network for solving the worst-case identification of nonlinear systems H(infinity ) problems. Based on this approximate transformable technique, the relationship between the single-layered neural network and multi-layered perceptron neural network is derived. It is shown that the Chebyshev Polynomials Based unified model neural network can be represented as a functional link network that is based on Chebyshev polynomials. We also derive a new learning algorithm such that the infinity norm of the transfer function from the input to the output is under a prescribed level. It turns out that the Chebyshev Polynomials Based unified model neural network not only has the same capability of universal approximator, but also has a faster learning speed than multi-layered perceptron or the recurrent neural network in the deterministic worst-case identification of nonlinear systems H(infinity ) problems.
Vibration of vehicle-pavement coupled system based on a Timoshenko beam on a nonlinear foundation
NASA Astrophysics Data System (ADS)
Ding, Hu; Yang, Yan; Chen, Li-Qun; Yang, Shao-Pu
2014-12-01
This paper focuses on the coupled nonlinear vibration of vehicle-pavement system. The pavement is modeled as a Timoshenko beam resting on a six-parameter foundation. The vehicle is simplified as a spring-mass-damper oscillator. For the first time, the dynamic response of vehicle-pavement coupled system is studied by modeling the pavement as a Timoshenko beam resting on a nonlinear foundation. Consequently, the shear effects and the rotational inertia of the pavement are included in the modeling process. The pavement model is assumed to be a linear-plus-cubic Pasternak-type foundation. Furthermore, the convergent Galerkin truncation is used to obtain approximate solutions to the coupled vibratory response of the vehicle-pavement coupled system. The dynamic responses of the vehicle-pavement system with the asphalt pavement on soft soil foundation are investigated via the numerical examples. The numerical results show that the calculation for the coupled vibratory response needs high-order modes. Moreover, the coupling effects between the pavement and the vehicle are numerically examined by using the convergent modal truncation. The physical parameters of the vehicle-pavement system such as the shear modulus are compared for determining their influences on the coupled vibratory response.
Liu, Yan-Jun; Tong, Shaocheng; Chen, C L Philip; Li, Dong-Juan
2016-01-01
This paper studies an adaptive neural control for nonlinear multiple-input multiple-output systems in interconnected form. The studied systems are composed of N subsystems in pure feedback structure and the interconnection terms are contained in every equation of each subsystem. Moreover, the studied systems consider the effects of Prandtl-Ishlinskii (PI) hysteresis model. It is for the first time to study the control problem for such a class of systems. In addition, the proposed scheme removes an important assumption imposed on the previous works that the bounds of the parameters in PI hysteresis are known. The radial basis functions neural networks are employed to approximate unknown functions. The adaptation laws and the controllers are designed by employing the backstepping technique. The closed-loop system can be proven to be stable by using Lyapunov theorem. A simulation example is studied to validate the effectiveness of the scheme.
DDI-based finite-time stability analysis for nonlinear switched systems with time-varying delays
NASA Astrophysics Data System (ADS)
Xue, Wenping; Li, Kangji; Liu, Guohai
2016-09-01
This paper investigates the finite-time stability (FTS) analysis problem for switched systems with both nonlinear perturbation and time-varying delays. For the system to be finite-time stable, a sufficient condition is proposed based on some delay differential inequalities (DDIs), rather than the Lyapunov-like functions which are commonly used in the FTS analysis of switched systems. Compared with the Lyapunov-like function method, the FTS conditions based on the DDI method are easier for checking and do not require FTS of each subsystem. Two examples are given to illustrate the effectiveness of the developed theory.
A VLF-based technique in applications to digital control of nonlinear hybrid multirate systems
NASA Astrophysics Data System (ADS)
Vassilyev, Stanislav; Ulyanov, Sergey; Maksimkin, Nikolay
2017-01-01
In this paper, a technique for rigorous analysis and design of nonlinear multirate digital control systems on the basis of the reduction method and sublinear vector Lyapunov functions is proposed. The control system model under consideration incorporates continuous-time dynamics of the plant and discrete-time dynamics of the controller and takes into account uncertainties of the plant, bounded disturbances, nonlinear characteristics of sensors and actuators. We consider a class of multirate systems where the control update rate is slower than the measurement sampling rates and periodic non-uniform sampling is admitted. The proposed technique does not use the preliminary discretization of the system, and, hence, allows one to eliminate the errors associated with the discretization and improve the accuracy of analysis. The technique is applied to synthesis of digital controller for a flexible spacecraft in the fine stabilization mode and decentralized controller for a formation of autonomous underwater vehicles. Simulation results are provided to validate the good performance of the designed controllers.
Choi, Yun Ho; Yoo, Sung Jin
2017-03-28
A minimal-approximation-based distributed adaptive consensus tracking approach is presented for strict-feedback multiagent systems with unknown heterogeneous nonlinearities and control directions under a directed network. Existing approximation-based consensus results for uncertain nonlinear multiagent systems in lower-triangular form have used multiple function approximators in each local controller to approximate unmatched nonlinearities of each follower. Thus, as the follower's order increases, the number of the approximators used in its local controller increases. However, the proposed approach employs only one function approximator to construct the local controller of each follower regardless of the order of the follower. The recursive design methodology using a new error transformation is derived for the proposed minimal-approximation-based design. Furthermore, a bounding lemma on parameters of Nussbaum functions is presented to handle the unknown control direction problem in the minimal-approximation-based distributed consensus tracking framework and the stability of the overall closed-loop system is rigorously analyzed in the Lyapunov sense.
Liu, Derong; Yang, Xiong; Wang, Ding; Wei, Qinglai
2015-07-01
The design of stabilizing controller for uncertain nonlinear systems with control constraints is a challenging problem. The constrained-input coupled with the inability to identify accurately the uncertainties motivates the design of stabilizing controller based on reinforcement-learning (RL) methods. In this paper, a novel RL-based robust adaptive control algorithm is developed for a class of continuous-time uncertain nonlinear systems subject to input constraints. The robust control problem is converted to the constrained optimal control problem with appropriately selecting value functions for the nominal system. Distinct from typical action-critic dual networks employed in RL, only one critic neural network (NN) is constructed to derive the approximate optimal control. Meanwhile, unlike initial stabilizing control often indispensable in RL, there is no special requirement imposed on the initial control. By utilizing Lyapunov's direct method, the closed-loop optimal control system and the estimated weights of the critic NN are proved to be uniformly ultimately bounded. In addition, the derived approximate optimal control is verified to guarantee the uncertain nonlinear system to be stable in the sense of uniform ultimate boundedness. Two simulation examples are provided to illustrate the effectiveness and applicability of the present approach.
NASA Technical Reports Server (NTRS)
Simon, J. S.; Valavani, L.
1991-01-01
The use of a closed-loop control to allow surge-free operation of a compression system beyond its uncontrolled surge line is addressed. In contrast to previous analyses which used a linearized model, the approach described directly addresses the nonlinear nature of the compressor characteristic using a Liapunov-based control law design formulation. The proposed approach is fairly generic and should be of interest for gas turbine engines as well as other applications.
Observer-based stabilisation of a class of nonlinear systems in the presence of measurement delay
NASA Astrophysics Data System (ADS)
He, Qing; Liu, Jinkun
2016-06-01
In this paper, the stabilising control problem for a class of nonlinear system in the presence of measurement delay is addressed. A full-order observer is designed to eliminate the effect of variable output time delay, which is bounded and known. Then, the estimated states are utilised for the state feedback control law to stabilise the considered control system. Lyapunov-Razumikhin approach is employed to analyse the stability of the closed-loop system. Unlike the previous work, the exponential convergence of the estimation error is ensured, rather than asymptotic convergence, by designing a delay-dependent gain of the observer. Moreover, comparison with similar work is also made in simulation to illustrate the effectiveness of the proposed strategy.
Low level monitoring and control of nonlinear systems
Cover, A.; Reneke, J.; Lenhart, S.; Protopopescu, V.
1994-12-31
In this paper, we propose a nonparametric method for monitoring and controlling nonlinear systems whose dynamics is, in general, unknown or only partially known. Our nonparametric method is based on the stochastic linearization of the underlying (unknown) nonlinear system.
Wang, Changyuan; Zhang, Jing; Mu, Jing
2012-01-01
A new filter named the maximum likelihood-based iterated divided difference filter (MLIDDF) is developed to improve the low state estimation accuracy of nonlinear state estimation due to large initial estimation errors and nonlinearity of measurement equations. The MLIDDF algorithm is derivative-free and implemented only by calculating the functional evaluations. The MLIDDF algorithm involves the use of the iteration measurement update and the current measurement, and the iteration termination criterion based on maximum likelihood is introduced in the measurement update step, so the MLIDDF is guaranteed to produce a sequence estimate that moves up the maximum likelihood surface. In a simulation, its performance is compared against that of the unscented Kalman filter (UKF), divided difference filter (DDF), iterated unscented Kalman filter (IUKF) and iterated divided difference filter (IDDF) both using a traditional iteration strategy. Simulation results demonstrate that the accumulated mean-square root error for the MLIDDF algorithm in position is reduced by 63% compared to that of UKF and DDF algorithms, and by 7% compared to that of IUKF and IDDF algorithms. The new algorithm thus has better state estimation accuracy and a fast convergence rate.
Chen, Lingji; Narendra, Kumpati S
2004-05-01
This paper presents a unified theoretical framework for the identification and control of a nonlinear discrete-time dynamical system, in which the nonlinear system is represented explicitly as a sum of its linearized component and the residual nonlinear component referred to as a "higher order function." This representation substantially simplifies the procedure of applying the implicit function theorem to derive local properties of the nonlinear system, and reveals the role played by the linearized system in a more transparent form. Under the assumption that the linearized system is controllable and observable, it is shown that: 1) the nonlinear system is also controllable and observable in a local domain; 2) a feedback law exists to stabilize the nonlinear system locally; and 3) the nonlinear system can exactly track a constant or a periodic sequence locally, if its linearized system can do so. With some additional assumptions, the nonlinear system is shown to have a well-defined relative degree (delay) and zero-dynamics. If the zero-dynamics of the linearized system is asymptotically stable, so is that of the nonlinear one, and in such a case, a control law exists for the nonlinear system to asymptotically track an arbitrary reference signal exactly, in a neighborhood of the equilibrium state. The tracking can be achieved by using the state vector for feedback, or by using only the input and the output, in which case the nonlinear autoregressive moving-average (NARMA) model is established and utilized. These results are important for understanding the use of neural networks as identifiers and controllers for general nonlinear discrete-time dynamical systems.
Lam, H K; Leung, Frank H F
2007-10-01
This correspondence presents the stability analysis and performance design of the continuous-time fuzzy-model-based control systems. The idea of the nonparallel-distributed-compensation (non-PDC) control laws is extended to the continuous-time fuzzy-model-based control systems. A nonlinear controller with non-PDC control laws is proposed to stabilize the continuous-time nonlinear systems in Takagi-Sugeno's form. To produce the stability-analysis result, a parameter-dependent Lyapunov function (PDLF) is employed. However, two difficulties are usually encountered: 1) the time-derivative terms produced by the PDLF will complicate the stability analysis and 2) the stability conditions are not in the form of linear-matrix inequalities (LMIs) that aid the design of feedback gains. To tackle the first difficulty, the time-derivative terms are represented by some weighted-sum terms in some existing approaches, which will increase the number of stability conditions significantly. In view of the second difficulty, some positive-definitive terms are added in order to cast the stability conditions into LMIs. In this correspondence, the favorable properties of the membership functions and nonlinear control laws, which allow the introduction of some free matrices, are employed to alleviate the two difficulties while retaining the favorable properties of PDLF-based approach. LMI-based stability conditions are derived to ensure the system stability. Furthermore, based on a common scalar performance index, LMI-based performance conditions are derived to guarantee the system performance. Simulation examples are given to illustrate the effectiveness of the proposed approach.
NASA Astrophysics Data System (ADS)
Lin, Cheng-Jian; Lee, Chi-Yung
2010-04-01
This article introduces a recurrent fuzzy neural network based on improved particle swarm optimisation (IPSO) for non-linear system control. An IPSO method which consists of the modified evolutionary direction operator (MEDO) and the Particle Swarm Optimisation (PSO) is proposed in this article. A MEDO combining the evolutionary direction operator and the migration operation is also proposed. The MEDO will improve the global search solution. Experimental results have shown that the proposed IPSO method controls the magnetic levitation system and the planetary train type inverted pendulum system better than the traditional PSO and the genetic algorithm methods.
Sampled-data fuzzy controller for time-delay nonlinear systems: fuzzy-model-based LMI approach.
Lam, H K; Leung, Frank H F
2007-06-01
This paper presents the stability analysis and performance design for a sampled-data fuzzy control system with time delay, which is formed by a nonlinear plant with time delay and a sampled-data fuzzy controller connected in a closed loop. As the sampled-data fuzzy controller can be implemented by a microcontroller or a digital computer, the implementation time and cost can be reduced. However, the sampling activity and time delay, which are potential causes of system instability, will complicate the system dynamics and make the stability analysis much more difficult than that for a pure continuous-time fuzzy control system. In this paper, a sampled-data fuzzy controller with enhanced nonlinearity compensation ability is proposed. Based on the fuzzy-model-based control approach, linear matrix inequality (LMI)-based stability conditions are derived to guarantee the system stability. By using a descriptor representation, the complexity of the sampled-data fuzzy control system with time delay can be reduced to ease the stability analysis, which effectively leads to a smaller number of LMI-stability conditions. Information of the membership functions of both the fuzzy plant model and fuzzy controller are considered, which allows arbitrary matrices to be introduced, to ease the satisfaction of the stability conditions. An application example will be given to show the merits and design procedure of the proposed approach. Furthermore, LMI-based performance conditions are derived to aid the design of a well-performed sampled-data fuzzy controller.
Liu, Yan-Jun; Li, Jing; Tong, Shaocheng; Chen, C L Philip
2016-07-01
In order to stabilize a class of uncertain nonlinear strict-feedback systems with full-state constraints, an adaptive neural network control method is investigated in this paper. The state constraints are frequently emerged in the real-life plants and how to avoid the violation of state constraints is an important task. By introducing a barrier Lyapunov function (BLF) to every step in a backstepping procedure, a novel adaptive backstepping design is well developed to ensure that the full-state constraints are not violated. At the same time, one remarkable feature is that the minimal learning parameters are employed in BLF backstepping design. By making use of Lyapunov analysis, we can prove that all the signals in the closed-loop system are semiglobal uniformly ultimately bounded and the output is well driven to follow the desired output. Finally, a simulation is given to verify the effectiveness of the method.
Fan, Quan-Yong; Yang, Guang-Hong
2016-01-01
This paper is concerned with the problem of integral sliding-mode control for a class of nonlinear systems with input disturbances and unknown nonlinear terms through the adaptive actor-critic (AC) control method. The main objective is to design a sliding-mode control methodology based on the adaptive dynamic programming (ADP) method, so that the closed-loop system with time-varying disturbances is stable and the nearly optimal performance of the sliding-mode dynamics can be guaranteed. In the first step, a neural network (NN)-based observer and a disturbance observer are designed to approximate the unknown nonlinear terms and estimate the input disturbances, respectively. Based on the NN approximations and disturbance estimations, the discontinuous part of the sliding-mode control is constructed to eliminate the effect of the disturbances and attain the expected equivalent sliding-mode dynamics. Then, the ADP method with AC structure is presented to learn the optimal control for the sliding-mode dynamics online. Reconstructed tuning laws are developed to guarantee the stability of the sliding-mode dynamics and the convergence of the weights of critic and actor NNs. Finally, the simulation results are presented to illustrate the effectiveness of the proposed method.
Kumar, Rajesh; Srivastava, Smriti; Gupta, J R P
2017-03-01
In this paper adaptive control of nonlinear dynamical systems using diagonal recurrent neural network (DRNN) is proposed. The structure of DRNN is a modification of fully connected recurrent neural network (FCRNN). Presence of self-recurrent neurons in the hidden layer of DRNN gives it an ability to capture the dynamic behaviour of the nonlinear plant under consideration (to be controlled). To ensure stability, update rules are developed using lyapunov stability criterion. These rules are then used for adjusting the various parameters of DRNN. The responses of plants obtained with DRNN are compared with those obtained when multi-layer feed forward neural network (MLFFNN) is used as a controller. Also, in example 4, FCRNN is also investigated and compared with DRNN and MLFFNN. Robustness of the proposed control scheme is also tested against parameter variations and disturbance signals. Four simulation examples including one-link robotic manipulator and inverted pendulum are considered on which the proposed controller is applied. The results so obtained show the superiority of DRNN over MLFFNN as a controller.
Consensus tracking for multiagent systems with nonlinear dynamics.
Dong, Runsha
2014-01-01
This paper concerns the problem of consensus tracking for multiagent systems with a dynamical leader. In particular, it proposes the corresponding explicit control laws for multiple first-order nonlinear systems, second-order nonlinear systems, and quite general nonlinear systems based on the leader-follower and the tree shaped network topologies. Several numerical simulations are given to verify the theoretical results.
McKinney, B A; Crowe, J E; Voss, H U; Crooke, P S; Barney, N; Moore, J H
2006-02-01
We introduce a grammar-based hybrid approach to reverse engineering nonlinear ordinary differential equation models from observed time series. This hybrid approach combines a genetic algorithm to search the space of model architectures with a Kalman filter to estimate the model parameters. Domain-specific knowledge is used in a context-free grammar to restrict the search space for the functional form of the target model. We find that the hybrid approach outperforms a pure evolutionary algorithm method, and we observe features in the evolution of the dynamical models that correspond with the emergence of favorable model components. We apply the hybrid method to both artificially generated time series and experimentally observed protein levels from subjects who received the smallpox vaccine. From the observed data, we infer a cytokine protein interaction network for an individual's response to the smallpox vaccine.
NASA Astrophysics Data System (ADS)
McKinney, B. A.; Crowe, J. E., Jr.; Voss, H. U.; Crooke, P. S.; Barney, N.; Moore, J. H.
2006-02-01
We introduce a grammar-based hybrid approach to reverse engineering nonlinear ordinary differential equation models from observed time series. This hybrid approach combines a genetic algorithm to search the space of model architectures with a Kalman filter to estimate the model parameters. Domain-specific knowledge is used in a context-free grammar to restrict the search space for the functional form of the target model. We find that the hybrid approach outperforms a pure evolutionary algorithm method, and we observe features in the evolution of the dynamical models that correspond with the emergence of favorable model components. We apply the hybrid method to both artificially generated time series and experimentally observed protein levels from subjects who received the smallpox vaccine. From the observed data, we infer a cytokine protein interaction network for an individual’s response to the smallpox vaccine.
NASA Astrophysics Data System (ADS)
Fakhimi Derakhshan, Siavash; Fatehi, Alireza
2015-09-01
A non-monotonic Lyapunov function (NMLF) is deployed to design a robust H2 fuzzy observer-based control problem for discrete-time nonlinear systems in the presence of parametric uncertainties. The uncertain nonlinear system is presented as a Takagi and Sugeno (T-S) fuzzy model with norm-bounded uncertainties. The states of the fuzzy system are estimated by a fuzzy observer and the control design is established based on a parallel distributed compensation scheme. In order to derive a sufficient condition to establish the global asymptotic stability of the proposed closed-loop fuzzy system, an NMLF is adopted and an upper bound on the quadratic cost function is provided. The existence of a robust H2 fuzzy observer-based controller is expressed as a sufficient condition in the form of linear matrix inequalities (LMIs) and a sub-optimal fuzzy observer-based controller in the sense of cost bound minimization is obtained by utilising the aforementioned LMI optimisation techniques. Finally, the effectiveness of the proposed scheme is shown through an example.
Wen, Guoxing; Chen, C L Philip; Liu, Yan-Jun; Liu, Zhi
2016-10-11
Compared with the existing neural network (NN) or fuzzy logic system (FLS) based adaptive consensus methods, the proposed approach can greatly alleviate the computation burden because it needs only to update a few adaptive parameters online. In the multiagent agreement control, the system uncertainties derive from the unknown nonlinear dynamics are counteracted by employing the adaptive NNs; the state delays are compensated by designing a Lyapunov-Krasovskii functional. Finally, based on Lyapunov stability theory, it is demonstrated that the proposed consensus scheme can steer a multiagent system synchronizing to the predefined reference signals. Two simulation examples, a numerical multiagent system and a practical multimanipulator system, are carried out to further verify and testify the effectiveness of the proposed agreement approach.
NASA Astrophysics Data System (ADS)
Zhang, Jian; Fujimoto, Koji; Kawamoto, Shunji
The aim of this letter is to show that the unstable equilibrium point of the Japanese standard one-machine infinite-bus system model is eliminated by adding a simple nonlinear complementary control input to the AVR, and then the critical clearing time of the system can be more enhanced in comparison with the PSS by introducing the proposed nonlinear generator control.
Ning, Hanwen; Qing, Guangyan; Jing, Xingjian
2016-11-01
The identification of nonlinear spatiotemporal dynamical systems given by partial differential equations has attracted a lot of attention in the past decades. Several methods, such as searching principle-based algorithms, partially linear kernel methods, and coupled lattice methods, have been developed to address the identification problems. However, most existing methods have some restrictions on sampling processes in that the sampling intervals should usually be very small and uniformly distributed in spatiotemporal domains. These are actually not applicable for some practical applications. In this paper, to tackle this issue, a novel kernel-based learning algorithm named integral least square regularization regression (ILSRR) is proposed, which can be used to effectively achieve accurate derivative estimation for nonlinear functions in the time domain. With this technique, a discretization method named inverse meshless collocation is then developed to realize the dimensional reduction of the system to be identified. Thereafter, with this novel inverse meshless collocation model, the ILSRR, and a multiple-kernel-based learning algorithm, a multistep identification method is systematically proposed to address the identification problem of spatiotemporal systems with pointwise nonuniform observations. Numerical studies for benchmark systems with necessary discussions are presented to illustrate the effectiveness and the advantages of the proposed method.
Nonlinear vibrating system identification via Hilbert decomposition
NASA Astrophysics Data System (ADS)
Feldman, Michael; Braun, Simon
2017-02-01
This paper deals with the identification of nonlinear vibration systems, based on measured signals for free and forced vibration regimes. Two categories of time domain signal are analyzed, one of a fast inter-modulation signal and a second as composed of several mono-components. To some extent, this attempts to imitate analytic studies of such systems, with its two major analysis groups - the perturbation and the harmonic balance methods. Two appropriate signal processing methods are then investigated, one based on demodulation and the other on signal decomposition. The Hilbert Transform (HT) has been shown to enable effective and simple methods of analysis. We show that precise identification of the nonlinear parameters can be obtained, contrary to other average HT based methods where only approximation parameters are obtained. The effectiveness of the proposed methods is demonstrated for the precise nonlinear system identification, using both the signal demodulation and the signal decomposition methods. Following the exposition of the tools used, both the signal demodulation as well as decomposition are applied to classical examples of nonlinear systems. Cases of nonlinear stiffness and damping forces are analyzed. These include, among other, an asymmetric Helmholtz oscillator, a backlash with nonlinear turbulent square friction, and a Duffing oscillator with dry friction.
Liu, Meiqin; Zhang, Senlin; Jin, Yaochu
2011-04-01
This paper is concerned with multi-sensor optimal H(∞) fusion filtering for a class of nonlinear intelligent systems with time delays. A unified model consisting of a linear dynamic system and a bounded static nonlinear operator is employed to describe these systems, such as neural networks and Takagi and Sugeno (T-S) fuzzy models. Based on the H(∞) performance analysis of this unified model using the linear matrix inequality (LMI) approach, centralized and distributed fusion filters are designed for multi-sensor time-delayed systems to guarantee the asymptotic stability of the fusion error systems and to reduce the influence of noise on the filtering error. The parameters of these filters are obtained by solving the eigenvalue problem (EVP). As most artificial neural networks or fuzzy systems with or without time delays can be described with this unified model, fusion filter design for these systems can be done in a unified way. Simulation examples are provided to illustrate the design procedure and effectiveness of the proposed approach. Copyright © 2010 Elsevier Ltd. All rights reserved.
Periodic motion in nonlinear systems
NASA Technical Reports Server (NTRS)
Williamson, D.
1975-01-01
In this paper it is shown how some basic ideas from system theory and differential geometry can be used to establish some new results on the existence of periodic motion in autonomous feedback systems. The conditions are expressed in terms of the frequency response characteristic of the open-loop system and certain general properties of the nonlinearities.
Oscillations in nonlinear feedback systems.
NASA Technical Reports Server (NTRS)
Williamson, D.
1973-01-01
It is shown how some basic ideas from system theory and differential geometry can be used to establish new results concerning the existance of oscillations for autonomous feedback systems. The conditions obtained are expressed in terms of the frequency response characteristic of the open-loop system and certain general properties of the nonlinearity.
NASA Astrophysics Data System (ADS)
Izzuan Jaafar, Hazriq; Mohd Ali, Nursabillilah; Mohamed, Z.; Asmiza Selamat, Nur; Faiz Zainal Abidin, Amar; Jamian, J. J.; Kassim, Anuar Mohamed
2013-12-01
This paper presents development of an optimal PID and PD controllers for controlling the nonlinear gantry crane system. The proposed Binary Particle Swarm Optimization (BPSO) algorithm that uses Priority-based Fitness Scheme is adopted in obtaining five optimal controller gains. The optimal gains are tested on a control structure that combines PID and PD controllers to examine system responses including trolley displacement and payload oscillation. The dynamic model of gantry crane system is derived using Lagrange equation. Simulation is conducted within Matlab environment to verify the performance of system in terms of settling time (Ts), steady state error (SSE) and overshoot (OS). This proposed technique demonstrates that implementation of Priority-based Fitness Scheme in BPSO is effective and able to move the trolley as fast as possible to the various desired position.
Nonlinear dynamical system approaches towards neural prosthesis
Torikai, Hiroyuki; Hashimoto, Sho
2011-04-19
An asynchronous discrete-state spiking neurons is a wired system of shift registers that can mimic nonlinear dynamics of an ODE-based neuron model. The control parameter of the neuron is the wiring pattern among the registers and thus they are suitable for on-chip learning. In this paper an asynchronous discrete-state spiking neuron is introduced and its typical nonlinear phenomena are demonstrated. Also, a learning algorithm for a set of neurons is presented and it is demonstrated that the algorithm enables the set of neurons to reconstruct nonlinear dynamics of another set of neurons with unknown parameter values. The learning function is validated by FPGA experiments.
Nonlinear characteristics of an autoparametric vibration system
NASA Astrophysics Data System (ADS)
Yan, Zhimiao; Taha, Haithem E.; Tan, Ting
2017-03-01
The nonlinear characteristics of an autoparametric vibration system are investigated. This system consists of a base structure and a cantilever beam with a tip mass. The dynamic equations for the system are derived using the extended Hamilton's principle. The method of multiple scales (MMS) is used to determine an approximate analytical solution of the nonlinear governing equations and, hence, analyze the stability and bifurcation of the system. Compared with the numerical simulation, the first-order MMS is not sufficient. A Lagrangian-based approach is proposed to perform a second-order analysis, which is applicable to a large class of nonlinear systems. The effects of the amplitude and frequency of the external force, damping and frequency of the attached cantilever beam, and the tip mass on the nonlinear responses of the autoparametric vibration system are determined. The results show that this system exhibits many interesting nonlinear phenomena including saturation, jumps, hysteresis and different kinds of bifurcations, such as saddle-node, supercritical pitchfork and subcritical pitchfork bifurcations. Power spectra, phase portraits and Poincare maps are employed to analyze the unstable behavior and the associated Hopf bifurcation and chaos. Depending on the application of such a system, its dynamical behaviors could be exploited or avoided.
Based on interval type-2 adaptive fuzzy H∞ tracking controller for SISO time-delay nonlinear systems
NASA Astrophysics Data System (ADS)
Lin, Tsung-Chih; Roopaei, Mehdi
2010-12-01
In this article, based on the adaptive interval type-2 fuzzy logic, by adjusting weights, centers and widths of proposed fuzzy neural network (FNN), the modeling errors can be eliminated for a class of SISO time-delay nonlinear systems. The proposed scheme has the advantage that can guarantee the H∞ tracking performance to attenuate the lumped uncertainties caused by the unmodelled dynamics, the approximation error and the external disturbances. Moreover, the stability analysis of the proposed control scheme will be guaranteed in the sense that all the states and signals are uniformly bounded and arbitrary small attenuation level. The simulation results are demonstrated to show the effectiveness of the advocated design methodology.
Analytical modeling of a single channel nonlinear fiber optic system based on QPSK.
Kumar, Shiva; Shahi, Sina Naderi; Yang, Dong
2012-12-03
A first order perturbation theory is used to develop analytical expressions for the power spectral density (PSD) of the nonlinear distortions due to intra-channel four-wave mixing (IFWM). For non-Gaussian pulses, the PSD can not be calculated analytically. However, using the stationary phase approximations, we found that convolutions become simple multiplications and a simple analytical expression for the PSD of the nonlinear distortion is found. The PSD of the nonlinear distortion is combined with the amplified spontaneous emission (ASE) PSD to obtain the total variance and bit error ratio (BER). The analytically estimated BER is found to be in good agreement with numerical simulations.
Wang, Huanqing; Liu, Peter Xiaoping; Shi, Peng
2017-09-01
This paper is concerned with the observer-based fuzzy output-feedback control for stochastic nonlinear multiple time-delay systems. On the basis of the consistent form of virtual input signals and increasing characteristics of the system upper bound functions, a variable splitting technique is employed to surmount the difficulty occurred in the nonlower-triangular form. In the controller design procedure, a state observer is first designed, and then an adaptive fuzzy output-feedback control method is presented by combining backstepping design together with fuzzy systems' universal approximation capability. The proposed adaptive controller guarantees the semi-global boundedness of closed-loop system trajectories in terms of fourth-moment. Two simulation examples are displayed to demonstrate the feasibility of the suggested controller.
Niu, Ben; Liu, Yanjun; Zong, Guangdeng; Han, Zhaoyu; Fu, Jun
2017-01-16
In this paper, a new adaptive approximation-based tracking controller design approach is developed for a class of uncertain nonlinear switched lower-triangular systems with an output constraint using neural networks (NNs). By introducing a novel barrier Lyapunov function (BLF), the constrained switched system is first transformed into a new system without any constraint, which means the control objectives of the both systems are equivalent. Then command filter technique is applied to solve the so-called "explosion of complexity" problem in traditional backstepping procedure, and radial basis function NNs are directly employed to model the unknown nonlinear functions. The designed controller ensures that all the closed-loop variables are ultimately boundedness, while the output limit is not transgressed and the output tracking error can be reduced arbitrarily small. Furthermore, the use of an asymmetric BLF is also explored to handle the case of asymmetric output constraint as a generalization result. Finally, the control performance of the presented control schemes is illustrated via two examples.
Wen, Yuntong; Ren, Xuemei
2011-10-01
This paper investigates a neural network (NN) state observer-based adaptive control for a class of time-varying delays nonlinear systems with unknown control direction. An adaptive neural memoryless observer, in which the knowledge of time-delay is not used, is designed to estimate the system states. Furthermore, by applying the property of the function tanh(2)(ϑ/ε)/ϑ (the function can be defined at ϑ = 0) and introducing a novel type appropriate Lyapunov-Krasovskii functional, an adaptive output feedback controller is constructed via backstepping method which can efficiently avoid the problem of controller singularity and compensate for the time-delay. It is highly proven that the closed-loop systems controller designed by the NN-basis function property, new kind parameter adaptive law and Nussbaum function in detecting the control direction is able to guarantee the semi-global uniform ultimate boundedness of all signals and the tracking error can converge to a small neighborhood of zero. The characteristic of the proposed approach is that it relaxes any restrictive assumptions of Lipschitz condition for the unknown nonlinear continuous functions. And the proposed scheme is suitable for the systems with mismatching conditions and unmeasurable states. Finally, two simulation examples are given to illustrate the effectiveness and applicability of the proposed approach. © 2011 IEEE
NASA Astrophysics Data System (ADS)
Wang, Yin-He; Luo, Liang; Fan, Yong-Qing; Zhang, Yun; Liu, Xiao-Ping; Zhang, Si-Ying
2014-03-01
Many practical engineering applications require various types of fuzzy logic systems (FLSs) to design adaptive controllers for nonlinear systems with uncertainties. In this article, we will consider a fundamental theoretical question: is it possible to find a unified adaptive control design method suited to various types of FLSs? In order to solve this problem, we will introduce scalers and saturators at the input and output terminals of FLSs to form the extended FLSs (EFLS). The scalers and saturators have adjustable parameters. By designing the updated laws of these parameters and the estimate values of the fuzzy approximate accuracies, stable adaptive fuzzy controllers can be realised for a class of nonlinear systems with unknown homogeneous drift functions and gains. The proposed design method is only dependent on the outputs of EFLS and the above updated laws, thus increasing its adaptability. The fuzzy control scheme introduced in this article is suitable for all fuzzy systems with or without fuzzy rules. Simulations will also be used to show the validity of the method proposed in this article.
Damage detection in initially nonlinear systems
Bornn, Luke; Farrar, Charles; Park, Gyuhae
2009-01-01
The primary goal of Structural Health Monitoring (SHM) is to detect structural anomalies before they reach a critical level. Because of the potential life-safety and economic benefits, SHM has been widely studied over the past decade. In recent years there has been an effort to provide solid mathematical and physical underpinnings for these methods; however, most focus on systems that behave linearly in their undamaged state - a condition that often does not hold in complex 'real world' systems and systems for which monitoring begins mid-lifecycle. In this work, we highlight the inadequacy of linear-based methodology in handling initially nonlinear systems. We then show how the recently developed autoregressive support vector machine (AR-SVM) approach to time series modeling can be used for detecting damage in a system that exhibits initially nonlinear response. This process is applied to data acquired from a structure with induced nonlinearity tested in a laboratory environment.
A new neural network-based approach for self-tuning control of nonlinear SISO discrete-time systems
NASA Astrophysics Data System (ADS)
Canelon, Jose I.; Shieh, Leang S.; Song, Gangbing
2010-12-01
This article presents a new neural network-based approach for self-tuning control of nonlinear single-input single-output (SISO) discrete-time dynamic systems. According to the approach, a neural network ARMAX (NN-ARMAX) model of the system is identified and continuously updated, using an online training algorithm. Control design is accomplished by solving an optimal discrete-time linear quadratic tracking problem using an observer-type linear state-space Kalman innovation model, which is built from the parameters of a local linear version of the NN-ARMAX model. The state-feedback control law is implemented using the Kalman state, which is calculated without estimating the noise covariance properties. The proposed control approach is shown to be very effective and outperforms the self-tuning control approach based on a linear ARMAX model on two simulation examples.
A Self-Check System for Mental Health Care based on Nonlinear and Chaos Analysis
NASA Astrophysics Data System (ADS)
Oyama-Higa, Mayumi; Miao, Tiejun; Cheng, Huaichang; Tang, Yuan Guang
2007-11-01
We applied nonlinear and chaos analysis to fingertip pulse wave data. The largest Lyapunov exponent, a measure of the "divergence" of the trajectory of the attractor in phase space, was found to be a useful index of mental health in humans, particularly for the early detection of dementia and depressive psychosis, and for monitoring mental changes in healthy persons. Most of the methods used for assessing mental health are subjective. A few of existing objective methods, such as those using EEG and ECG, for example, are not simple to use and expansive. Therefore, we developed an easy-to-use economical device, a PC mouse with an integrated sensor for measuring the pulse waves, and its required software, to make the measurements. After about 1 min of measurement, the Lyapunov exponent is calculated and displayed as a graph on the PC. An advantage of this system is that the measurements can be made very easily, and hence mental health can be assessed during operating a PC using the pulse wave mouse. Moreover, the measured data can be saved according to the time and date, so diurnal changes and changes over longer time periods can be monitored as a time series and history. At the time the pulse waves are measured, we ask the subject about his or her physical health and mood, and use their responses, along with the Lyapunov exponents, as factors causing variation in the divergence. The changes in the Lyapunov exponent are displayed on the PC as constellation graphs, which we developed to facilitate simpler self-diagnosis and problem resolution.
NASA Astrophysics Data System (ADS)
Yu, Zhaoxu; Li, Shugang; Li, Fangfei
2016-01-01
The problem of adaptive output feedback stabilisation is addressed for a more general class of non-strict-feedback stochastic nonlinear systems in this paper. The neural network (NN) approximation and the variable separation technique are utilised to deal with the unknown subsystem functions with the whole states. Based on the design of a simple input-driven observer, an adaptive NN output feedback controller which contains only one parameter to be updated is developed for such systems by using the dynamic surface control method. The proposed control scheme ensures that all signals in the closed-loop systems are bounded in probability and the error signals remain semi-globally uniformly ultimately bounded in fourth moment (or mean square). Two simulation examples are given to illustrate the effectiveness of the proposed control design.
NASA Astrophysics Data System (ADS)
Yuan, Lei; Wu, Han-Song
2010-12-01
A terminal sliding mode fuzzy control based on multiple sliding surfaces was proposed for ship course tracking steering, which takes account of rudder characteristics and parameter uncertainty. In order to solve the problem, the controller was designed by employing the universal approximation property of fuzzy logic system, the advantage of Nussbaum function, and using multiple sliding mode control algorithm based on the recursive technique. In the last step of designing, a nonsingular terminal sliding mode was utilized to drive the last state of the system to converge in a finite period of time, and high-order sliding mode control law was designed to eliminate the chattering and make the system robust. The simulation results showed that the controller designed here could track a desired course fast and accurately. It also exhibited strong robustness peculiarly to system, and had better adaptive ability than traditional PID control algorithms.
NASA Astrophysics Data System (ADS)
Guesmi, Latifa; Menif, Mourad
2016-04-01
The field of fiber optics nonlinearity is more discussed last years due to such remarkable enhancement in the nonlinear processes efficiency. In this paper, and for optical performance monitoring (OPM), a new achievement of nonlinear effects has been investigated. The use of cross-phase modulation (XPM) and four-wave mixing (FWM) effects between input optical signal and inserted continuous-wave probe has proposed for impairments monitoring. Indeed, transmitting a multi-channels phase modulated signal at high data rate (1 Tbps WDM Nyquist NRZ- DP-QPSK) improves the sensitivity and the dynamic range monitoring. It was observed by simulation results that various optical parameters including optical power, wavelength, chromatic dispersion (CD), polarization mode dispersion (PMD), optical signal-to-noise ratio (OSNR), Q-factor and so on, can be monitored. Also, the effect of increasing the channel spacing between WDM signals is studied and proved its use for FWM power monitoring.
Hwang, Chih-Lyang; Jan, Chau
2016-02-01
At the beginning, an approximate nonlinear autoregressive moving average (NARMA) model is employed to represent a class of multivariable nonlinear dynamic systems with time-varying delay. It is known that the disadvantages of robust control for the NARMA model are as follows: 1) suitable control parameters for larger time delay are more sensitive to achieving desirable performance; 2) it only deals with bounded uncertainty; and 3) the nominal NARMA model must be learned in advance. Due to the dynamic feature of the NARMA model, a recurrent neural network (RNN) is online applied to learn it. However, the system performance becomes deteriorated due to the poor learning of the larger variation of system vector functions. In this situation, a simple network is employed to compensate the upper bound of the residue caused by the linear parameterization of the approximation error of RNN. An e -modification learning law with a projection for weight matrix is applied to guarantee its boundedness without persistent excitation. Under suitable conditions, the semiglobally ultimately bounded tracking with the boundedness of estimated weight matrix is obtained by the proposed RNN-based multivariable adaptive control. Finally, simulations are presented to verify the effectiveness and robustness of the proposed control.
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.
Discrete time learning control in nonlinear systems
NASA Technical Reports Server (NTRS)
Longman, Richard W.; Chang, Chi-Kuang; Phan, Minh
1992-01-01
In this paper digital learning control methods are developed primarily for use in single-input, single-output nonlinear dynamic systems. Conditions for convergence of the basic form of learning control based on integral control concepts are given, and shown to be satisfied by a large class of nonlinear problems. It is shown that it is not the gross nonlinearities of the differential equations that matter in the convergence, but rather the much smaller nonlinearities that can manifest themselves during the short time interval of one sample time. New algorithms are developed that eliminate restrictions on the size of the learning gain, and on knowledge of the appropriate sign of the learning gain, for convergence to zero error in tracking a feasible desired output trajectory. It is shown that one of the new algorithms can give guaranteed convergence in the presence of actuator saturation constraints, and indicate when the requested trajectory is beyond the actuator capabilities.
Liu, Yan-Jun; Tong, Shaocheng
2016-11-01
In this paper, we propose an optimal control scheme-based adaptive neural network design for a class of unknown nonlinear discrete-time systems. The controlled systems are in a block-triangular multi-input-multi-output pure-feedback structure, i.e., there are both state and input couplings and nonaffine functions to be included in every equation of each subsystem. The design objective is to provide a control scheme, which not only guarantees the stability of the systems, but also achieves optimal control performance. The main contribution of this paper is that it is for the first time to achieve the optimal performance for such a class of systems. Owing to the interactions among subsystems, making an optimal control signal is a difficult task. The design ideas are that: 1) the systems are transformed into an output predictor form; 2) for the output predictor, the ideal control signal and the strategic utility function can be approximated by using an action network and a critic network, respectively; and 3) an optimal control signal is constructed with the weight update rules to be designed based on a gradient descent method. The stability of the systems can be proved based on the difference Lyapunov method. Finally, a numerical simulation is given to illustrate the performance of the proposed scheme.
A Nonlinear Dynamical Systems based Model for Stochastic Simulation of Streamflow
NASA Astrophysics Data System (ADS)
Erkyihun, S. T.; Rajagopalan, B.; Zagona, E. A.
2014-12-01
Traditional time series methods model the evolution of the underlying process as a linear or nonlinear function of the autocorrelation. These methods capture the distributional statistics but are incapable of providing insights into the dynamics of the process, the potential regimes, and predictability. This work develops a nonlinear dynamical model for stochastic simulation of streamflows. In this, first a wavelet spectral analysis is employed on the flow series to isolate dominant orthogonal quasi periodic timeseries components. The periodic bands are added denoting the 'signal' component of the time series and the residual being the 'noise' component. Next, the underlying nonlinear dynamics of this combined band time series is recovered. For this the univariate time series is embedded in a d-dimensional space with an appropriate lag T to recover the state space in which the dynamics unfolds. Predictability is assessed by quantifying the divergence of trajectories in the state space with time, as Lyapunov exponents. The nonlinear dynamics in conjunction with a K-nearest neighbor time resampling is used to simulate the combined band, to which the noise component is added to simulate the timeseries. We demonstrate this method by applying it to the data at Lees Ferry that comprises of both the paleo reconstructed and naturalized historic annual flow spanning 1490-2010. We identify interesting dynamics of the signal in the flow series and epochal behavior of predictability. These will be of immense use for water resources planning and management.
Periodic response of nonlinear systems
NASA Technical Reports Server (NTRS)
Nataraj, C.; Nelson, H. D.
1988-01-01
A procedure is developed to determine approximate periodic solutions of autonomous and non-autonomous systems. The trignometric collocation method (TCM) is formalized to allow for the analysis of relatively small order systems directly in physical coordinates. The TCM is extended to large order systems by utilizing modal analysis in a component mode synthesis strategy. The procedure was coded and verified by several check cases. Numerical results for two small order mechanical systems and one large order rotor dynamic system are presented. The method allows for the possibility of approximating periodic responses for large order forced and self-excited nonlinear systems.
2004-01-01
characteristics, and applied to presented small-gain theorems guaranteeing the lack of oscillatory or more complicated behavior in a large class of Lotka ... Volterra systems with predator-prey interactions as well as chemostats, which describe the interaction between microbial species which are competing
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.
Integrated analysis and design for controlled nonlinear multibody systems
NASA Technical Reports Server (NTRS)
Wu, Shih-Chin; Juang, Jer-Nan; Belvin, W. Keith; Woodard, Stanley E.
1991-01-01
A hybrid approach for integrated analysis and design of nonlinear multibody systems is proposed. Based on the approach, a general-purpose design tool is developed for nonlinear dynamic systems subjected to nonlinear design constraints. For analysis purposes, second-order nonlinear equations of motion of the system are automatically generated using general-purpose multibody formulations. Once the equations are solved, they are written in first-order form to take advantage of the first-order formulations of design sensitivity analysis for dynamic systems. A nonlinear programming technique is then used to optimize the nonlinear systems, such that a nonlinear cost function is minimized and performance constraints are satisfied. The approach proved to be very general and useful for design and analysis of controlled multibody systems. The approach is applied to the design of passive dynamic controllers for slewing control of multibody systems.
Nonlinear multi-analysis of agent-based financial market dynamics by epidemic system.
Lu, Yunfan; Wang, Jun; Niu, Hongli
2015-10-01
Based on the epidemic dynamical system, we construct a new agent-based financial time series model. In order to check and testify its rationality, we compare the statistical properties of the time series model with the real stock market indices, Shanghai Stock Exchange Composite Index and Shenzhen Stock Exchange Component Index. For analyzing the statistical properties, we combine the multi-parameter analysis with the tail distribution analysis, the modified rescaled range analysis, and the multifractal detrended fluctuation analysis. For a better perspective, the three-dimensional diagrams are used to present the analysis results. The empirical research in this paper indicates that the long-range dependence property and the multifractal phenomenon exist in the real returns and the proposed model. Therefore, the new agent-based financial model can recurrence some important features of real stock markets.
Nonlinear multi-analysis of agent-based financial market dynamics by epidemic system
NASA Astrophysics Data System (ADS)
Lu, Yunfan; Wang, Jun; Niu, Hongli
2015-10-01
Based on the epidemic dynamical system, we construct a new agent-based financial time series model. In order to check and testify its rationality, we compare the statistical properties of the time series model with the real stock market indices, Shanghai Stock Exchange Composite Index and Shenzhen Stock Exchange Component Index. For analyzing the statistical properties, we combine the multi-parameter analysis with the tail distribution analysis, the modified rescaled range analysis, and the multifractal detrended fluctuation analysis. For a better perspective, the three-dimensional diagrams are used to present the analysis results. The empirical research in this paper indicates that the long-range dependence property and the multifractal phenomenon exist in the real returns and the proposed model. Therefore, the new agent-based financial model can recurrence some important features of real stock markets.
Spanos, Pol D.; Giaralis, Agathoklis
2008-07-08
A stochastic approach is proposed to obtain reliable estimates of the peak response of nonlinear systems to excitations specified via a response/design seismic spectrum. This is achieved without resorting to numerical integration of the governing nonlinear equations of motion. First, a numerical scheme is utilized to derive a power spectrum which is compatible in a stochastic sense to a given elastic design spectrum. This spectrum is then treated as the excitation spectrum in the context of the statistical linearization method to determine effective parameters, damping and stiffness, corresponding to an equivalent linear system (ELS). The obtained parameters are used in conjunction with the linear design spectrum, for various values of damping, to estimate the response of certain nonlinear systems. The case of single-degree-of-freedom systems with cubic stiffness nonlinearity and hysteretic systems whose restoring force traces a bilinear law are considered in conjunction with the elastic design spectrum prescribed by the European aseismic code provisions (EC8). Monte Carlo simulations pertaining to an ensemble of non-stationary EC 8 design spectrum compatible accelerograms are conducted to confirm that the average peak response of the nonlinear systems compare reasonably well with that of the ELS. This is true, even in cases where the response of the nonlinear oscillators deviates significantly from the linear one. In this manner, the proposed approach yields ELS which can reliably replace the original nonlinear systems in carrying out computationally efficient analyses in the initial stages of the aseismic design of structures under severe seismic excitations. Furthermore, the potential of this approach for developing inelastic design spectra from a given elastic design spectrum is established.
NASA Astrophysics Data System (ADS)
Cheng, C. M.; Peng, Z. K.; Zhang, W. M.; Meng, G.
2017-03-01
Nonlinear problems have drawn great interest and extensive attention from engineers, physicists and mathematicians and many other scientists because most real systems are inherently nonlinear in nature. To model and analyze nonlinear systems, many mathematical theories and methods have been developed, including Volterra series. In this paper, the basic definition of the Volterra series is recapitulated, together with some frequency domain concepts which are derived from the Volterra series, including the general frequency response function (GFRF), the nonlinear output frequency response function (NOFRF), output frequency response function (OFRF) and associated frequency response function (AFRF). The relationship between the Volterra series and other nonlinear system models and nonlinear problem solving methods are discussed, including the Taylor series, Wiener series, NARMAX model, Hammerstein model, Wiener model, Wiener-Hammerstein model, harmonic balance method, perturbation method and Adomian decomposition. The challenging problems and their state of arts in the series convergence study and the kernel identification study are comprehensively introduced. In addition, a detailed review is then given on the applications of Volterra series in mechanical engineering, aeroelasticity problem, control engineering, electronic and electrical engineering.
NASA Astrophysics Data System (ADS)
Liu, Jian; Zhu, Ka-Di
2017-02-01
In the present paper, we provide a scheme to probe the gradient of gravity at the nanoscale in a levitated nanomechanical resonator coupled to a cavity via two-field optical control. The enhanced sharp peak on the probe spectrum will suffer a distinct shift with the nonuniform force being taken into consideration. The nonlinear optics with very narrow bandwidth (10-8 Hz ) resulting from the extremely high-quality factor will lead to a superresolution of 10-20 N /m for the measurement of gravity gradient. The improved sensitivity may offer new opportunities for detecting Yukawa moduli forces and Kaluza-Klein gravitons in extra dimensions.
Almanji, Amur; Payne, Alex R; Amor, Robert; Davies, T Claire
2015-11-01
This paper provides a detailed model for analyzing movement time performance during rapid goal-directed point- and-click motions with a computer mouse. Twelve typically developed individuals and eleven youths with cerebral palsy conducted point and click computer tasks from which the model was developed. The proposed model is nonlinear and based on both system (target width and movement amplitude) and human effects (erroneous clicks, number of submovements, number of slip-offs, curvature index, and average speed). To ensure successful targeting by youths with cerebral palsy, the index of difficulty was limited to a range of 1.58 - 3.0 bits. For consistency, the same range was used with both groups. The most significant contributing human effect to movement time was found to be the curvature index for both typically developed individuals and individuals with cerebral palsy. This model will assist in algorithm development to improve cursor speed and accuracy for youths with cerebral palsy.
Yan, Zheng; Wang, Jun
2014-03-01
This paper presents a neural network approach to robust model predictive control (MPC) for constrained discrete-time nonlinear systems with unmodeled dynamics affected by bounded uncertainties. The exact nonlinear model of underlying process is not precisely known, but a partially known nominal model is available. This partially known nonlinear model is first decomposed to an affine term plus an unknown high-order term via Jacobian linearization. The linearization residue combined with unmodeled dynamics is then modeled using an extreme learning machine via supervised learning. The minimax methodology is exploited to deal with bounded uncertainties. The minimax optimization problem is reformulated as a convex minimization problem and is iteratively solved by a two-layer recurrent neural network. The proposed neurodynamic approach to nonlinear MPC improves the computational efficiency and sheds a light for real-time implementability of MPC technology. Simulation results are provided to substantiate the effectiveness and characteristics of the proposed approach.
Consensus Tracking for Multiagent Systems with Nonlinear Dynamics
2014-01-01
This paper concerns the problem of consensus tracking for multiagent systems with a dynamical leader. In particular, it proposes the corresponding explicit control laws for multiple first-order nonlinear systems, second-order nonlinear systems, and quite general nonlinear systems based on the leader-follower and the tree shaped network topologies. Several numerical simulations are given to verify the theoretical results. PMID:25197689
Zhao, Qiming; Xu, Hao; Jagannathan, Sarangapani
2015-03-01
In this paper, the finite-horizon optimal control design for nonlinear discrete-time systems in affine form is presented. In contrast with the traditional approximate dynamic programming methodology, which requires at least partial knowledge of the system dynamics, in this paper, the complete system dynamics are relaxed utilizing a neural network (NN)-based identifier to learn the control coefficient matrix. The identifier is then used together with the actor-critic-based scheme to learn the time-varying solution, referred to as the value function, of the Hamilton-Jacobi-Bellman (HJB) equation in an online and forward-in-time manner. Since the solution of HJB is time-varying, NNs with constant weights and time-varying activation functions are considered. To properly satisfy the terminal constraint, an additional error term is incorporated in the novel update law such that the terminal constraint error is also minimized over time. Policy and/or value iterations are not needed and the NN weights are updated once a sampling instant. The uniform ultimate boundedness of the closed-loop system is verified by standard Lyapunov stability theory under nonautonomous analysis. Numerical examples are provided to illustrate the effectiveness of the proposed method.
2012-01-01
Background The estimation of parameter values for mathematical models of biological systems is an optimization problem that is particularly challenging due to the nonlinearities involved. One major difficulty is the existence of multiple minima in which standard optimization methods may fall during the search. Deterministic global optimization methods overcome this limitation, ensuring convergence to the global optimum within a desired tolerance. Global optimization techniques are usually classified into stochastic and deterministic. The former typically lead to lower CPU times but offer no guarantee of convergence to the global minimum in a finite number of iterations. In contrast, deterministic methods provide solutions of a given quality (i.e., optimality gap), but tend to lead to large computational burdens. Results This work presents a deterministic outer approximation-based algorithm for the global optimization of dynamic problems arising in the parameter estimation of models of biological systems. Our approach, which offers a theoretical guarantee of convergence to global minimum, is based on reformulating the set of ordinary differential equations into an equivalent set of algebraic equations through the use of orthogonal collocation methods, giving rise to a nonconvex nonlinear programming (NLP) problem. This nonconvex NLP is decomposed into two hierarchical levels: a master mixed-integer linear programming problem (MILP) that provides a rigorous lower bound on the optimal solution, and a reduced-space slave NLP that yields an upper bound. The algorithm iterates between these two levels until a termination criterion is satisfied. Conclusion The capabilities of our approach were tested in two benchmark problems, in which the performance of our algorithm was compared with that of the commercial global optimization package BARON. The proposed strategy produced near optimal solutions (i.e., within a desired tolerance) in a fraction of the CPU time required by
Miró, Anton; Pozo, Carlos; Guillén-Gosálbez, Gonzalo; Egea, Jose A; Jiménez, Laureano
2012-05-10
The estimation of parameter values for mathematical models of biological systems is an optimization problem that is particularly challenging due to the nonlinearities involved. One major difficulty is the existence of multiple minima in which standard optimization methods may fall during the search. Deterministic global optimization methods overcome this limitation, ensuring convergence to the global optimum within a desired tolerance. Global optimization techniques are usually classified into stochastic and deterministic. The former typically lead to lower CPU times but offer no guarantee of convergence to the global minimum in a finite number of iterations. In contrast, deterministic methods provide solutions of a given quality (i.e., optimality gap), but tend to lead to large computational burdens. This work presents a deterministic outer approximation-based algorithm for the global optimization of dynamic problems arising in the parameter estimation of models of biological systems. Our approach, which offers a theoretical guarantee of convergence to global minimum, is based on reformulating the set of ordinary differential equations into an equivalent set of algebraic equations through the use of orthogonal collocation methods, giving rise to a nonconvex nonlinear programming (NLP) problem. This nonconvex NLP is decomposed into two hierarchical levels: a master mixed-integer linear programming problem (MILP) that provides a rigorous lower bound on the optimal solution, and a reduced-space slave NLP that yields an upper bound. The algorithm iterates between these two levels until a termination criterion is satisfied. The capabilities of our approach were tested in two benchmark problems, in which the performance of our algorithm was compared with that of the commercial global optimization package BARON. The proposed strategy produced near optimal solutions (i.e., within a desired tolerance) in a fraction of the CPU time required by BARON.
Nonlinear systems approach to control system design
NASA Technical Reports Server (NTRS)
Meyer, G.
1984-01-01
Consider some of the control system design methods for plants with nonlinear dynamics. If the nonlinearity is weak relative to the size of the operating region, then the linear methods apply directly. Fixed-gain design may be feasible even for significant nonlinearities. It may be possible to find a single gain which provides adequate control of the linear models at several perturbation points. If the nonlinearity is restricted to a sector, that fact may be used to obtain a fixed-gain controller. Otherwise, a gain may have to be associated with each perturbation point Pi. A gain schedule K(p(v)) is obtained by connecting the perturbation points by a function, say p(v), of the scheduling parameter v (i.e., speed). When the scheduling parameter must be multidimensional, this approach is difficult; the objective is to develop an easier procedure.
Shahnazi, Reza
2015-01-01
An adaptive fuzzy output feedback controller is proposed for a class of uncertain MIMO nonlinear systems with unknown input nonlinearities. The input nonlinearities can be backlash-like hysteresis or dead-zone. Besides, the gains of unknown input nonlinearities are unknown nonlinear functions. Based on universal approximation theorem, the unknown nonlinear functions are approximated by fuzzy systems. The proposed method does not need the availability of the states and an observer based on strictly positive real (SPR) theory is designed to estimate the states. An adaptive robust structure is used to cope with fuzzy approximation error and external disturbances. The semi-global asymptotic stability of the closed-loop system is guaranteed via Lyapunov approach. The applicability of the proposed method is also shown via simulations. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
Optimized spectral estimation for nonlinear synchronizing systems
NASA Astrophysics Data System (ADS)
Sommerlade, Linda; Mader, Malenka; Mader, Wolfgang; Timmer, Jens; Thiel, Marco; Grebogi, Celso; Schelter, Björn
2014-03-01
In many fields of research nonlinear dynamical systems are investigated. When more than one process is measured, besides the distinct properties of the individual processes, their interactions are of interest. Often linear methods such as coherence are used for the analysis. The estimation of coherence can lead to false conclusions when applied without fulfilling several key assumptions. We introduce a data driven method to optimize the choice of the parameters for spectral estimation. Its applicability is demonstrated based on analytical calculations and exemplified in a simulation study. We complete our investigation with an application to nonlinear tremor signals in Parkinson's disease. In particular, we analyze electroencephalogram and electromyogram data.
Optimized spectral estimation for nonlinear synchronizing systems.
Sommerlade, Linda; Mader, Malenka; Mader, Wolfgang; Timmer, Jens; Thiel, Marco; Grebogi, Celso; Schelter, Björn
2014-03-01
In many fields of research nonlinear dynamical systems are investigated. When more than one process is measured, besides the distinct properties of the individual processes, their interactions are of interest. Often linear methods such as coherence are used for the analysis. The estimation of coherence can lead to false conclusions when applied without fulfilling several key assumptions. We introduce a data driven method to optimize the choice of the parameters for spectral estimation. Its applicability is demonstrated based on analytical calculations and exemplified in a simulation study. We complete our investigation with an application to nonlinear tremor signals in Parkinson's disease. In particular, we analyze electroencephalogram and electromyogram data.
Liu, Derong; Wang, Ding; Wang, Fei-Yue; Li, Hongliang; Yang, Xiong
2014-12-01
In this paper, the infinite horizon optimal robust guaranteed cost control of continuous-time uncertain nonlinear systems is investigated using neural-network-based online solution of Hamilton-Jacobi-Bellman (HJB) equation. By establishing an appropriate bounded function and defining a modified cost function, the optimal robust guaranteed cost control problem is transformed into an optimal control problem. It can be observed that the optimal cost function of the nominal system is nothing but the optimal guaranteed cost of the original uncertain system. A critic neural network is constructed to facilitate the solution of the modified HJB equation corresponding to the nominal system. More importantly, an additional stabilizing term is introduced for helping to verify the stability, which reinforces the updating process of the weight vector and reduces the requirement of an initial stabilizing control. The uniform ultimate boundedness of the closed-loop system is analyzed by using the Lyapunov approach as well. Two simulation examples are provided to verify the effectiveness of the present control approach.
Zhang, Jilie; Zhang, Huaguang; Liu, Zhenwei; Wang, Yingchun
2015-07-01
In this paper, we consider the problem of developing a controller for continuous-time nonlinear systems where the equations governing the system are unknown. Using the measurements, two new online schemes are presented for synthesizing a controller without building or assuming a model for the system, by two new implementation schemes based on adaptive dynamic programming (ADP). To circumvent the requirement of the prior knowledge for systems, a precompensator is introduced to construct an augmented system. The corresponding Hamilton-Jacobi-Bellman (HJB) equation is solved by adaptive dynamic programming, which consists of the least-squared technique, neural network approximator and policy iteration (PI) algorithm. The main idea of our method is to sample the information of state, state derivative and input to update the weighs of neural network by least-squared technique. The update process is implemented in the framework of PI. In this paper, two new implementation schemes are presented. Finally, several examples are given to illustrate the effectiveness of our schemes.
Noise in Nonlinear Dynamical Systems
NASA Astrophysics Data System (ADS)
Moss, Frank; McClintock, P. V. E.
2009-08-01
List of contributors; Preface; Introduction to volume three; 1. The effects of coloured quadratic noise on a turbulent transition in liquid He II J. T. Tough; 2. Electrohydrodynamic instability of nematic liquid crystals: growth process and influence of noise S. Kai; 3. Suppression of electrohydrodynamic instabilities by external noise Helmut R. Brand; 4. Coloured noise in dye laser fluctuations R. Roy, A. W. Yu and S. Zhu; 5. Noisy dynamics in optically bistable systems E. Arimondo, D. Hennequin and P. Glorieux; 6. Use of an electronic model as a guideline in experiments on transient optical bistability W. Lange; 7. Computer experiments in nonlinear stochastic physics Riccardo Mannella; 8. Analogue simulations of stochastic processes by means of minimum component electronic devices Leone Fronzoni; 9. Analogue techniques for the study of problems in stochastic nonlinear dynamics P. V. E. McClintock and Frank Moss; Index.
NASA Astrophysics Data System (ADS)
Jaafar, Hazriq Izzuan; Latif, Norfaneysa Abd; Kassim, Anuar Mohamed; Abidin, Amar Faiz Zainal; Hussien, Sharifah Yuslinda Syed; Aras, Mohd Shahrieel Mohd
2015-05-01
Advanced manufacturing technology made Gantry Crane System (GCS) is one of the suitable heavy machinery transporters and frequently employed in handling with huge materials. The interconnection of trolley movement and payload oscillation has a technical impact which needs to be considered. Once the trolley moves to the desired position with high speed, this will induce undesirable's payload oscillation. This frequent unavoidable load swing causes an efficiency drop, load damages and even accidents. In this paper, a new control strategy of Firefly Algorithm (FA) will be developed to obtain five optimal controller parameters (PID and PD) via Priority-based Fitness Scheme (PFS). Combinations of these five parameters are utilized for controlling trolley movement and minimizing the angle of payload oscillation. This PFS is prioritized based on steady-state error (SSE), overshoot (OS) and settling time (Ts) according to the needs and circumstances. Lagrange equation will be chosen for modeling and simulation will be conducted by using related software. Simulation results show that the proposed control strategy is efficient to control the trolley movement to the desired position and minimize the angle of payload oscillation.
Augmented nonlinear differentiator design and application to nonlinear uncertain systems.
Shao, Xingling; Liu, Jun; Li, Jie; Cao, Huiliang; Shen, Chong; Zhang, Xiaoming
2017-03-01
In this paper, an augmented nonlinear differentiator (AND) based on sigmoid function is developed to calculate the noise-less time derivative under noisy measurement condition. The essential philosophy of proposed AND in achieving high attenuation of noise effect is established by expanding the signal dynamics with extra state variable representing the integrated noisy measurement, then with the integral of measurement as input, the augmented differentiator is formulated to improve the estimation quality. The prominent advantages of the present differentiation technique are: (i) better noise suppression ability can be achieved without appreciable delay; (ii) the improved methodology can be readily extended to construct augmented high-order differentiator to obtain multiple derivatives. In addition, the convergence property and robustness performance against noises are investigated via singular perturbation theory and describing function method, respectively. Also, comparison with several classical differentiators is given to illustrate the superiority of AND in noise suppression. Finally, the robust control problems of nonlinear uncertain systems, including a numerical example and a mass spring system, are addressed to demonstrate the effectiveness of AND in precisely estimating the disturbance and providing the unavailable differential estimate to implement output feedback based controller.
NASA Astrophysics Data System (ADS)
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.
Ma, Lifeng; Wang, Zidong; Lam, Hak-Keung; Kyriakoulis, Nikos
2016-07-07
In this paper, the distributed set-membership filtering problem is investigated for a class of discrete time-varying system with an event-based communication mechanism over sensor networks. The system under consideration is subject to sector-bounded nonlinearity, unknown but bounded noises and sensor saturations. Each intelligent sensing node transmits the data to its neighbors only when certain triggering condition is violated. By means of a set of recursive matrix inequalities, sufficient conditions are derived for the existence of the desired distributed event-based filter which is capable of confining the system state in certain ellipsoidal regions centered at the estimates. Within the established theoretical framework, two additional optimization problems are formulated: one is to seek the minimal ellipsoids (in the sense of matrix trace) for the best filtering performance, and the other is to maximize the triggering threshold so as to reduce the triggering frequency with satisfactory filtering performance. A numerically attractive chaos algorithm is employed to solve the optimization problems. Finally, an illustrative example is presented to demonstrate the effectiveness and applicability of the proposed algorithm.
Han, Jian; Zhang, Huaguang; Wang, Yingchun; Liu, Yang
2015-11-01
This paper addresses the problems of fault estimation (FE) and fault tolerant control (FTC) for fuzzy systems with local nonlinear models, external disturbances, sensor and actuator faults, simultaneously. Disturbance observer (DO) and FE observer are designed, simultaneously. Compared with the existing results, the proposed observer is with a wider application range. Using the estimation information, a novel fuzzy dynamic output feedback fault tolerant controller (DOFFTC) is designed. The controller can be used for the fuzzy systems with unmeasurable local nonlinear models, mismatched input disturbances, and measurement output affecting by sensor faults and disturbances. At last, the simulation shows the effectiveness of the proposed methods.
Research on Nonlinear Dynamical Systems.
1983-01-10
Professor J. P. LaSalle Grant DAAG29-79 C 0161 September 1, 1979 - September 24, 1982 Principal Investigators: H. T. Banks C. M. Dafermos J. K. Hale E...F. Infante J. P. LaSalle . J. Mallet-Paret Lefschetz Center for Dynamical Systems Division of Applied Mathematics D T I Brown University L emtc...publications LaSALLE , J.P. [94] Stability of nonautonomous systems, Journal of Nonlinear Analysis: Theory, Methods, and Applications, Vol.1, No.1
Li, Da-Peng; Li, Dong-Juan; Liu, Yan-Jun; Tong, Shaocheng; Chen, C L Philip
2017-10-01
This paper deals with the tracking control problem for a class of nonlinear multiple input multiple output unknown time-varying delay systems with full state constraints. To overcome the challenges which cause by the appearances of the unknown time-varying delays and full-state constraints simultaneously in the systems, an adaptive control method is presented for such systems for the first time. The appropriate Lyapunov-Krasovskii functions and a separation technique are employed to eliminate the effect of unknown time-varying delays. The barrier Lyapunov functions are employed to prevent the violation of the full state constraints. The singular problems are dealt with by introducing the signal function. Finally, it is proven that the proposed method can both guarantee the good tracking performance of the systems output, all states are remained in the constrained interval and all the closed-loop signals are bounded in the design process based on choosing appropriate design parameters. The practicability of the proposed control technique is demonstrated by a simulation study in this paper.
Application of nonlinear time series models to driven systems
Hunter, N.F. Jr.
1990-01-01
In our laboratory we have been engaged in an effort to model nonlinear systems using time series methods. Our objectives have been, first, to understand how the time series response of a nonlinear system unfolds as a function of the underlying state variables, second, to model the evolution of the state variables, and finally, to predict nonlinear system responses. We hope to address the relationship between model parameters and system parameters in the near future. Control of nonlinear systems based on experimentally derived parameters is also a planned topic of future research. 28 refs., 15 figs., 2 tabs.
Indirect learning control for nonlinear dynamical systems
NASA Technical Reports Server (NTRS)
Ryu, Yeong Soon; Longman, Richard W.
1993-01-01
In a previous paper, learning control algorithms were developed based on adaptive control ideas for linear time variant systems. The learning control methods were shown to have certain advantages over their adaptive control counterparts, such as the ability to produce zero tracking error in time varying systems, and the ability to eliminate repetitive disturbances. In recent years, certain adaptive control algorithms have been developed for multi-body dynamic systems such as robots, with global guaranteed convergence to zero tracking error for the nonlinear system euations. In this paper we study the relationship between such adaptive control methods designed for this specific class of nonlinear systems, and the learning control problem for such systems, seeking to converge to zero tracking error in following a specific command repeatedly, starting from the same initial conditions each time. The extension of these methods from the adaptive control problem to the learning control problem is seen to be trivial. The advantages and disadvantages of using learning control based on such adaptive control concepts for nonlinear systems, and the use of other currently available learning control algorithms are discussed.
Flamedoctor™: Nonlinear Burner Diagnostic System
NASA Astrophysics Data System (ADS)
Bailey, Ralph; Daw, Stuart; Finney, Charles; Flynn, Tom; Fuller, Tim
2003-08-01
Utility power plants are employing advanced control systems to improve performance over the load range. The performance of the boiler combustion system is critical to the overall performance. Flame Doctor™, which has been developed by McDermott Technology, Inc. and Oak Ridge National Laboratory under sponsorship of Electric Power Research Institute, performs diagnostics on an individual burner basis. The system consists of analogue-to-digital signal conversion and conditioning hardware, analysis software, and a graphical user interface. Time varying voltage signals from all of the burner flame scanners on a boiler are analyzed simultaneously. Nonlinear techniques such as symbolization and time asymmetry along with linear techniques such as power spectral analysis are used. The nonlinear techniques discriminate stability features in the combustion dynamics not possible with the linear techniques alone. The assessments for a variety of flame conditions are collected in a reference library. Libraries have been created for a number of flame scanners types. The Flame Doctor™ burner diagnostic system is described. Results from the first utility installation at Ameren UE Meramec power plant are shown. A live hook-up to the power plant is demonstrated. Flame Doctor™ is being offered commercially under alpha and beta demonstrations through the Electric Power Research Institute and Babcock & Wilcox.
NASA Astrophysics Data System (ADS)
Isasa, I.; Hot, A.; Cogan, S.; Sadoulet-Reboul, E.
2011-10-01
Improving the fidelity of numerical simulations using available test data is an important activity in the overall process of model verification and validation. While model updating or calibration of linear elastodynamic behaviors has been extensively studied for both academic and industrial applications over the past three decades, methodologies capable of treating non-linear dynamics remain relatively immature. The authors propose a novel strategy for updating an important subclass of non-linear models characterized by globally linear stiffness and damping behaviors in the presence of local non-linear effects. The approach combines two well-known methods for structural dynamic analysis. The first is the multi-harmonic balance (MHB) method for solving the non-linear equations of motion of a mechanical system under periodic excitation. This approach has the advantage of being much faster than time domain integration procedures while allowing a wide range of non-linear effects to be taken into account. The second method is the extended constitutive relation error (ECRE) that has been used in the past for error localization and updating of linear elastodynamic models. The proposed updating strategy will be illustrated using academic examples.
NASA Astrophysics Data System (ADS)
El Amrani, A.; El Amraoui, M.; El Abbassi, A.; Messaoudi, C.
2014-11-01
In the present work, we report the indoor photo-electrical measurements of monocrystalline silicon based photovoltaic (PV) module associated with 4 Ah lead acid battery as a storage unit for low power PV system applications. Concerning the PV module, our measurements show, at low illumination regime, that the short circuit current ISC increases linearly with the illumination power levels. Moreover, for high illumination levels, the mechanism of bimolecular recombination and space charge limitation may be intensified and hence the short current of the PV module ISCMod depends sublinearly on the incident optical power; the behavior is nonlinear. For the open circuit voltage of the PV module VOCMod measurements, a linear variation of the VOCMod versus the short circuit current in semi-logarithmic scale has been noticed. The diode ideality factor n and diode saturation current Is have been investigated; the values of n and Is are approximately of 1.3 and 10-9 A, respectively. In addition, we have shown, for different discharging-charging currents rates (i.e. 0.35 A, 0.2 A and 0.04 A), that the battery voltage decreases with discharging time as well as discharging battery capacity, and on the other hand it increases with the charging time and will rise up until it maximized value. The initial result shows the possibility to use such lead acid battery for low power PV system, which is generally designed for the motorcycle battery.
Neural network-based robust actuator fault diagnosis for a non-linear multi-tank system.
Mrugalski, Marcin; Luzar, Marcel; Pazera, Marcin; Witczak, Marcin; Aubrun, Christophe
2016-03-01
The paper is devoted to the problem of the robust actuator fault diagnosis of the dynamic non-linear systems. In the proposed method, it is assumed that the diagnosed system can be modelled by the recurrent neural network, which can be transformed into the linear parameter varying form. Such a system description allows developing the designing scheme of the robust unknown input observer within H∞ framework for a class of non-linear systems. The proposed approach is designed in such a way that a prescribed disturbance attenuation level is achieved with respect to the actuator fault estimation error, while guaranteeing the convergence of the observer. The application of the robust unknown input observer enables actuator fault estimation, which allows applying the developed approach to the fault tolerant control tasks. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.
NASA Astrophysics Data System (ADS)
Saltogianni, Vasso; Stiros, Stathis
2012-11-01
The adjustment of systems of highly non-linear, redundant equations, deriving from observations of certain geophysical processes and geodetic data cannot be based on conventional least-squares techniques, and is based on various numerical inversion techniques. Still these techniques lead to solutions trapped in local minima, to correlated estimates and to solution with poor error control. To overcome these problems, we propose an alternative numerical-topological approach inspired by lighthouse beacon navigation, usually used in 2-D, low-accuracy applications. In our approach, an m-dimensional grid G of points around the real solution (an m-dimensional vector) is at first specified. Then, for each equation an uncertainty is assigned to the corresponding measurement, and the sets of the grid points which satisfy the condition are detected. This process is repeated for all equations, and the common section A of the sets of grid points is defined. From this set of grid points, which define a space including the real solution, we compute its center of weight, which corresponds to an estimate of the solution, and its variance-covariance matrix. An optimal solution can be obtained through optimization of the uncertainty in each observation. The efficiency of the overall process was assessed in comparison with conventional least squares adjustment.
Nonlinear dynamic macromodeling techniques for audio systems
NASA Astrophysics Data System (ADS)
Ogrodzki, Jan; Bieńkowski, Piotr
2015-09-01
This paper develops a modelling method and a models identification technique for the nonlinear dynamic audio systems. Identification is performed by means of a behavioral approach based on a polynomial approximation. This approach makes use of Discrete Fourier Transform and Harmonic Balance Method. A model of an audio system is first created and identified and then it is simulated in real time using an algorithm of low computational complexity. The algorithm consists in real time emulation of the system response rather than in simulation of the system itself. The proposed software is written in Python language using object oriented programming techniques. The code is optimized for a multithreads environment.
Lam, H K; Leung, F H F; Lee, Y S
2004-04-01
This paper deals with nonlinear plants subject to unknown parameters. A fuzzy model is first used to represent the plant. An equivalent switching plant model is then derived, which supports the design of a switching controller. It will be shown that the closed-loop system formed by the plant and the switching controller is a linear system. Hence, the system performance of the closed-loop system can be designed. An application example on controlling a two-inverted pendulum system on a cart will be given to illustrate the design procedure of the proposed switching controller.
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.
Spectral decomposition of nonlinear systems with memory
NASA Astrophysics Data System (ADS)
Svenkeson, Adam; Glaz, Bryan; Stanton, Samuel; West, Bruce J.
2016-02-01
We present an alternative approach to the analysis of nonlinear systems with long-term memory that is based on the Koopman operator and a Lévy transformation in time. Memory effects are considered to be the result of interactions between a system and its surrounding environment. The analysis leads to the decomposition of a nonlinear system with memory into modes whose temporal behavior is anomalous and lacks a characteristic scale. On average, the time evolution of a mode follows a Mittag-Leffler function, and the system can be described using the fractional calculus. The general theory is demonstrated on the fractional linear harmonic oscillator and the fractional nonlinear logistic equation. When analyzing data from an ill-defined (black-box) system, the spectral decomposition in terms of Mittag-Leffler functions that we propose may uncover inherent memory effects through identification of a small set of dynamically relevant structures that would otherwise be obscured by conventional spectral methods. Consequently, the theoretical concepts we present may be useful for developing more general methods for numerical modeling that are able to determine whether observables of a dynamical system are better represented by memoryless operators, or operators with long-term memory in time, when model details are unknown.
NASA Astrophysics Data System (ADS)
Milic, Vladimir; Kasac, Josip; Novakovic, Branko
2015-10-01
This paper is concerned with ?-gain optimisation of input-affine nonlinear systems controlled by analytic fuzzy logic system. Unlike the conventional fuzzy-based strategies, the non-conventional analytic fuzzy control method does not require an explicit fuzzy rule base. As the first contribution of this paper, we prove, by using the Stone-Weierstrass theorem, that the proposed fuzzy system without rule base is universal approximator. The second contribution of this paper is an algorithm for solving a finite-horizon minimax problem for ?-gain optimisation. The proposed algorithm consists of recursive chain rule for first- and second-order derivatives, Newton's method, multi-step Adams method and automatic differentiation. Finally, the results of this paper are evaluated on a second-order nonlinear system.
Tsai, Jason S-H; Hsu, Wen-Teng; Lin, Long-Guei; Guo, Shu-Mei; Tann, Joseph W
2014-01-01
A modified nonlinear autoregressive moving average with exogenous inputs (NARMAX) model-based state-space self-tuner with fault tolerance is proposed in this paper for the unknown nonlinear stochastic hybrid system with a direct transmission matrix from input to output. Through the off-line observer/Kalman filter identification method, one has a good initial guess of modified NARMAX model to reduce the on-line system identification process time. Then, based on the modified NARMAX-based system identification, a corresponding adaptive digital control scheme is presented for the unknown continuous-time nonlinear system, with an input-output direct transmission term, which also has measurement and system noises and inaccessible system states. Besides, an effective state space self-turner with fault tolerance scheme is presented for the unknown multivariable stochastic system. A quantitative criterion is suggested by comparing the innovation process error estimated by the Kalman filter estimation algorithm, so that a weighting matrix resetting technique by adjusting and resetting the covariance matrices of parameter estimate obtained by the Kalman filter estimation algorithm is utilized to achieve the parameter estimation for faulty system recovery. Consequently, the proposed method can effectively cope with partially abrupt and/or gradual system faults and input failures by the fault detection.
Nonlinear identification of MDOF systems using Volterra series approximation
NASA Astrophysics Data System (ADS)
Prawin, J.; Rao, A. Rama Mohan
2017-02-01
Most of the practical engineering structures exhibit nonlinearity due to nonlinear dynamic characteristics of structural joints, nonlinear boundary conditions and nonlinear material properties. Meanwhile, the presence of non-linearity in the system can lead to a wide range of structural behavior, for example, jumps, limit cycles, internal resonances, modal coupling, super and sub-harmonic resonances, etc. In this paper, we present a Volterra series approximation approach based on the adaptive filter concept for nonlinear identification of multi-degree of freedom systems, without sacrificing the benefits associated with the traditional Volterra series approach. The effectiveness of the proposed approach is demonstrated using two classical single degrees of freedom systems (breathing crack problem and Duffing Holmes oscillator) and later we extend to multi-degree of freedom systems.
NASA Astrophysics Data System (ADS)
Sadeghi, Hassan; Ghaffarzadeh, Navid
2016-09-01
This paper uses a new algorithm namely biogeography based optimization (BBO) intended for the simultaneous placement of the distributed generation (DG) units and the capacitor banks in the distribution network. The procedure of optimization has been conducted in the presence of nonlinear loads (a cause of harmonic injection). The purpose of simultaneous optimal placement of the DG and the capacitor is the reduction of active and reactive losses. The difference in the values of loss reduction at different levels of the load have been included in the objective function and the considered objective function includes the constraints of voltage, size and the number of DG units and capacitor banks and the allowable range of the total harmonic distortion (THD) of the total voltage in accordance with the IEEE 519 standards. In this paper the placement has been performed on two load types ie constant and mixed power, moreover the effects of load models on the results and the effects of optimal placement on reduction of the THD levels have also been analyzed. The mentioned cases have been studied on a 33 bus radial distribution system.
NASA Astrophysics Data System (ADS)
Azou, Stéphane; Bejan, Șerban; Morel, Pascal; Sharaiha, Ammar
2015-02-01
Coherent-Optical OFDM systems are known to be sensitive to large peak-to-average power ratio (PAPR) at the transmitter output, due to nonlinear properties of some components involved in the transmission link. In this paper, we investigate the impact of an amplification of such signals via a semiconductor optical amplifier (SOA), considering some recent experimental results. An efficient tradeoff between BER performance, computational complexity and power efficiency is performed by a proper design of Wang's nonlinear companding function, considered for the first time in an optical communication context. A BER advantage of around 3 dB can hence be obtained over a standard system implementation not using PAPR reduction. The designed function also proves to be more efficient than μ-law function, considered in the literature as an efficient companding scheme.
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.
NASA Astrophysics Data System (ADS)
Zhao, Yifan; Mehnen, Jörn; Sirikham, Adisorn; Roy, Rajkumar
2017-02-01
This paper introduces a new method to improve the reliability and confidence level of defect depth measurement based on pulsed thermographic inspection by addressing the over-fitting problem. Different with existing methods using a fixed model structure for all pixels, the proposed method adaptively detects the optimal model structure for each pixel thus targeting to achieve better model fitting while using less model terms. Results from numerical simulations and real experiments suggest that (a) the new method is able to measure defect depth more accurately without a pre-set model structure (error is usually within 1 % when SNR>32 dB) in comparison with existing methods, (b) the number of model terms should be 8 for signals with SNR∈ [ 30 dB , 40 dB ] , 8-10 for SNR>40 dB and 5-8 for SNR<30 dB, and (c) a data length with at least 100 data points and 2-3 times of the characteristic time usually produces the best results.
Nonlinear signal-based control with an error feedback action for nonlinear substructuring control
NASA Astrophysics Data System (ADS)
Enokida, Ryuta; Kajiwara, Koichi
2017-01-01
A nonlinear signal-based control (NSBC) method utilises the 'nonlinear signal' that is obtained from the outputs of a controlled system and its linear model under the same input signal. Although this method has been examined in numerical simulations of nonlinear systems, its application in physical experiments has not been studied. In this paper, we study an application of NSBC in physical experiments and incorporate an error feedback action into the method to minimise the error and enhance the feasibility in practice. Focusing on NSBC in substructure testing methods, we propose nonlinear substructuring control (NLSC), that is a more general form of linear substructuring control (LSC) developed for dynamical substructured systems. In this study, we experimentally and numerically verified the proposed NLSC via substructuring tests on a rubber bearing used in base-isolated structures. In the examinations, NLSC succeeded in gaining accurate results despite significant nonlinear hysteresis and unknown parameters in the substructures. The nonlinear signal feedback action in NLSC was found to be notably effective in minimising the error caused by nonlinearity or unknown properties in the controlled system. In addition, the error feedback action in NLSC was found to be essential for maintaining stability. A stability analysis based on the Nyquist criterion, which is used particularly for linear systems, was also found to be efficient for predicting the instability conditions of substructuring tests with NLSC and useful for the error feedback controller design.
Nonlinear knowledge-based classification.
Mangasarian, Olvi L; Wild, Edward W
2008-10-01
In this brief, prior knowledge over general nonlinear sets is incorporated into nonlinear kernel classification problems as linear constraints in a linear program. These linear constraints are imposed at arbitrary points, not necessarily where the prior knowledge is given. The key tool in this incorporation is a theorem of the alternative for convex functions that converts nonlinear prior knowledge implications into linear inequalities without the need to kernelize these implications. Effectiveness of the proposed formulation is demonstrated on publicly available classification data sets, including a cancer prognosis data set. Nonlinear kernel classifiers for these data sets exhibit marked improvements upon the introduction of nonlinear prior knowledge compared to nonlinear kernel classifiers that do not utilize such knowledge.
Adaptive control for a class of second-order nonlinear systems with unknown input nonlinearities.
Zhang, T; Guay, M
2003-01-01
An adaptive controller is developed for a class of second-order nonlinear dynamic systems with input nonlinearities using artificial neural networks (ANN). The unknown input nonlinearities are continuous and monotone and satisfy a sector constraint. In contrast to conventional Lyapunov-based design techniques, an alternative Lyapunov function, which depends on both system states and control input variable, is used for the development of a control law and a learning algorithm. The proposed adaptive controller guarantees the stability of the closed-loop system and convergence of the output tracking error to an adjustable neighbour of the origin.
A canonical form for nonlinear systems
NASA Technical Reports Server (NTRS)
Su, R.; Hunt, L. R.
1986-01-01
The concepts of transformation and canonical form have been used in analyzing linear systems. These ideas are extended to nonlinear systems. A coordinate system and a corresponding canonical form are developed for general nonlinear control systems. Their usefulness is demonstrated by showing that every feedback linearizable system becomes a system with only feedback paths in the canonical form. For control design involving a nonlinear system, one approach is to put the system in its canonical form and approximate by that part having only feedback paths.
Zhang, Guowu; Zhang, Junwei; Hong, Xuezhi; He, Sailing
2017-02-20
A novel frequency domain nonlinear compensation method, FD-NC, is proposed for orthogonal frequency division multiplexing (OFDM) based visible light communication (VLC) system. By tackling the memory nonlinear impairments from light emitting diodes (LEDs) in the frequency domain rather than in the time domain, the proposed method has much lower computational complexity than the conventional time domain Volterra nonlinear compensation method (TD-NC). Both theoretical derivation and experimental investigation of the proposed method in OFDM based VLC systems with four types of commercial LEDs are presented. The results of experiments show that the proposed low-complexity FD-NC method with a moderate truncation factor achieves a performance comparable to that of the TD-NC. The application of FD-NC method in the bit-power loading OFDM VLC system is also experimentally demonstrated. Compared with the linear equalization case, at a bit error rate (BER) of 3.8 × 10^{-3} (a), the transmission distance of a 960 Mbps VLC system can be extended from 0.7 m to 1.8 m by the FD-NC, and (b) the achievable system capacity can be enhanced by 18.7%~36.5% for transmission distance in the range of 0.5 m~2 m with the FD-NC. The complexity analysis shows that the required number of real-valued multiplications (RNRM) of the FD-NC is independent of linear or nonlinear memory length. The reduction of RNRM achieved by the FD-NC over the TD-NC becomes more profound for a larger nonlinear memory length or a smaller truncation factor.
Maximized Gust Loads of a Closed-Loop, Nonlinear Aeroelastic System Using Nonlinear Systems Theory
NASA Technical Reports Server (NTRS)
Silva, Walter A.
1999-01-01
The problem of computing the maximized gust load for a nonlinear, closed-loop aeroelastic aircraft is discusses. The Volterra theory of nonlinear systems is applied in order to define a linearized system that provides a bounds on the response of the nonlinear system of interest. The method is applied to a simplified model of an Airbus A310.
Controllability of non-linear biochemical systems.
Ervadi-Radhakrishnan, Anandhi; Voit, Eberhard O
2005-07-01
Mathematical methods of biochemical pathway analysis are rapidly maturing to a point where it is possible to provide objective rationale for the natural design of metabolic systems and where it is becoming feasible to manipulate these systems based on model predictions, for instance, with the goal of optimizing the yield of a desired microbial product. So far, theory-based metabolic optimization techniques have mostly been applied to steady-state conditions or the minimization of transition time, using either linear stoichiometric models or fully kinetic models within biochemical systems theory (BST). This article addresses the related problem of controllability, where the task is to steer a non-linear biochemical system, within a given time period, from an initial state to some target state, which may or may not be a steady state. For this purpose, BST models in S-system form are transformed into affine non-linear control systems, which are subjected to an exact feedback linearization that permits controllability through independent variables. The method is exemplified with a small glycolytic-glycogenolytic pathway that had been analyzed previously by several other authors in different contexts.
Identification of the nonlinear vibration system of power transformers
NASA Astrophysics Data System (ADS)
Jing, Zheng; Hai, Huang; Pan, Jie; Yanni, Zhang
2017-01-01
This paper focuses on the identification of the nonlinear vibration system of power transformers. A Hammerstein model is used to identify the system with electrical inputs and the vibration of the transformer tank as the output. The nonlinear property of the system is modelled using a Fourier neural network consisting of a nonlinear element and a linear dynamic block. The order and weights of the network are determined based on the Lipschitz criterion and the back-propagation algorithm. This system identification method is tested on several power transformers. Promising results for predicting the transformer vibration and extracting system parameters are presented and discussed.
State Identification in Nonlinear Systems
Holloway, James Paul
2005-02-06
A state estimation method based on finding a system state that causes a model to match a set of system measurements is regularized by requiring that sudden changes in system state be avoided. The required optimization is accomplished by a pattern search algorithm. The method does not require derivative information or linearization of the model. Is has been applied to a 10 dimensional model of a fast reactor system.
Shaocheng Tong; Yue Li; Yongming Li; Yanjun Liu
2011-12-01
In this paper, two adaptive fuzzy output feedback control approaches are proposed for a class of uncertain stochastic nonlinear strict-feedback systems without the measurements of the states. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed for estimating the unmeasured states. On the basis of the fuzzy state observer, and by combining the adaptive backstepping technique with fuzzy adaptive control design, an adaptive fuzzy output feedback control approach is developed. To overcome the problem of "explosion of complexity" inherent in the proposed control method, the dynamic surface control (DSC) technique is incorporated into the first adaptive fuzzy control scheme, and a simplified adaptive fuzzy output feedback DSC approach is developed. It is proved that these two control approaches can guarantee that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) in mean square, and the observer errors and the output of the system converge to a small neighborhood of the origin. A simulation example is provided to show the effectiveness of the proposed approaches.
Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong
2016-07-18
Most of previous quantum computations only take use of one degree of freedom (DoF) of photons. An experimental system may possess various DoFs simultaneously. In this paper, with the weak cross-Kerr nonlinearity, we investigate the parallel quantum computation dependent on photonic systems with two DoFs. We construct nearly deterministic controlled-not (CNOT) gates operating on the polarization spatial DoFs of the two-photon or one-photon system. These CNOT gates show that two photonic DoFs can be encoded as independent qubits without auxiliary DoF in theory. Only the coherent states are required. Thus one half of quantum simulation resources may be saved in quantum applications if more complicated circuits are involved. Hence, one may trade off the implementation complexity and simulation resources by using different photonic systems. These CNOT gates are also used to complete various applications including the quantum teleportation and quantum superdense coding.
NASA Astrophysics Data System (ADS)
Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong
2016-07-01
Most of previous quantum computations only take use of one degree of freedom (DoF) of photons. An experimental system may possess various DoFs simultaneously. In this paper, with the weak cross-Kerr nonlinearity, we investigate the parallel quantum computation dependent on photonic systems with two DoFs. We construct nearly deterministic controlled-not (CNOT) gates operating on the polarization spatial DoFs of the two-photon or one-photon system. These CNOT gates show that two photonic DoFs can be encoded as independent qubits without auxiliary DoF in theory. Only the coherent states are required. Thus one half of quantum simulation resources may be saved in quantum applications if more complicated circuits are involved. Hence, one may trade off the implementation complexity and simulation resources by using different photonic systems. These CNOT gates are also used to complete various applications including the quantum teleportation and quantum superdense coding.
NASA Astrophysics Data System (ADS)
Li, Chung-Yi; Ying, Cheng-Ling; Lin, Chun-Yu; Chu, Chien-An
2015-12-01
This study evaluated a directly modulated distributed feedback (DFB) laser diode (LD) for cable TV systems with respect to carrier-to-nonlinear distortion of LDs. The second-order distortion-to-carrier ratio is found to be proportional to that of the second-order coefficient-to-first-order coefficient of the DFB laser diode driving current and to the optical modulation index (OMI). Furthermore, the third-order distortion-to-carrier ratio is proportional to that of the third-order coefficient-to-first-order coefficient of the DFB laser diode driving current, and to the OMI2.
Zhang, Huaguang; Song, Ruizhuo; Wei, Qinglai; Zhang, Tieyan
2011-12-01
In this paper, a novel heuristic dynamic programming (HDP) iteration algorithm is proposed to solve the optimal tracking control problem for a class of nonlinear discrete-time systems with time delays. The novel algorithm contains state updating, control policy iteration, and performance index iteration. To get the optimal states, the states are also updated. Furthermore, the "backward iteration" is applied to state updating. Two neural networks are used to approximate the performance index function and compute the optimal control policy for facilitating the implementation of HDP iteration algorithm. At last, we present two examples to demonstrate the effectiveness of the proposed HDP iteration algorithm.
Robust nonlinear variable selective control for networked systems
NASA Astrophysics Data System (ADS)
Rahmani, Behrooz
2016-10-01
This paper is concerned with the networked control of a class of uncertain nonlinear systems. In this way, Takagi-Sugeno (T-S) fuzzy modelling is used to extend the previously proposed variable selective control (VSC) methodology to nonlinear systems. This extension is based upon the decomposition of the nonlinear system to a set of fuzzy-blended locally linearised subsystems and further application of the VSC methodology to each subsystem. To increase the applicability of the T-S approach for uncertain nonlinear networked control systems, this study considers the asynchronous premise variables in the plant and the controller, and then introduces a robust stability analysis and control synthesis. The resulting optimal switching-fuzzy controller provides a minimum guaranteed cost on an H2 performance index. Simulation studies on three nonlinear benchmark problems demonstrate the effectiveness of the proposed method.
Nonlinear Dynamics of Parametrically Excited Gyroscopic Systems
Namachchivaya. N.S.
2001-06-01
The primary objective of this project is to determine how some of the powerful geometric methods of dynamical systems can be applied to study nonlinear gyroscopic systems. We proposed to develop techniques to predict local and global behavior and instability mechanisms and to analyze the interactions between noise, stability, and nonlinearities inherent in gyroscopic systems. In order to obtain these results we use the method of normal forms, global bifurcation techniques, and various other dynamical systems tools.
NASA Astrophysics Data System (ADS)
Ding, Bo; Fang, Huajing
2016-12-01
This paper is concerned with the fault detection and estimation for nonlinear stochastic system with additive multi-faults. The states of system are estimated by the improved particle filter which composed of basic particle filter and preliminary fault estimation. Since the preliminary fault estimation contains noise, the faults are detected by the method of hypothesis testing, while the amplitude of each fault is estimated by the average of the sample of preliminary fault estimation. Meanwhile, the relationship of the sample size, the significance level of two types of error, the amplitude of fault and the variance of the error of preliminary fault estimation are also given. The effectiveness of the proposed method is verified by the simulation of three-vessel water tank system.
A new, challenging benchmark for nonlinear system identification
NASA Astrophysics Data System (ADS)
Tiso, Paolo; Noël, Jean-Philippe
2017-02-01
The progress accomplished during the past decade in nonlinear system identification in structural dynamics is considerable. The objective of the present paper is to consolidate this progress by challenging the community through a new benchmark structure exhibiting complex nonlinear dynamics. The proposed structure consists of two offset cantilevered beams connected by a highly flexible element. For increasing forcing amplitudes, the system sequentially features linear behaviour, localised nonlinearity associated with the buckling of the connecting element, and distributed nonlinearity resulting from large elastic deformations across the structure. A finite element-based code with time integration capabilities is made available at https://sem.org/nonlinear-systems-imac-focus-group/. This code permits the numerical simulation of the benchmark dynamics in response to arbitrary excitation signals.
Nonlinear normal modes in electrodynamic systems: A nonperturbative approach
Kudrin, A. V. Kudrina, O. A.; Petrov, E. Yu.
2016-06-15
We consider electromagnetic nonlinear normal modes in cylindrical cavity resonators filled with a nonlinear nondispersive medium. The key feature of the analysis is that exact analytic solutions of the nonlinear field equations are employed to study the mode properties in detail. Based on such a nonperturbative approach, we rigorously prove that the total energy of free nonlinear oscillations in a distributed conservative system, such as that considered in our work, can exactly coincide with the sum of energies of the normal modes of the system. This fact implies that the energy orthogonality property, which has so far been known to hold only for linear oscillations and fields, can also be observed in a nonlinear oscillatory system.
Spline approximations for nonlinear hereditary control systems
NASA Technical Reports Server (NTRS)
Daniel, P. L.
1982-01-01
A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.
Nonlinear waves in PT -symmetric systems
NASA Astrophysics Data System (ADS)
Konotop, Vladimir V.; Yang, Jianke; Zezyulin, Dmitry A.
2016-07-01
Recent progress on nonlinear properties of parity-time (PT )-symmetric systems is comprehensively reviewed in this article. PT symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying PT symmetry could exhibit all-real spectra. This concept later spread out to optics, Bose-Einstein condensates, electronic circuits, and many other physical fields, where a judicious balancing of gain and loss constitutes a PT -symmetric system. The natural inclusion of nonlinearity into these PT systems then gave rise to a wide array of new phenomena which have no counterparts in traditional dissipative systems. Examples include the existence of continuous families of nonlinear modes and integrals of motion, stabilization of nonlinear modes above PT -symmetry phase transition, symmetry breaking of nonlinear modes, distinctive soliton dynamics, and many others. In this article, nonlinear PT -symmetric systems arising from various physical disciplines are presented, nonlinear properties of these systems are thoroughly elucidated, and relevant experimental results are described. In addition, emerging applications of PT symmetry are pointed out.
Shannon's theory in nonlinear systems
NASA Astrophysics Data System (ADS)
Killey, Robert I.; Behrens, Carsten
2011-01-01
An exponential growth in the capacity of optical networks has taken place over the last decade, but the extent to which future capacity growth can continue is limited by physical laws governing signal propagation through optical fibres. While the classic theory of communication developed by Claude Shannon allows the analytical calculation of information spectral density limits for linear channels with white additive Gaussian noise, the nonlinear nature of optical fibres makes these limits much more difficult to determine for long-haul optical transmission. Accurately predicting the ultimate limits has been the focus of much recent research. This paper describes the sources of linear and nonlinear signal impairments, reviews progress on extending Shannon's theory to the case of nonlinear signal propagation, and discusses new optical and electronic signal processing techniques that may be used to approach the Shannon limit in future networks.
De, Suvranu; Deo, Dhannanjay; Sankaranarayanan, Ganesh; Arikatla, Venkata S
2011-08-01
BACKGROUND: While an update rate of 30 Hz is considered adequate for real time graphics, a much higher update rate of about 1 kHz is necessary for haptics. Physics-based modeling of deformable objects, especially when large nonlinear deformations and complex nonlinear material properties are involved, at these very high rates is one of the most challenging tasks in the development of real time simulation systems. While some specialized solutions exist, there is no general solution for arbitrary nonlinearities. METHODS: In this work we present PhyNNeSS - a Physics-driven Neural Networks-based Simulation System - to address this long-standing technical challenge. The first step is an off-line pre-computation step in which a database is generated by applying carefully prescribed displacements to each node of the finite element models of the deformable objects. In the next step, the data is condensed into a set of coefficients describing neurons of a Radial Basis Function network (RBFN). During real-time computation, these neural networks are used to reconstruct the deformation fields as well as the interaction forces. RESULTS: We present realistic simulation examples from interactive surgical simulation with real time force feedback. As an example, we have developed a deformable human stomach model and a Penrose-drain model used in the Fundamentals of Laparoscopic Surgery (FLS) training tool box. CONCLUSIONS: A unique computational modeling system has been developed that is capable of simulating the response of nonlinear deformable objects in real time. The method distinguishes itself from previous efforts in that a systematic physics-based pre-computational step allows training of neural networks which may be used in real time simulations. We show, through careful error analysis, that the scheme is scalable, with the accuracy being controlled by the number of neurons used in the simulation. PhyNNeSS has been integrated into SoFMIS (Software Framework for Multimodal
Discretization analysis of bifurcation based nonlinear amplifiers
NASA Astrophysics Data System (ADS)
Feldkord, Sven; Reit, Marco; Mathis, Wolfgang
2017-09-01
Recently, for modeling biological amplification processes, nonlinear amplifiers based on the supercritical Andronov-Hopf bifurcation have been widely analyzed analytically. For technical realizations, digital systems have become the most relevant systems in signal processing applications. The underlying continuous-time systems are transferred to the discrete-time domain using numerical integration methods. Within this contribution, effects on the qualitative behavior of the Andronov-Hopf bifurcation based systems concerning numerical integration methods are analyzed. It is shown exemplarily that explicit Runge-Kutta methods transform the truncated normalform equation of the Andronov-Hopf bifurcation into the normalform equation of the Neimark-Sacker bifurcation. Dependent on the order of the integration method, higher order terms are added during this transformation.A rescaled normalform equation of the Neimark-Sacker bifurcation is introduced that allows a parametric design of a discrete-time system which corresponds to the rescaled Andronov-Hopf system. This system approximates the characteristics of the rescaled Hopf-type amplifier for a large range of parameters. The natural frequency and the peak amplitude are preserved for every set of parameters. The Neimark-Sacker bifurcation based systems avoid large computational effort that would be caused by applying higher order integration methods to the continuous-time normalform equations.
Distributed Adaptive Neural Control for Stochastic Nonlinear Multiagent Systems.
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.
Parameter identification for nonlinear aerodynamic systems
NASA Technical Reports Server (NTRS)
Pearson, Allan E.
1990-01-01
Parameter identification for nonlinear aerodynamic systems is examined. It is presumed that the underlying model can be arranged into an input/output (I/O) differential operator equation of a generic form. The algorithm estimation is especially efficient since the equation error can be integrated exactly given any I/O pair to obtain an algebraic function of the parameters. The algorithm for parameter identification was extended to the order determination problem for linear differential system. The degeneracy in a least squares estimate caused by feedback was addressed. A method of frequency analysis for determining the transfer function G(j omega) from transient I/O data was formulated using complex valued Fourier based modulating functions in contrast with the trigonometric modulating functions for the parameter estimation problem. A simulation result of applying the algorithm is given under noise-free conditions for a system with a low pass transfer function.
Impulse position control algorithms for nonlinear systems
Sesekin, A. N.; Nepp, A. N.
2015-11-30
The article is devoted to the formalization and description of impulse-sliding regime in nonlinear dynamical systems that arise in the application of impulse position controls of a special kind. The concept of trajectory impulse-sliding regime formalized as some limiting network element Euler polygons generated by a discrete approximation of the impulse position control This paper differs from the previously published papers in that it uses a definition of solutions of systems with impulse controls, it based on the closure of the set of smooth solutions in the space of functions of bounded variation. The need for the study of such regimes is the fact that they often arise when parry disturbances acting on technical or economic control system.
Impulse position control algorithms for nonlinear systems
NASA Astrophysics Data System (ADS)
Sesekin, A. N.; Nepp, A. N.
2015-11-01
The article is devoted to the formalization and description of impulse-sliding regime in nonlinear dynamical systems that arise in the application of impulse position controls of a special kind. The concept of trajectory impulse-sliding regime formalized as some limiting network element Euler polygons generated by a discrete approximation of the impulse position control This paper differs from the previously published papers in that it uses a definition of solutions of systems with impulse controls, it based on the closure of the set of smooth solutions in the space of functions of bounded variation. The need for the study of such regimes is the fact that they often arise when parry disturbances acting on technical or economic control system.
A canonical form for nonlinear systems
NASA Technical Reports Server (NTRS)
Su, R.; Hunt, L. R.
1985-01-01
The conceptions of transformation and canonical form have been much used to analyze the structure of linear systems. A coordinate system and a corresponding canonical form are developed for general nonlinear control systems. Their usefulness is demonstrated by showing that every feedback linearizable system becomes a system with only feedback paths in the canonical form.
An experimental study of nonlinear dynamic system identification
NASA Technical Reports Server (NTRS)
Stry, Greselda I.; Mook, D. Joseph
1990-01-01
A technique for robust identification of nonlinear dynamic systems is developed and illustrated using both simulations and analog experiments. The technique is based on the Minimum Model Error optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature of the current work is the ability to identify nonlinear dynamic systems without prior assumptions regarding the form of the nonlinearities, in constrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length.
Stabilization of nonlinear systems using linear observers
NASA Technical Reports Server (NTRS)
Strane, R. E.; Vogt, W. G.
1974-01-01
It is shown that a linear observer can always be employed to stabilize a nonlinear system which contains a true Popov type nonlinearity in the closed interval from 0 to k, where k is finite, provided the nonlinear function and a completely observable output of the linear portion are available as inputs to the observer. Taking into consideration the case in which a completely observable output is not available from the linear portion, stabilization is shown to be possible if the original linear approximation of the system is asymptotically stable.
New stability conditions for nonlinear time varying delay systems
NASA Astrophysics Data System (ADS)
Elmadssia, S.; Saadaoui, K.; Benrejeb, M.
2016-07-01
In this paper, new practical stability conditions for a class of nonlinear time varying delay systems are proposed. The study is based on the use of a specific state space description, known as the Benrejeb characteristic arrow form matrix, and aggregation techniques to obtain delay-dependent stability conditions. Application of this method to delayed Lurie-Postnikov nonlinear systems is given. Illustrative examples are presented to show the effectiveness of the proposed approach.
The transmissibility of nonlinear energy sink based on nonlinear output frequency-response functions
NASA Astrophysics Data System (ADS)
Yang, Kai; Zhang, Ye-Wei; Ding, Hu; Chen, Li-Qun
2017-03-01
For the first time, a new representation of transmissibility based on nonlinear output frequency-response functions (NOFRFs) is proposed in the present study. Furthermore, the transmissibility is applied to evaluate the vibration isolation performance of a nonlinear energy sink (NES) in frequency domain. A two-degree-of-freedom (2-DOF) structure with the NES attached system is adopted. Numerical simulations have been performed for the 2-DOF structure. Moreover, the effects of NES parameters on the transmissibility of the nonlinear system are evaluated. By increasing the viscous damping and mass, as well as decreasing the cubic nonlinear stiffness of the NES, the analytical results show that the transmissibility of the 2-DOF structure with NES is reduced over all resonance regions. Therefore, the present paper produces a novel method for NES design in frequency domain.
NASA Technical Reports Server (NTRS)
Young, G.
1982-01-01
A design methodology capable of dealing with nonlinear systems, such as a controlled ecological life support system (CELSS), containing parameter uncertainty is discussed. The methodology was applied to the design of discrete time nonlinear controllers. The nonlinear controllers can be used to control either linear or nonlinear systems. Several controller strategies are presented to illustrate the design procedure.
A study of nonlinear flight control system designs
NASA Astrophysics Data System (ADS)
Tian, Lijun
This thesis discusses both normal aircraft flight control where the control surfaces are the primary effectors, and unconventional emergency flight control by engines only. It has long been realized that nonlinearity in aircraft dynamics is a prominent consideration in design of high-performance conventional flight control systems. The engine-only flight control problem also faces strong nonlinearity, although due to different reasons. A nonlinear predictive control method and an approximate receding-horizon control method are used for normal and engine-only flight control system designs for an F-18 aircraft. The comparison of the performance with that of linear flight controllers provides some insight into when nonlinear controllers may render a much improved performance. The concept of nonlinear flight control system design is extended to output tracking control problem. The capability of the nonlinear controller to stabilize the aircraft and accomplish output tracking control for non-minimum phase system is successfully demonstrated. Numerical simulation results of longitudinal motion based on two typical flight conditions for an F-18 aircraft is presented to illustrate some of these aspects. It is suggested in this thesis that nonlinear flight control system design, particularly the engine-only controller design and output tracking control design for non-minimum phase system by using a nonlinear method is more effective for the highly nonlinear environment. The recently developed continuous-time predictive control approach and an approximate receding-horizon control method are shown to be effective methods in the situation while the conventional linear or popular nonlinear control designs are either ineffective or inapplicable.
Patterns in a Nonlinear Optical System
NASA Astrophysics Data System (ADS)
Arecchi, F. T.; Ramazza, P. L.
We discuss the general features of patten formation in nonlinear optics, regarding the system sizes along the coordinates longitudinal and transverse to the wavefront propagation as the crucial parameters in determining the possible dynamical behaviours. As a specific example of optical pattern forming system, we review the phenomena observed in a prototypical nonlinear interferometer formed by a Kerr-like medium with optical feedback. Particular attention is devoted to the role of nonlocal interactions in determining the pattern forming scenarios observed.
Optimal second order sliding mode control for nonlinear uncertain systems.
Das, Madhulika; Mahanta, Chitralekha
2014-07-01
In this paper, a chattering free optimal second order sliding mode control (OSOSMC) method is proposed to stabilize nonlinear systems affected by uncertainties. The nonlinear optimal control strategy is based on the control Lyapunov function (CLF). For ensuring robustness of the optimal controller in the presence of parametric uncertainty and external disturbances, a sliding mode control scheme is realized by combining an integral and a terminal sliding surface. The resulting second order sliding mode can effectively reduce chattering in the control input. Simulation results confirm the supremacy of the proposed optimal second order sliding mode control over some existing sliding mode controllers in controlling nonlinear systems affected by uncertainty.
An experimental study of nonlinear dynamic system identification
NASA Technical Reports Server (NTRS)
Stry, Greselda I.; Mook, D, Joseph
1991-01-01
A technique based on the Minimum Model Error optimal estimation approach is employed for robust identification of a nonlinear dynamic system. A simple harmonic oscillator with quadratic position feedback was simulated on an analog computer. With the aid of analog measurements and an assumed linear model, the Minimum Model Error Algorithm accurately identifies the quadratic nonlinearity. The tests demonstrate that the method is robust with respect to prior ignorance of the nonlinear system model and with respect to measurement record length, regardless of initial conditions.
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.
Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong
2016-01-01
Most of previous quantum computations only take use of one degree of freedom (DoF) of photons. An experimental system may possess various DoFs simultaneously. In this paper, with the weak cross-Kerr nonlinearity, we investigate the parallel quantum computation dependent on photonic systems with two DoFs. We construct nearly deterministic controlled-not (CNOT) gates operating on the polarization spatial DoFs of the two-photon or one-photon system. These CNOT gates show that two photonic DoFs can be encoded as independent qubits without auxiliary DoF in theory. Only the coherent states are required. Thus one half of quantum simulation resources may be saved in quantum applications if more complicated circuits are involved. Hence, one may trade off the implementation complexity and simulation resources by using different photonic systems. These CNOT gates are also used to complete various applications including the quantum teleportation and quantum superdense coding. PMID:27424767
Dynamical systems approaches to nonlinear problems in systems and circuits
Salam, F.M.A.; Levi, M.L.
1988-01-01
Applications of dynamical-systems analysis to nonlinear circuits and physical systems are discussed in reviews and reports. Topics addressed include general analytical methods, general simulation methods, nonlinear circuits and systems in electrical engineering, control systems, solids and vibrations, and mechanical systems. Consideration is given to the applicability of the Mel'nikov method to highly dissipative systems, damping in nonlinear solid mechanics, a three-dimensional rotation instrument for displaying strange attractors, a chaotic saddle catastrophe in forced oscillators, soliton experiments in annular Josephson junctions, local bifurcation control, periodic and chaotic motions of a buckled beam experiencing parametric and external excitation, and robust nonlinear computed torque control for robot manipulators.
NASA Astrophysics Data System (ADS)
Wang, Danshi; Zhang, Min; Cai, Zhongle; Cui, Yue; Li, Ze; Han, Huanhuan; Fu, Meixia; Luo, Bin
2016-06-01
An effective machine learning algorithm, the support vector machine (SVM), is presented in the context of a coherent optical transmission system. As a classifier, the SVM can create nonlinear decision boundaries to mitigate the distortions caused by nonlinear phase noise (NLPN). Without any prior information or heuristic assumptions, the SVM can learn and capture the link properties from only a few training data. Compared with the maximum likelihood estimation (MLE) algorithm, a lower bit-error rate (BER) is achieved by the SVM for a given launch power; moreover, the launch power dynamic range (LPDR) is increased by 3.3 dBm for 8 phase-shift keying (8 PSK), 1.2 dBm for QPSK, and 0.3 dBm for BPSK. The maximum transmission distance corresponding to a BER of 1 ×10-3 is increased by 480 km for the case of 8 PSK. The larger launch power range and longer transmission distance improve the tolerance to amplitude and phase noise, which demonstrates the feasibility of the SVM in digital signal processing for M-PSK formats. Meanwhile, in order to apply the SVM method to 16 quadratic amplitude modulation (16 QAM) detection, we propose a parameter optimization scheme. By utilizing a cross-validation and grid-search techniques, the optimal parameters of SVM can be selected, thus leading to the LPDR improvement by 2.8 dBm. Additionally, we demonstrate that the SVM is also effective in combating the laser phase noise combined with the inphase and quadrature (I/Q) modulator imperfections, but the improvement is insignificant for the linear noise and separate I/Q imbalance. The computational complexity of SVM is also discussed. The relatively low complexity makes it possible for SVM to implement the real-time processing.
The effect of system nonlinearities on system noise statistics
NASA Technical Reports Server (NTRS)
Robinson, L. H., Jr.
1971-01-01
The effects are studied of nonlinearities in a baseline communications system on the system noise amplitude statistics. So that a meaningful identification of system nonlinearities can be made, the baseline system is assumed to transmit a single biphase-modulated signal through a relay satellite to the receiving equipment. The significant nonlinearities thus identified include square-law or product devices (e.g., in the carrier reference recovery loops in the receivers), bandpass limiters, and traveling wave tube amplifiers.
Automated reverse engineering of nonlinear dynamical systems.
Bongard, Josh; Lipson, Hod
2007-06-12
Complex nonlinear dynamics arise in many fields of science and engineering, but uncovering the underlying differential equations directly from observations poses a challenging task. The ability to symbolically model complex networked systems is key to understanding them, an open problem in many disciplines. Here we introduce for the first time a method that can automatically generate symbolic equations for a nonlinear coupled dynamical system directly from time series data. This method is applicable to any system that can be described using sets of ordinary nonlinear differential equations, and assumes that the (possibly noisy) time series of all variables are observable. Previous automated symbolic modeling approaches of coupled physical systems produced linear models or required a nonlinear model to be provided manually. The advance presented here is made possible by allowing the method to model each (possibly coupled) variable separately, intelligently perturbing and destabilizing the system to extract its less observable characteristics, and automatically simplifying the equations during modeling. We demonstrate this method on four simulated and two real systems spanning mechanics, ecology, and systems biology. Unlike numerical models, symbolic models have explanatory value, suggesting that automated "reverse engineering" approaches for model-free symbolic nonlinear system identification may play an increasing role in our ability to understand progressively more complex systems in the future.
Fault diagnosis for a class of nonlinear systems via ESO.
Yan, Bingyong; Tian, Zuohua; Shi, Songjiao; Weng, Zhengxin
2008-10-01
In this paper, a novel fault detection and identification (FDI) scheme for a class of nonlinear systems is presented. First of all, an augment system is constructed by making the unknown system faults as an extended system state. Then based on the ESO theory, a novel fault diagnosis filter is constructed to diagnose the nonlinear system faults. An extension to a class of nonlinear uncertain systems is then made. An outstanding feature of this scheme is that it can simultaneously detect and identify the shape and magnitude of the system faults in real time without training the network compared with the neural network-based FDI schemes. Finally, simulation examples are given to illustrate the feasibility and effectiveness of the proposed approach.
Systems of Nonlinear Hyperbolic Partial Differential Equations
1997-12-01
McKinney) Travelling wave solutions of the modified Korteweg - deVries -Burgers Equation . J. Differential Equations , 116 (1995), 448-467. 4. (with D.G...SUBTITLE Systems of Nonlinear Hyperbolic Partial Differential Equations 6. AUTHOR’S) Michael Shearer PERFORMING ORGANIZATION NAMES(S) AND...DISTRIBUTION CODE 13. ABSTRACT (Maximum 200 words) This project concerns properties of wave propagation in partial differential equations that are nonlinear
NASA Astrophysics Data System (ADS)
Diamond, P.; Kuznetsov, N.; Rachinskii, D.
2001-09-01
The paper studies existence, uniqueness, and stability of large-amplitude periodic cycles arising in Hopf bifurcation at infinity of autonomous control systems with bounded nonlinear feedback. We consider systems with functional nonlinearities of Landesman-Lazer type and a class of systems with hysteresis nonlinearities. The method is based on the technique of parameter functionalization and methods of monotone concave and convex operators.
Experimental nonlinear laser systems: Bigger data for better science?
Kane, D. M.; Toomey, J. P.; McMahon, C.; Noblet, Y.; Argyris, A.; Syvridis, D.
2014-10-06
Bigger data is supporting knowledge discovery in nonlinear laser systems as will be demonstrated with examples from three semiconductor laser based systems – one with optical feedback, a photonic integrated circuit (PIC) chaotic laser and a frequency shifted feedback laser system.
Connective stability of nonlinear matrix systems
NASA Technical Reports Server (NTRS)
Siljak, D. D.
1974-01-01
Consideration of stability under structural perturbations of free dynamic systems described by the differential equation dx/dt = A(t,x)x, where the matrix A(t,x) has time-varying nonlinear elements. The concept of 'connective stability' is introduced to study the structural properties of competitive-cooperative nonlinear matrix systems. It is shown that stability reliability in such systems is high and that they remain stable despite time-varying (including 'on-off') interaction among individual agents present in the system. The results obtained can be used to study stability aspects of mathematical models arising in as diverse fields as economics, biology, arms races, and transistor circuits.
QCL-based nonlinear sensing of independent targets dynamics.
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.
NASA Astrophysics Data System (ADS)
Zhang, B.; Billings, S. A.
2015-08-01
Although a vast number of techniques for the identification of nonlinear discrete-time systems have been introduced, the identification of continuous-time nonlinear systems is still extremely difficult. In this paper, the Nonlinear Difference Equation with Moving Average noise (NDEMA) model which is a general representation of nonlinear systems and contains, as special cases, both continuous-time and discrete-time models, is first proposed. Then based on this new representation, a systematic framework for the identification of nonlinear continuous-time models is developed. The new approach can not only detect the model structure and estimate the model parameters, but also work for noisy nonlinear systems. Both simulation and experimental examples are provided to illustrate how the new approach can be applied in practice.
Nonlinear transmission line based electron beam driver
French, David M.; Hoff, Brad W.; Tang Wilkin; Heidger, Susan; Shiffler, Don; Allen-Flowers, Jordan
2012-12-15
Gated field emission cathodes can provide short electron pulses without the requirement of laser systems or cathode heating required by photoemission or thermionic cathodes. The large electric field requirement for field emission to take place can be achieved by using a high aspect ratio cathode with a large field enhancement factor which reduces the voltage requirement for emission. In this paper, a cathode gate driver based on the output pulse train from a nonlinear transmission line is experimentally demonstrated. The application of the pulse train to a tufted carbon fiber field emission cathode generates short electron pulses. The pulses are approximately 2 ns in duration with emission currents of several mA, and the train contains up to 6 pulses at a frequency of 100 MHz. Particle-in-cell simulation is used to predict the characteristic of the current pulse train generated from a single carbon fiber field emission cathode using the same technique.
Parametric Identification of Nonlinear Dynamical Systems
NASA Technical Reports Server (NTRS)
Feeny, Brian
2002-01-01
In this project, we looked at the application of harmonic balancing as a tool for identifying parameters (HBID) in a nonlinear dynamical systems with chaotic responses. The main idea is to balance the harmonics of periodic orbits extracted from measurements of each coordinate during a chaotic response. The periodic orbits are taken to be approximate solutions to the differential equations that model the system, the form of the differential equations being known, but with unknown parameters to be identified. Below we summarize the main points addressed in this work. The details of the work are attached as drafts of papers, and a thesis, in the appendix. Our study involved the following three parts: (1) Application of the harmonic balance to a simulation case in which the differential equation model has known form for its nonlinear terms, in contrast to a differential equation model which has either power series or interpolating functions to represent the nonlinear terms. We chose a pendulum, which has sinusoidal nonlinearities; (2) Application of the harmonic balance to an experimental system with known nonlinear forms. We chose a double pendulum, for which chaotic response were easily generated. Thus we confronted a two-degree-of-freedom system, which brought forth challenging issues; (3) A study of alternative reconstruction methods. The reconstruction of the phase space is necessary for the extraction of periodic orbits from the chaotic responses, which is needed in this work. Also, characterization of a nonlinear system is done in the reconstructed phase space. Such characterizations are needed to compare models with experiments. Finally, some nonlinear prediction methods can be applied in the reconstructed phase space. We developed two reconstruction methods that may be considered if the common method (method of delays) is not applicable.
Asymmetric wave propagation in nonlinear systems.
Lepri, Stefano; Casati, Giulio
2011-04-22
A mechanism for asymmetric (nonreciprocal) wave transmission is presented. As a reference system, we consider a layered nonlinear, nonmirror-symmetric model described by the one-dimensional discrete nonlinear Schrödinger equation with spatially varying coefficients embedded in an otherwise linear lattice. We construct a class of exact extended solutions such that waves with the same frequency and incident amplitude impinging from left and right directions have very different transmission coefficients. This effect arises already for the simplest case of two nonlinear layers and is associated with the shift of nonlinear resonances. Increasing the number of layers considerably increases the complexity of the family of solutions. Finally, numerical simulations of asymmetric wave packet transmission are presented which beautifully display the rectifying effect.
On Stabilization of Nonautonomous Nonlinear Systems
Bogdanov, A. Yu.
2008-10-30
The procedures to obtain the sufficient conditions of asymptotic stability for nonlinear nonstationary continuous-time systems are discussed. We consider different types of the following general controlled system: x = X(t,x,u) = F(t,x)+B(t,x)u, x(t{sub 0}) = x{sub 0}. (*) The basis of investigation is limiting equations, limiting Lyapunov functions, etc. The improved concept of observability of the pair of functional matrices is presented. By these results the problem of synthesis of asymptotically stable control nonlinear nonautonomous systems (with linear parts) involving the quadratic time-dependent Lyapunov functions is solved as well as stabilizing a given unstable system with nonlinear control law.
The Design of Stable Nonlinear Controllers for a Class of Nonlinear Plants Based on Neutral Networks
NASA Technical Reports Server (NTRS)
Adetona, Olawale; Garcia, Ephrahim; Sathananthan, Sivapragasm; Keel, Lee H.
1998-01-01
Extensive empirical evidence has been published in the literature to demonstrate the enormous potential of multilayer neural network controllers. In spite of these results, practical implementation of these control schemes has been held back by the lack of an analytical proof of the stability of the controlled system. The objective of this paper is to present a nonlinear control scheme based on multilayer neural networks for the control of a class of nonlinear plants. The stability of the closed loop system will be rigorously established.
Controllability of Nonlinear Fractional Delay Dynamical Systems
NASA Astrophysics Data System (ADS)
Nirmala, R. Joice; Balachandran, K.; Rodríguez-Germa, L.; Trujillo, J. J.
2016-02-01
This paper is concerned with controllability of nonlinear fractional delay dynamical systems with delay in state variables. The solution representations of fractional delay differential equations have been established by using the Laplace transform technique and the Mittag-Leffler function. Necessary and sufficient conditions for the controllability criteria of linear fractional delay systems are established. Further sufficient condition for the controllability of nonlinear fractional delay dynamical system are obtained by using the fixed point argument. Examples and numerical simulation are presented to illustrate the results.
Zaher, Ashraf A
2007-05-01
A model-based control methodology for suppressing chaos for nonlinear systems is introduced. The proposed methodology generates new periodic orbits or steady states, which are not the solutions of the free system, using output feedback and state observers. The design uses the certainty equivalence principle to construct a linear closed loop system that can follow desired outputs with zero steady state offsets via using a pole-placement-like approach. The combined dynamics of both the controller and the state observer are carefully studied using the well-known Rössler system. The similarities and differences between the proposed control technique and both the double-notch filter feedback and the time-delay autosynchronization are investigated. The effect of parameter uncertainties is studied and robustness of the proposed controller is analyzed.
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.
Dong, Jiuxiang; Wang, Youyi; Yang, Guang-Hong
2010-12-01
This paper considers the output feedback control problem for nonlinear discrete-time systems, which are represented by a type of fuzzy systems with local nonlinear models. By using the estimations of the states and nonlinear functions in local models, sufficient conditions for designing observer-based controllers are given for discrete-time nonlinear systems. First, a separation property, i.e., the controller and the observer can be independently designed, is proved for the class of fuzzy systems. Second, a two-step procedure with cone complementarity linearization algorithms is also developed for solving the H( ∞) dynamic output feedback (DOF) control problem. Moreover, for the case where the nonlinear functions in local submodels are measurable, a convex condition for designing H(∞) controllers is given by a new DOF control scheme. In contrast to the existing methods, the new methods can design output feedback controllers with fewer fuzzy rules as well as less computational burden, which is helpful for controller designs and implementations. Lastly, numerical examples are given to illustrate the effectiveness of the proposed methods.
System interaction with linear and nonlinear characteristics
Lin, C.W. ); Tseng, W.S. )
1991-01-01
This book is covered under some of the following topics: seismic margins in piping systems, vibrational power flow in a cylindrical shell, inelastic pipework dynamics and aseismic design, an efficient method for dynamic analysis of a linearly elastic piping system with nonlinear supports.
Aeroelasticity of Nonlinear Tail / Rudder Systems with Freeplay
NASA Astrophysics Data System (ADS)
Rishel, Evan
This thesis details the development of a linear/nonlinear three degree of freedom aeroelastic system designed and manufactured at the University of Washington (UW). Describing function analysis was carried out in the frequency domain. Time domain simulations were carried out to account for all types of motion. Nonlinear aeroelastic behavior may lead to limit cycles which can be captured in the frequency domain using describing function approximation and numerically using Runga-Kutta integration. Linear and nonlinear aeroelastic tests were conducted in the UW 3x3 low-speed wind tunnel to determine the linear flutter speed and frequency of the system as well as its nonlinear behavior when freeplay is introduced. The test data is presented along with the results of the MATLAB-based simulations. The correlation between test and numerical results is very high.
A nonlinear filtering process diagnostic system for the Space Station
NASA Technical Reports Server (NTRS)
Yoel, Raymond R.; Buchner, M.; Loparo, K.; Cubukcu, Arif
1988-01-01
A nonlinear filtering process diagnostic system, terrestrial simulation and real time implementation studies is presented. Possible applications to Space Station subsystem elements are discussed. A process diagnostic system using model based nonlinear filtering for systems with random structure was shown to provide improvements in stability, robustness, and overall performance in comparison to linear filter based systems. A suboptimal version of the nonlinear filter (zero order approximation filter, or ZOA filter) was used in simulation studies, initially, with a pressurized water reactor model and then with water/steam heat exchanger models. Finally, a real time implementation for leak detection in a water/steam heat exchanger was conducted using the ZOA filter and heat exchanger models.
Nonlinear coupling in the human motor system
Chen, C.C.; Kilner, J.M.; Friston, K.J.; Kiebel, S. J.; Jolly, R.K.; Ward, N. S.
2010-01-01
The synchronous discharge of neuronal assemblies is thought to facilitate communication between areas within distributed networks in the human brain. This oscillatory activity is especially interesting, given the pathological modulation of specific frequencies in diseases affecting the motor system. Many studies investigating oscillatory activity have focussed on same frequency, or linear, coupling between areas of a network. In this study, our aim was to establish a functional architecture in the human motor system responsible for induced responses as measured in normal subjects with magnetoencephalography. Specifically, we looked for evidence for additional nonlinear (between-frequency) coupling among neuronal sources and, in particular, whether nonlinearities were found predominantly in connections within areas (intrinsic), between areas (extrinsic) or both. We modelled the event-related modulation of spectral responses during a simple hand-grip using dynamic casual modelling. We compared models with and without nonlinear connections under conditions of symmetric and asymmetric interhemispheric connectivity. Bayesian model comparison suggested that the task-dependent motor network was asymmetric during right hand movements. Furthermore, it revealed very strong evidence for nonlinear coupling between sources in this distributed network, but interactions among frequencies within a source appeared linear in nature. Our results provide empirical evidence for nonlinear coupling among distributed neuronal sources in the motor system and that these play an important role in modulating spectral responses under normal conditions. PMID:20573886
System characterization in nonlinear random vibration
Paez, T.L.; Gregory, D.L.
1986-01-01
Linear structural models are frequently used for structural system characterization and analysis. In most situations they can provide satisfactory results, but under some circumstances they are insufficient for system definition. The present investigation proposes a model for nonlinear structure characterization, and demonstrates how the functions describing the model can be identified using a random vibration experiment. Further, it is shown that the model is sufficient to completely characterize the stationary random vibration response of a structure that has a harmonic frequency generating form of nonlinearity. An analytical example is presented to demonstrate the plausibility of the model.
Chaotic Oscillations in Weakly Nonlinear Systems
NASA Astrophysics Data System (ADS)
Belogortsev, Andrey B.
1995-01-01
The weakly nonlinear oscillator is a classical model widely used for studying various nonlinear phenomena in such fields as physics, mechanics, biology, and electrical engineering. This work is devoted to the study of the properties of weakly nonlinear systems, which result in the appearance of their chaotic behavior. The analysis is concentrated on three classical types of weakly nonlinear systems: the Duffing oscillator, the van der Pol oscillator, and the relaxation oscillator. The method of averaging is applied to the original equations of motion of these systems to obtain the averaged equations, which serve as the basic mathematical models in this work. The secondary averaging method is applied to the Duffing and van der Pol oscillators, driven by a quasiperiodic force, and an analysis of their properties is performed. Analytical expressions for the response curves and bifurcation conditions of various types in these systems have been obtained for the first time. The theoretical results have been compared with numerical ones, which agree closely. An approach using a discrete mapping has also been applied to the quasiperiodically forced Duffing and van der Pol oscillators. Corresponding maps have been derived and analyzed for the first time. The analytical results obtained for the response curves of the oscillators and bifurcation conditions of the quasiperiodic solutions are in good agreement with the results obtained using the secondary averaging technique and with numerical results. The mechanisms for the appearance of chaotic motion in weakly nonlinear oscillators with different types of hysteresis (due to nonisochronism and due to a relaxation element) have been analysed and discussed. The bifurcation portraits of the weakly nonlinear oscillators have been obtained numerically and the general characteristics of the transition from regular to chaotic motion in such systems have been analyzed. The theoretical results are in good agreement with the numerical
Talebi, H A; Khorasani, K; Tafazoli, S
2009-01-01
This paper presents a robust fault detection and isolation (FDI) scheme for a general class of nonlinear systems using a neural-network-based observer strategy. Both actuator and sensor faults are considered. The nonlinear system considered is subject to both state and sensor uncertainties and disturbances. Two recurrent neural networks are employed to identify general unknown actuator and sensor faults, respectively. The neural network weights are updated according to a modified backpropagation scheme. Unlike many previous methods developed in the literature, our proposed FDI scheme does not rely on availability of full state measurements. The stability of the overall FDI scheme in presence of unknown sensor and actuator faults as well as plant and sensor noise and uncertainties is shown by using the Lyapunov's direct method. The stability analysis developed requires no restrictive assumptions on the system and/or the FDI algorithm. Magnetorquer-type actuators and magnetometer-type sensors that are commonly employed in the attitude control subsystem (ACS) of low-Earth orbit (LEO) satellites for attitude determination and control are considered in our case studies. The effectiveness and capabilities of our proposed fault diagnosis strategy are demonstrated and validated through extensive simulation studies.
Fernandes, Edite M. G. P.
2015-01-01
This paper addresses the challenging task of computing multiple roots of a system of nonlinear equations. A repulsion algorithm that invokes the Nelder-Mead (N-M) local search method and uses a penalty-type merit function based on the error function, known as ‘erf’, is presented. In the N-M algorithm context, different strategies are proposed to enhance the quality of the solutions and improve the overall efficiency. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm. PMID:25875591
Ramadas, Gisela C V; Rocha, Ana Maria A C; Fernandes, Edite M G P
2015-01-01
This paper addresses the challenging task of computing multiple roots of a system of nonlinear equations. A repulsion algorithm that invokes the Nelder-Mead (N-M) local search method and uses a penalty-type merit function based on the error function, known as 'erf', is presented. In the N-M algorithm context, different strategies are proposed to enhance the quality of the solutions and improve the overall efficiency. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm.
Adaptive control of nonlinear systems with actuator failures and uncertainties
NASA Astrophysics Data System (ADS)
Tang, Xidong
2005-11-01
Actuator failures have damaging effect on the performance of control systems, leading to undesired system behavior or even instability. Actuator failures are unknown in terms of failure time instants, failure patterns, and failure parameters. For system safety and reliability, the compensation of actuator failures is of both theoretical and practical significance. This dissertation is to further the study of adaptive designs for actuator failure compensation to nonlinear systems. In this dissertation a theoretical framework for adaptive control of nonlinear systems with actuator failures and system uncertainties is established. The contributions are the development of new adaptive nonlinear control schemes to handle unknown actuator failures for convergent tracking performance, the specification of conditions as a guideline for applications and system designs, and the extension of the adaptive nonlinear control theory. In the dissertation, adaptive actuator failure compensation is studied for several classes of nonlinear systems. In particular, adaptive state feedback schemes are developed for feedback linearizable systems and parametric strict-feedback systems. Adaptive output feedback schemes are deigned for output-feedback systems and a class of systems with unknown state-dependent nonlinearities. Furthermore, adaptive designs are addressed for MIMO systems with actuator failures, based on two grouping techniques: fixed grouping and virtual grouping. Theoretical issues such as controller structures, actuation schemes, zero dynamics, observation, grouping conditions, closed-loop stability, and tracking performance are extensively investigated. For each scheme, design conditions are clarified, and detailed stability and performance analysis is presented. A variety of applications including a wing-rock model, twin otter aircraft, hypersonic aircraft, and cooperative multiple manipulators are addressed with simulation results showing the effectiveness of the
Evolutionary quantitative genetics of nonlinear developmental systems.
Morrissey, Michael B
2015-08-01
In quantitative genetics, the effects of developmental relationships among traits on microevolution are generally represented by the contribution of pleiotropy to additive genetic covariances. Pleiotropic additive genetic covariances arise only from the average effects of alleles on multiple traits, and therefore the evolutionary importance of nonlinearities in development is generally neglected in quantitative genetic views on evolution. However, nonlinearities in relationships among traits at the level of whole organisms are undeniably important to biology in general, and therefore critical to understanding evolution. I outline a system for characterizing key quantitative parameters in nonlinear developmental systems, which yields expressions for quantities such as trait means and phenotypic and genetic covariance matrices. I then develop a system for quantitative prediction of evolution in nonlinear developmental systems. I apply the system to generating a new hypothesis for why direct stabilizing selection is rarely observed. Other uses will include separation of purely correlative from direct and indirect causal effects in studying mechanisms of selection, generation of predictions of medium-term evolutionary trajectories rather than immediate predictions of evolutionary change over single generation time-steps, and the development of efficient and biologically motivated models for separating additive from epistatic genetic variances and covariances.
Applications of equivalent linearization approaches to nonlinear piping systems
Park, Y.; Hofmayer, C.; Chokshi, N.
1997-04-01
The piping systems in nuclear power plants, even with conventional snubber supports, are highly complex nonlinear structures under severe earthquake loadings mainly due to various mechanical gaps in support structures. Some type of nonlinear analysis is necessary to accurately predict the piping responses under earthquake loadings. The application of equivalent linearization approaches (ELA) to seismic analyses of nonlinear piping systems is presented. Two types of ELA`s are studied; i.e., one based on the response spectrum method and the other based on the linear random vibration theory. The test results of main steam and feedwater piping systems supported by snubbers and energy absorbers are used to evaluate the numerical accuracy and limitations.
A nonlinear complementarity approach for the national energy modeling system
Gabriel, S.A.; Kydes, A.S.
1995-03-08
The National Energy Modeling System (NEMS) is a large-scale mathematical model that computes equilibrium fuel prices and quantities in the U.S. energy sector. At present, to generate these equilibrium values, NEMS sequentially solves a collection of linear programs and nonlinear equations. The NEMS solution procedure then incorporates the solutions of these linear programs and nonlinear equations in a nonlinear Gauss-Seidel approach. The authors describe how the current version of NEMS can be formulated as a particular nonlinear complementarity problem (NCP), thereby possibly avoiding current convergence problems. In addition, they show that the NCP format is equally valid for a more general form of NEMS. They also describe several promising approaches for solving the NCP form of NEMS based on recent Newton type methods for general NCPs. These approaches share the feature of needing to solve their direction-finding subproblems only approximately. Hence, they can effectively exploit the sparsity inherent in the NEMS NCP.
Nonlinear dynamical system identification using unscented Kalman filter
NASA Astrophysics Data System (ADS)
Rehman, M. Javvad ur; Dass, Sarat Chandra; Asirvadam, Vijanth Sagayan
2016-11-01
Kalman Filter is the most suitable choice for linear state space and Gaussian error distribution from decades. In general practical systems are not linear and Gaussian so these assumptions give inconsistent results. System Identification for nonlinear dynamical systems is a difficult task to perform. Usually, Extended Kalman Filter (EKF) is used to deal with non-linearity in which Jacobian method is used for linearizing the system dynamics, But it has been observed that in highly non-linear environment performance of EKF is poor. Unscented Kalman Filter (UKF) is proposed here as a better option because instead of analytical linearization of state space, UKF performs statistical linearization by using sigma point calculated from deterministic samples. Formation of the posterior distribution is based on the propagation of mean and covariance through sigma points.
Hierarchical robust nonlinear switching control design for propulsion systems
NASA Astrophysics Data System (ADS)
Leonessa, Alexander
1999-09-01
The desire for developing an integrated control system- design methodology for advanced propulsion systems has led to significant activity in modeling and control of flow compression systems in recent years. In this dissertation we develop a novel hierarchical switching control framework for addressing the compressor aerodynamic instabilities of rotating stall and surge. The proposed control framework accounts for the coupling between higher-order modes while explicitly addressing actuator rate saturation constraints and system modeling uncertainty. To develop a hierarchical nonlinear switching control framework, first we develop generalized Lyapunov and invariant set theorems for nonlinear dynamical systems wherein all regularity assumptions on the Lyapunov function and the system dynamics are removed. In particular, local and global stability theorems are given using lower semicontinuous Lyapunov functions. Furthermore, generalized invariant set theorems are derived wherein system trajectories converge to a union of largest invariant sets contained in intersections over finite intervals of the closure of generalized Lyapunov level surfaces. The proposed results provide transparent generalizations to standard Lyapunov and invariant set theorems. Using the generalized Lyapunov and invariant set theorems, a nonlinear control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving system equilibria is developed. Specifically, using equilibria- dependent Lyapunov functions, a hierarchical nonlinear control strategy is developed that stabilizes a given nonlinear system by stabilizing a collection of nonlinear controlled subsystems. The switching nonlinear controller architecture is designed based on a generalized lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized system equilibria. The proposed framework provides a
Anti-synchronization of two hyperchaotic systems via nonlinear control
NASA Astrophysics Data System (ADS)
Al-Sawalha, M. Mossa; Noorani, M. S. M.
2009-08-01
Based on the nonlinear control theory, the anti-synchronization between two different hyperchaotic systems is investigated. Through rigorous mathematical theory, the sufficient condition is drawn for the stability of the error dynamics, where the controllers are designed by using the sum of the relevant variables in hyperchaotic systems. Numerical simulations are performed for the hyperchaotic Chen system and the hyperchaotic Lü system to demonstrate the effectiveness of the proposed control strategy.
Nonlinear amplitude approximation for bilinear systems
NASA Astrophysics Data System (ADS)
Jung, Chulwoo; D'Souza, Kiran; Epureanu, Bogdan I.
2014-06-01
An efficient method to predict vibration amplitudes at the resonant frequencies of dynamical systems with piecewise-linear nonlinearity is developed. This technique is referred to as bilinear amplitude approximation (BAA). BAA constructs a single vibration cycle at each resonant frequency to approximate the periodic steady-state response of the system. It is postulated that the steady-state response is piece-wise linear and can be approximated by analyzing the response over two time intervals during which the system behaves linearly. Overall the dynamics is nonlinear, but the system is in a distinct linear state during each of the two time intervals. Thus, the approximated vibration cycle is constructed using linear analyses. The equation of motion for analyzing the vibration of each state is projected along the overlapping space spanned by the linear mode shapes active in each of the states. This overlapping space is where the vibratory energy is transferred from one state to the other when the system switches from one state to the other. The overlapping space can be obtained using singular value decomposition. The space where the energy is transferred is used together with transition conditions of displacement and velocity compatibility to construct a single vibration cycle and to compute the amplitude of the dynamics. Since the BAA method does not require numerical integration of nonlinear models, computational costs are very low. In this paper, the BAA method is first applied to a single-degree-of-freedom system. Then, a three-degree-of-freedom system is introduced to demonstrate a more general application of BAA. Finally, the BAA method is applied to a full bladed disk with a crack. Results comparing numerical solutions from full-order nonlinear analysis and results obtained using BAA are presented for all systems.
A tensor approach to modeling of nonhomogeneous nonlinear systems
NASA Technical Reports Server (NTRS)
Yurkovich, S.; Sain, M.
1980-01-01
Model following control methodology plays a key role in numerous application areas. Cases in point include flight control systems and gas turbine engine control systems. Typical uses of such a design strategy involve the determination of nonlinear models which generate requested control and response trajectories for various commands. Linear multivariable techniques provide trim about these motions; and protection logic is added to secure the hardware from excursions beyond the specification range. This paper reports upon experience in developing a general class of such nonlinear models based upon the idea of the algebraic tensor product.
Research on Nonlinear Dynamical Systems.
1976-10-19
LaSalle , J .P ., “Stability theory and invariance principles ” , Dynamical Systems, An International Symposium, Vol.1, pp. 2 11—222 , Academic Press...1974 — 31 November 1975 Principal Investigator: Professor J. P. LaSalle Grant DAA G 29/76/G/0052 1 December 1975 - 31 August 1976 Principal...Investigator: Professor 3. P. LaSalle L.fsch.ts Cente r for. Dynamical Syst.m. Division of Appli.d Mathematics Brown Univ.r sity Providena., Rhod. ~~~~~ 02912 D
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.
Numerical studies of identification in nonlinear distributed parameter systems
NASA Technical Reports Server (NTRS)
Banks, H. T.; Lo, C. K.; Reich, Simeon; Rosen, I. G.
1989-01-01
An abstract approximation framework and convergence theory for the identification of first and second order nonlinear distributed parameter systems developed previously by the authors and reported on in detail elsewhere are summarized and discussed. The theory is based upon results for systems whose dynamics can be described by monotone operators in Hilbert space and an abstract approximation theorem for the resulting nonlinear evolution system. The application of the theory together with numerical evidence demonstrating the feasibility of the general approach are discussed in the context of the identification of a first order quasi-linear parabolic model for one dimensional heat conduction/mass transport and the identification of a nonlinear dissipation mechanism (i.e., damping) in a second order one dimensional wave equation. Computational and implementational considerations, in particular, with regard to supercomputing, are addressed.
NASA Astrophysics Data System (ADS)
Wei, Guoliang; Liu, Shuai; Wang, Licheng; Wang, Yongxiong
2016-07-01
In this paper, based on the event-triggered mechanism, the problem of distributed set-membership filtering is concerned for a class of time-varying non-linear systems over sensor networks subject to saturation effects. Different from the traditional periodic sample-data approach, the filter is updated only when the predefined event is satisfied, which the event is defined according to the measurement output. For each node, the proposed novel event-triggered mechanism can reduce the unnecessary information transmission between sensors and filters. The purpose of the addressed problem is to design a series of distributed set-membership filters, for all the admissible unknown but bounded noises, non-linearities and sensor saturation, such that the set of all possible states can be determined. The desired filter parameters are obtained by solving a recursive linear matrix inequality that can be computed recursively using the available MATLAB toolbox. Finally, a simulation example is exploited to show the effectiveness of the proposed design approach in this paper.
Finding sets of solutions to systems of nonlinear inequalities
NASA Astrophysics Data System (ADS)
Evtushenko, Yu. G.; Posypkin, M. A.; Rybak, L. A.; Turkin, A. V.
2017-08-01
The problem of approximating the set of all solutions to a system of nonlinear inequalities is studied. A method based on the concept of nonuniform coverings is proposed. It allows one to obtain an interior and exterior approximation of this set with a prescribed accuracy. The efficiency of the method is demonstrated by determining the workspace of a parallel robot.
On stabilisability of nonlinear systems on time scales
NASA Astrophysics Data System (ADS)
Bartosiewicz, Zbigniew; Piotrowska, Ewa
2013-01-01
In this article, stabilisability of nonlinear finite-dimensional control systems on arbitrary time scales is studied. The classical results on stabilisation of nonlinear continuous-time and discrete-time systems are extended to systems on arbitrary time scales with bounded graininess function. It is shown that uniform exponential stability of the linear approximation of a nonlinear system implies uniform exponential stability of the nonlinear system. Then this result is used to show a similar implication for uniform exponential stabilisability.
Nonlinear plants, factorizations and stable feedback systems
NASA Technical Reports Server (NTRS)
Desoer, Charles A.; Kabuli, M. Guntekin
1987-01-01
For nonlinear plants represented by causal maps defined over extended spaces, right factorization and normalized right-coprime factorization concepts are discussed in terms of well-posed stable feedback systems. This setup covers continuous-time, discrete-time, time-invariant or time-varying input-output maps. The nonlinear maps are factored in terms of causal bounded-input bounded-output stable maps. In factored form, all instabilities of the original map are represented by the inverse of a causal stable `denominator' map. The existence of maps with right factorizations and normalized right-coprime factorizations is shown using a well-posed stable unity-feedback system. In the case where one of the subsystems has a normalized right-coprime factorization, the stability of the feedback system is equivalent to the stability of the pseudostate map.
Accidental degeneracies in nonlinear quantum deformed systems
NASA Astrophysics Data System (ADS)
Aleixo, A. N. F.; Balantekin, A. B.
2011-09-01
We construct a multi-parameter nonlinear deformed algebra for quantum confined systems that includes many other deformed models as particular cases. We demonstrate that such systems exhibit the property of accidental pairwise energy level degeneracies. We also study, as a special case of our multi-parameter deformation formalism, the extension of the Tamm-Dancoff cutoff deformed oscillator and the occurrence of accidental pairwise degeneracy in the energy levels of the deformed system. As an application, we discuss the case of a trigonometric Rosen-Morse potential, which is successfully used in models for quantum confined systems, ranging from electrons in quantum dots to quarks in hadrons.
Model reduction of systems with localized nonlinearities.
Segalman, Daniel Joseph
2006-03-01
An LDRD funded approach to development of reduced order models for systems with local nonlinearities is presented. This method is particularly useful for problems of structural dynamics, but has potential application in other fields. The key elements of this approach are (1) employment of eigen modes of a reference linear system, (2) incorporation of basis functions with an appropriate discontinuity at the location of the nonlinearity. Galerkin solution using the above combination of basis functions appears to capture the dynamics of the system with a small basis set. For problems involving small amplitude dynamics, the addition of discontinuous (joint) modes appears to capture the nonlinear mechanics correctly while preserving the modal form of the predictions. For problems involving large amplitude dynamics of realistic joint models (macro-slip), the use of appropriate joint modes along with sufficient basis eigen modes to capture the frequencies of the system greatly enhances convergence, though the modal nature the result is lost. Also observed is that when joint modes are used in conjunction with a small number of elastic eigen modes in problems of macro-slip of realistic joint models, the resulting predictions are very similar to those of the full solution when seen through a low pass filter. This has significance both in terms of greatly reducing the number of degrees of freedom of the problem and in terms of facilitating the use of much larger time steps.
Dynamic analysis of nonlinear rotor-housing systems
NASA Technical Reports Server (NTRS)
Noah, Sherif T.
1988-01-01
Nonlinear analysis methods are developed which will enable the reliable prediction of the dynamic behavior of the space shuttle main engine (SSME) turbopumps in the presence of bearing clearances and other local nonlinearities. A computationally efficient convolution method, based on discretized Duhamel and transition matrix integral formulations, is developed for the transient analysis. In the formulation, the coupling forces due to the nonlinearities are treated as external forces acting on the coupled subsystems. Iteration is utilized to determine their magnitudes at each time increment. The method is applied to a nonlinear generic model of the high pressure oxygen turbopump (HPOTP). As compared to the fourth order Runge-Kutta numerical integration methods, the convolution approach proved to be more accurate and more highly efficient. For determining the nonlinear, steady-state periodic responses, an incremental harmonic balance method was also developed. The method was successfully used to determine dominantly harmonic and subharmonic responses fo the HPOTP generic model with bearing clearances. A reduction method similar to the impedance formulation utilized with linear systems is used to reduce the housing-rotor models to their coordinates at the bearing clearances. Recommendations are included for further development of the method, for extending the analysis to aperiodic and chaotic regimes and for conducting critical parameteric studies of the nonlinear response of the current SSME turbopumps.
A Cumulant-based Analysis of Nonlinear Magnetospheric Dynamics
Jay R. Johnson; Simon Wing
2004-01-28
Understanding magnetospheric dynamics and predicting future behavior of the magnetosphere is of great practical interest because it could potentially help to avert catastrophic loss of power and communications. In order to build good predictive models it is necessary to understand the most critical nonlinear dependencies among observed plasma and electromagnetic field variables in the coupled solar wind/magnetosphere system. In this work, we apply a cumulant-based information dynamical measure to characterize the nonlinear dynamics underlying the time evolution of the Dst and Kp geomagnetic indices, given solar wind magnetic field and plasma input. We examine the underlying dynamics of the system, the temporal statistical dependencies, the degree of nonlinearity, and the rate of information loss. We find a significant solar cycle dependence in the underlying dynamics of the system with greater nonlinearity for solar minimum. The cumulant-based approach also has the advantage that it is reliable even in the case of small data sets and therefore it is possible to avoid the assumption of stationarity, which allows for a measure of predictability even when the underlying system dynamics may change character. Evaluations of several leading Kp prediction models indicate that their performances are sub-optimal during active times. We discuss possible improvements of these models based on this nonparametric approach.
Robust H ∞ control of a nonlinear uncertain system via a stable nonlinear output feedback controller
NASA Astrophysics Data System (ADS)
Harno, Hendra G.; Petersen, Ian R.
2011-04-01
A new approach to solving a nonlinear robust H ∞ control problem using a stable nonlinear output feedback controller is presented in this article. The class of nonlinear uncertain systems being considered is characterised in terms of integral quadratic constraints and global Lipschitz conditions describing the admissible uncertainties and nonlinearities, respectively. The nonlinear controller is able to exploit the plant nonlinearities through the inclusion of a copy of the known plant nonlinearities in the controller. The H ∞ control objective is to obtain an absolutely stable closed-loop system with a specified disturbance attenuation level. The solution to this control problem involves stabilising solutions to parametrised algebraic Riccati equations. We apply a differential evolution algorithm to solve a non-convex nonlinear optimisation problem arising in the controller synthesis.
Nonlinear Analysis and Optimal Design of Dynamic Mechanical Systems for Spacecraft Application.
1986-02-01
Mechanisms, vibrational analysis, optimization , geometric nonlinearity , material nonlinearity 20. AUSTRACT (C..,I.,.. 01 ".Id*If oO...p .,d Id.MII( by... nonlinear finite element analysis procedure for three-dimensional mechanisms. A niew optimization algorithm has also been developed based on the Gauss DD I...1986 NONLINEAR ANALYSIS AND OPTIMAL DESIGN OF DYNAMIC MECHANICAL SYSTEMS FOR SPACECRAFT APPLICATION Air Force Office of Scientific Research Grant No
An adaptive pattern based nonlinear PID controller.
Segovia, Juan Pablo; Sbarbaro, Daniel; Ceballos, Eric
2004-04-01
This paper presents a nonlinear proportional-integral-derivative (PID) controller, combining a pattern based adaptive algorithm to cope with the problem of tuning the controller, and an associative memory to store the parameters, according to different operating conditions. The simplicity of the algorithm enables its implementation in current programmable logic controller technology. Several real-time experiments, carried out in a pressurized tank, illustrate the performance of the proposed controller.
Lee, Hanna; Park, Eun Suk; Yu, Jae Kook; Yun, Eun Kyoung
2015-10-01
The purpose of this study was to develop a system dynamics model for adolescent obesity in Korea that could be used for obesity policy analysis. On the basis of the casual loop diagram, a model was developed by converting to stock and flow diagram. The Vensim DSS 5.0 program was used in the model development. We simulated method of moments to the calibration of this model with data from The Korea Youth Risk Behavior Web-based Survey 2005 to 2013. We ran the scenario simulation. This model can be used to understand the current adolescent obesity rate, predict the future obesity rate, and be utilized as a tool for controlling the risk factors. The results of the model simulation match well with the data. It was identified that a proper model, able to predict obesity probability, was established. These results of stock and flow diagram modeling in adolescent obesity can be helpful in development of obesity by policy planners and other stakeholders to better anticipate the multiple effects of interventions in both the short and the long term. In the future we suggest the development of an expanded model based on this adolescent obesity model.
Singularity perturbed zero dynamics of nonlinear systems
NASA Technical Reports Server (NTRS)
Isidori, A.; Sastry, S. S.; Kokotovic, P. V.; Byrnes, C. I.
1992-01-01
Stability properties of zero dynamics are among the crucial input-output properties of both linear and nonlinear systems. Unstable, or 'nonminimum phase', zero dynamics are a major obstacle to input-output linearization and high-gain designs. An analysis of the effects of regular perturbations in system equations on zero dynamics shows that whenever a perturbation decreases the system's relative degree, it manifests itself as a singular perturbation of zero dynamics. Conditions are given under which the zero dynamics evolve in two timescales characteristic of a standard singular perturbation form that allows a separate analysis of slow and fast parts of the zero dynamics.
Approximations of nonlinear systems having outputs
NASA Technical Reports Server (NTRS)
Hunt, L. R.; Su, R.
1985-01-01
For a nonlinear system with output derivative x = f(x) and y = h(x), two types of linearizations about a point x(0) in state space are considered. One is the usual Taylor series approximation, and the other is defined by linearizing the appropriate Lie derivatives of the output with respect to f about x(0). The latter is called the obvservation model and appears to be quite natural for observation. It is noted that there is a coordinate system in which these two kinds of linearizations agree. In this coordinate system, a technique to construct an observer is introduced.
Hou, Zhongsheng; Liu, Shida; Tian, Taotao
2016-05-18
In this paper, a novel data-driven model-free adaptive predictive control method based on lazy learning technique is proposed for a class of discrete-time single-input and single-output nonlinear systems. The feature of the proposed approach is that the controller is designed only using the input-output (I/O) measurement data of the system by means of a novel dynamic linearization technique with a new concept termed pseudogradient (PG). Moreover, the predictive function is implemented in the controller using a lazy-learning (LL)-based PG predictive algorithm, such that the controller not only shows good robustness but also can realize the effect of model-free adaptive prediction for the sudden change of the desired signal. Further, since the LL technique has the characteristic of database queries, both the online and offline I/O measurement data are fully and simultaneously utilized to real-time adjust the controller parameters during the control process. Moreover, the stability of the proposed method is guaranteed by rigorous mathematical analysis. Meanwhile, the numerical simulations and the laboratory experiments implemented on a practical three-tank water level control system both verify the effectiveness of the proposed approach.
Modeling and measurement of geometrically nonlinear damping in a microcantilever-nanotube system.
Jeong, Bongwon; Cho, Hanna; Yu, Min-Feng; Vakakis, Alexander F; McFarland, Donald Michael; Bergman, Lawrence A
2013-10-22
Nonlinear mechanical systems promise broadband resonance and instantaneous hysteretic switching that can be used for high sensitivity sensing. However, to introduce nonlinear resonances in widely used microcantilever systems, such as AFM probes, requires driving the cantilever to an amplitude that is too large for any practical applications. We introduce a novel design for a microcantilever with a strong nonlinearity at small cantilever oscillation amplitude arising from the geometrical integration of a single BN nanotube. The dynamics of the system was modeled theoretically and confirmed experimentally. The system, besides providing a practical design of a nonlinear microcantilever-based probe, demonstrates also an effective method of studying the nonlinear damping properties of the attached nanotube. Beyond the typical linear mechanical damping, the nonlinear damping contribution from the attached nanotube was found to be essential for understanding the dynamical behavior of the designed system. Experimental results obtained through laser microvibrometry validated the developed model incorporating the nonlinear damping contribution.
Thumati, Balaje T; Jagannathan, S
2010-03-01
In this paper, a novel, unified model-based fault-detection and prediction (FDP) scheme is developed for nonlinear multiple-input-multiple-output (MIMO) discrete-time systems. The proposed scheme addresses both state and output faults by considering separate time profiles. The faults, which could be incipient or abrupt, are modeled using input and output signals of the system. The fault-detection (FD) scheme comprises online approximator in discrete time (OLAD) with a robust adaptive term. An output residual is generated by comparing the FD estimator output with that of the measured system output. A fault is detected when this output residual exceeds a predefined threshold. Upon detecting the fault, the robust adaptive terms and the OLADs are initiated wherein the OLAD approximates the unknown fault dynamics online while the robust adaptive terms help in ensuring asymptotic stability of the FD design. Using the OLAD outputs, a fault diagnosis scheme is introduced. A stable parameter update law is developed not only to tune the OLAD parameters but also to estimate the time to failure (TTF), which is considered as a first step for prognostics. The asymptotic stability of the FDP scheme enhances the detection and TTF accuracy. The effectiveness of the proposed approach is demonstrated using a fourth-order MIMO satellite system.
NASA Astrophysics Data System (ADS)
Singh, S. N.
1982-03-01
Using the invariance principle of LaSalle (1962) sufficient conditions for the existence of linear and nonlinear control laws for local and global asymptotic stability of nonlinear Hamiltonian systems are derived. An instability theorem is also presented which identifies the control laws from the given class which cannot achieve asymptotic stability. Some of the stability results are based on certain results for the univalence of nonlinear maps. A similar approach for the stabilization of bilinear systems which include nonconservative systems in elasticity is used and a necessary and sufficient condition for stabilization is obtained. An application to attitude control of a gyrostat Satellite is presented.
Nercessian, Shahan C; Panetta, Karen A; Agaian, Sos S
2013-09-01
Image enhancement is a crucial pre-processing step for various image processing applications and vision systems. Many enhancement algorithms have been proposed based on different sets of criteria. However, a direct multi-scale image enhancement algorithm capable of independently and/or simultaneously providing adequate contrast enhancement, tonal rendition, dynamic range compression, and accurate edge preservation in a controlled manner has yet to be produced. In this paper, a multi-scale image enhancement algorithm based on a new parametric contrast measure is presented. The parametric contrast measure incorporates not only the luminance masking characteristic, but also the contrast masking characteristic of the human visual system. The formulation of the contrast measure can be adapted for any multi-resolution decomposition scheme in order to yield new human visual system-inspired multi-scale transforms. In this article, it is exemplified using the Laplacian pyramid, discrete wavelet transform, stationary wavelet transform, and dual-tree complex wavelet transform. Consequently, the proposed enhancement procedure is developed. The advantages of the proposed method include: 1) the integration of both the luminance and contrast masking phenomena; 2) the extension of non-linear mapping schemes to human visual system inspired multi-scale contrast coefficients; 3) the extension of human visual system-based image enhancement approaches to the stationary and dual-tree complex wavelet transforms, and a direct means of; 4) adjusting overall brightness; and 5) achieving dynamic range compression for image enhancement within a direct multi-scale enhancement framework. Experimental results demonstrate the ability of the proposed algorithm to achieve simultaneous local and global enhancements.
NASA Astrophysics Data System (ADS)
Nagi Reddy, M. V. V.; Pisipati, V. G. K. M.; Madhavi Latha, D.; Datta Prasad, P. V.
2011-02-01
The non-linearity parameter B/ A is estimated for a number of liquid crystal materials of the type N-(p-n-alkoxy benzylidene)-p-n-alkyl anilines, popularly known as nO. m, where n and m are the aliphatic chains on either side of the rigid core, which can be varied from 1 to 18 to realize a number of LC materials with a variety LC phase variants. The B/ A values are computed from both density and sound velocity data following standard relations reported in literature. This systematic study in a homologous series provides an opportunity to study how this parameter behaves with (1) either the alkoxy and/or alkyl chain number, (2) with the total chain number ( n+ m), (3) with increase in molecular weight and (4) whether the linear relations reported in literature either with αT [thermal expansion coefficient ( α) and temperature ( T)] and sound velocity ( u) will hold good or not and if so to what extent. The results are discussed with the body of data available in literature on liquids, liquid mixtures and other LC materials.
Globally uniformly asymptotical stabilisation of time-delay nonlinear systems
NASA Astrophysics Data System (ADS)
Cai, Xiushan; Han, Zhengzhi; Zhang, Wei
2011-07-01
Globally uniformly asymptotical stabilisation of nonlinear systems in feedback form with a delay arbitrarily large in the input is dealt with based on the backstepping approach in this article. The design strategy depends on the construction of a Lyapunov-Krasovskii functional. A continuously differentiable control law is obtained to globally uniformly asymptotically stabilise the closed-loop system. The simulation shows the effectiveness of the method.
Non-linear dynamic compensation system
NASA Technical Reports Server (NTRS)
Lin, Yu-Hwan (Inventor); Lurie, Boris J. (Inventor)
1992-01-01
A non-linear dynamic compensation subsystem is added in the feedback loop of a high precision optical mirror positioning control system to smoothly alter the control system response bandwidth from a relatively wide response bandwidth optimized for speed of control system response to a bandwidth sufficiently narrow to reduce position errors resulting from the quantization noise inherent in the inductosyn used to measure mirror position. The non-linear dynamic compensation system includes a limiter for limiting the error signal within preselected limits, a compensator for modifying the limiter output to achieve the reduced bandwidth response, and an adder for combining the modified error signal with the difference between the limited and unlimited error signals. The adder output is applied to control system motor so that the system response is optimized for accuracy when the error signal is within the preselected limits, optimized for speed of response when the error signal is substantially beyond the preselected limits and smoothly varied therebetween as the error signal approaches the preselected limits.
Control of nonlinear time-varying systems
NASA Technical Reports Server (NTRS)
Hunt, L. R.; Su, R.
1981-01-01
Necessary and sufficient conditions are given for a time-varying nonlinear system of specific form to be transformed into a time-invariant controllable linear system. Since the present work will be in a neighborhood of the origin, it is unnecessary to name specific sets and it is assumed that all assumptions, conditions and results hold in an open set in the appropriate Euclidean space that contains the origin. This theory can be combined with the global inverse function theorems to produce global results.
Multiple model self-tuning control for a class of nonlinear systems
NASA Astrophysics Data System (ADS)
Huang, Miao; Wang, Xin; Wang, Zhenlei
2015-10-01
This study develops a novel nonlinear multiple model self-tuning control method for a class of nonlinear discrete-time systems. An increment system model and a modified robust adaptive law are proposed to expand the application range, thus eliminating the assumption that either the nonlinear term of the nonlinear system or its differential term is global-bounded. The nonlinear self-tuning control method can address the situation wherein the nonlinear system is not subject to a globally uniformly asymptotically stable zero dynamics by incorporating the pole-placement scheme. A novel, nonlinear control structure based on this scheme is presented to improve control precision. Stability and convergence can be confirmed when the proposed multiple model self-tuning control method is applied. Furthermore, simulation results demonstrate the effectiveness of the proposed method.
NONLINEAR TIDES IN CLOSE BINARY SYSTEMS
Weinberg, Nevin N.; Arras, Phil; Quataert, Eliot; Burkart, Josh
2012-06-01
We study the excitation and damping of tides in close binary systems, accounting for the leading-order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct physical effects: three-mode nonlinear interactions, i.e., the redistribution of energy among stellar modes of oscillation, and nonlinear excitation of stellar normal modes by the time-varying gravitational potential of the companion. This paper, the first in a series, presents the formalism for studying nonlinear tides and studies the nonlinear stability of the linear tidal flow. Although the formalism we present is applicable to binaries containing stars, planets, and/or compact objects, we focus on non-rotating solar-type stars with stellar or planetary companions. Our primary results include the following: (1) The linear tidal solution almost universally used in studies of binary evolution is unstable over much of the parameter space in which it is employed. More specifically, resonantly excited internal gravity waves in solar-type stars are nonlinearly unstable to parametric resonance for companion masses M' {approx}> 10-100 M{sub Circled-Plus} at orbital periods P Almost-Equal-To 1-10 days. The nearly static 'equilibrium' tidal distortion is, however, stable to parametric resonance except for solar binaries with P {approx}< 2-5 days. (2) For companion masses larger than a few Jupiter masses, the dynamical tide causes short length scale waves to grow so rapidly that they must be treated as traveling waves, rather than standing waves. (3) We show that the global three-wave treatment of parametric instability typically used in the astrophysics literature does not yield the fastest-growing daughter modes or instability threshold in many cases. We find a form of parametric instability in which a single parent wave excites a very large number of daughter waves (N Almost-Equal-To 10{sup 3}[P/10 days] for a solar-type star) and drives them as a single coherent unit with
Adaptive Control of Nonlinear Flexible Systems
1994-05-26
nonlinear plants which admit a finite- dimensional state-space description of the form S= f(Z) + g(z)u for which the State-Space Exact Linearization Problem...robust state-feedback law and the sensi- i tivity of the exact - linearization based control law. 2.6.3 Example 2 I Consider the following one state...is also available for exact linearization , Now apply the certainty equivalence based control one can bring an input-output approach to a particu- law
NASA Astrophysics Data System (ADS)
Zhang, Xu; Lin, Yan
2014-02-01
We investigate the problem of global stabilisation by linear output feedback for a class of uncertain nonlinear systems with zero-dynamics. Compared with the previous works, new dilation-based assumptions are introduced that allow the system nonlinearities and its bounding functions to be coupled with all the states. The nonlinear systems of this paper can be considered as an extended form of some low triangular and feedforward systems. Dynamic gain scaling technique is applied to the controller design and stability analysis. It is proved that with a unifying linear controller structure and flexible adaptive laws for the observer gain, global stabilisation of the nonlinear systems can be achieved.
Deterministic and stochastic responses of nonlinear systems
NASA Astrophysics Data System (ADS)
Abou-Rayan, Ashraf Mohamed
The responses of nonlinear systems to both deterministic and stochastic excitations are discussed. For a single degree of freedom system, the response of a simply supported buckled beam to parametric excitations is investigated. Two types of excitations are examined: deterministic and random. For the nonlinear response to a harmonic axial load, the method of multiple scales is used to determine to second order the amplitude and phase modulation equations. Floquet theory is used to analyze the stability of periodic responses. The perturbation results are verified by integrating the governing equation using both digital and analog computers. For small excitation amplitudes, the analytical results are in good agreement with the numerical solutions. The large amplitude responses are investigated by using simulations on a digital computer and are compared with results obtained using an analog computer. For the stochastic response to a wide-band random excitation, the Gaussian and non-Gaussian closure schemes are used to determine the response statistics. The results are compared with those obtained from real-time analysis (analog-computer simulation). The normality assumption is examined. A comparison between the responses to deterministic and random excitation is presented. For two degree of freedom systems, two methods are used to study the response under the action of broad-band random excitations. The first method is applicable to systems having cubic nonlinearities. It involves an averaging approach to reduce the number of moment equations for the non-Gaussian closure scheme from 69 to 14 equations. The results are compared with those obtained from numerical integrations of the moment equations and the exact stationary solution of the Fokker-Planck-Komologorov equation. The second method is applicable to systems having quadratic and cubic nonlinearities. Stationary solutions of the moment equations are determined and their stability is ascertained by examining the
NASA Astrophysics Data System (ADS)
Zhang, Xing-Hui; Xie, Xue-Jun
2014-03-01
This paper studies the state feedback control problem for a class of nonlinear systems with high-order and low-order nonlinearities. The introduction of the sign function together with the method of adding a power integrator and Lyapunov stability theorem makes the closed-loop system globally asymptotically stable. Exploiting the idea of how to deal with growth nonlinearities with both high order and low order being relaxed to some intervals is the focus of this work.
NASA Astrophysics Data System (ADS)
Lin, Zhidan; Xue, Lu
2017-09-01
According to the serial system of bearing with column, the natural frequency of serial system is investigated, and the effects of axial load and different rubber bearings are discussed. Taking into account the effects of the cross-section rotation, shear distortion and compression axial force, the mathematical model for free vibration of the system is established. The differential quadrature element method is employed for the discrete processing in governing equations and boundary conditions. The natural frequency of serial system with clampedfree boundary conditions is solved numerically, and the figures of natural frequency with compression axial force are presented. It is shown that the axial force will reduce the lower order natural frequencies significantly, and in certain case of total height, the equivalent bending stiffness of rubber bearings reduces the natural frequencies to different extent.
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.
Observability and Information Structure of Nonlinear Systems,
1985-10-01
defined by Shannon and used as a measure of mut.:al infor-mation between event x. and y4. If p(x.l IY.) I I(x., y.) xil -in (1/p(x.)) =- JInp (x.) (2...entropy H(x,y) in a similar way as H(x,y) = - fx,yp(xiy)lnp(x,y)cdlY, = -E[ JInp (x,y)]. (3-13) With the above definitions, mutual information between x...Observabiity of Nonlinear Systems, Eng. Cybernetics, Volume 1, pp 338-345, 1972. 18. Sen , P., Chidambara, M.R., Observability of a Class of Nonli-.ear
Feedback nonlinear discrete-time systems
NASA Astrophysics Data System (ADS)
Yu, Miao; Wang, Jiasen; Qi, Donglian
2014-11-01
In this paper, we design an adaptive iterative learning control method for a class of high-order nonlinear output feedback discrete-time systems with random initial conditions and iteration-varying desired trajectories. An n-step ahead predictor approach is employed to estimate future outputs. The discrete Nussbaum gain method is incorporated into the control design to deal with unknown control directions. The proposed control algorithm ensures that the tracking error converges to zero asymptotically along the iterative learning axis except for the beginning outputs affected by random initial conditions. A numerical simulation is carried out to demonstrate the efficacy of the presented control laws.
Particle systems and nonlinear Landau damping
Villani, Cédric
2014-03-15
Some works dealing with the long-time behavior of interacting particle systems are reviewed and put into perspective, with focus on the classical Kolmogorov–Arnold–Moser theory and recent results of Landau damping in the nonlinear perturbative regime, obtained in collaboration with Clément Mouhot. Analogies are discussed, as well as new qualitative insights in the theory. Finally, the connection with a more recent work on the inviscid Landau damping near the Couette shear flow, by Bedrossian and Masmoudi, is briefly discussed.
Design of suboptimal regulators for nonlinear systems
NASA Technical Reports Server (NTRS)
Balaram, J.; Saridis, G. N.
1985-01-01
An optimal feedback control law is preferred for the regulation of a deterministic nonlinear system. In this paper, a practical, iterative design method leading to a sequence of suboptimal control laws with successively improved performance is presented. The design method requires the determination of an upper bound to the performance of each successive control law. This is obtained by solving a partial differential inequality by means of a linear programming technique. Robustness properties and the application of the design method to the control of a robot manipulator arm are also presented.
Particle systems and nonlinear Landau dampinga)
NASA Astrophysics Data System (ADS)
Villani, Cédric
2014-03-01
Some works dealing with the long-time behavior of interacting particle systems are reviewed and put into perspective, with focus on the classical Kolmogorov-Arnold-Moser theory and recent results of Landau damping in the nonlinear perturbative regime, obtained in collaboration with Clément Mouhot. Analogies are discussed, as well as new qualitative insights in the theory. Finally, the connection with a more recent work on the inviscid Landau damping near the Couette shear flow, by Bedrossian and Masmoudi, is briefly discussed.
NASA Astrophysics Data System (ADS)
Bryuhanov, Yu. A.
2010-08-01
We consider a method for calculating forced oscillations in nonlinear discrete-time systems under periodic external actions. The method is based on representing the stationary oscillations in the form of an invariant set of nonlinear discrete point mappings and allows one to calculate the nonlinear-system response in the steady-state regime. The examples of using this method for calculating forced oscillations in the first- and second-order nonlinear recursive systems under the harmonic-signal action on such systems are presented.
ERIC Educational Resources Information Center
Strobel, Johannes; Jonassen, David H.; Ionas, Ioan Gelu
2008-01-01
Learning in complex and ill-structured knowledge domains requires accommodation of multiple perspectives embedded in authentic activities and the reconciliation of those perspectives with personal beliefs resulting in conceptual change. Cognitive flexibility hypertext systems support that process by enabling learners to explore authentic cases…
Double nonlinear resonance in ferromagnets and other dynamic systems
NASA Astrophysics Data System (ADS)
Bakai, A. S.
2010-08-01
The phenomenon of double nonlinear resonances in nonlinear oscillators of general type is described. The results are used to describe a double nonlinear ferromagnetic resonance in a uniaxial ferromagnet. The possibility of a similar resonance in the system of brain biocurrents is considered.
Restricted Complexity Framework for Nonlinear Adaptive Control in Complex Systems
Williams, Rube B.
2004-02-04
Control law adaptation that includes implicit or explicit adaptive state estimation, can be a fundamental underpinning for the success of intelligent control in complex systems, particularly during subsystem failures, where vital system states and parameters can be impractical or impossible to measure directly. A practical algorithm is proposed for adaptive state filtering and control in nonlinear dynamic systems when the state equations are unknown or are too complex to model analytically. The state equations and inverse plant model are approximated by using neural networks. A framework for a neural network based nonlinear dynamic inversion control law is proposed, as an extrapolation of prior developed restricted complexity methodology used to formulate the adaptive state filter. Examples of adaptive filter performance are presented for an SSME simulation with high pressure turbine failure to support extrapolations to adaptive control problems.
Restricted Complexity Framework for Nonlinear Adaptive Control in Complex Systems
NASA Astrophysics Data System (ADS)
Williams, Rube B.
2004-02-01
Control law adaptation that includes implicit or explicit adaptive state estimation, can be a fundamental underpinning for the success of intelligent control in complex systems, particularly during subsystem failures, where vital system states and parameters can be impractical or impossible to measure directly. A practical algorithm is proposed for adaptive state filtering and control in nonlinear dynamic systems when the state equations are unknown or are too complex to model analytically. The state equations and inverse plant model are approximated by using neural networks. A framework for a neural network based nonlinear dynamic inversion control law is proposed, as an extrapolation of prior developed restricted complexity methodology used to formulate the adaptive state filter. Examples of adaptive filter performance are presented for an SSME simulation with high pressure turbine failure to support extrapolations to adaptive control problems.
Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems
NASA Technical Reports Server (NTRS)
Banks, H. T.; Reich, Simeon; Rosen, I. G.
1988-01-01
An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems. A set of relatively easily verified conditions is provided which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite dimensional identification problems. The approach is based on the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasilinear elliptic operators along with some applications are presented and discussed.
PVODE and KINSOL: parallel software for differential and nonlinear systems
Hindmarsh, A.C.; Taylor, A.G.
1998-02-01
In this project, parallel general-purpose software for two classes of mathematical problems has been developed. PVODE is a portable solver for ordinary differential equation systems, based on robustmathematical algorithms, and targeted at large systems on parallel machines. It is the parallel extension of the earlier sequential solver CVODE. A related solver called KINSOL has been developed for systems of nonlinear algebraic equations. KINSOL was first developed as a sequential solver, on a design that permitted extending it to a parallel version with fairly minimal additions. Both PVODE and KINSOL are being used within a parallel version of the tokamak edge plasma model UEDGE. KINSOL is also being applied in the ParFlow groundwater flow model to solve a nonlinear pressure equation.
Nonlinear Process Fault Diagnosis Based on Serial Principal Component Analysis.
Deng, Xiaogang; Tian, Xuemin; Chen, Sheng; Harris, Chris J
2016-12-22
Many industrial processes contain both linear and nonlinear parts, and kernel principal component analysis (KPCA), widely used in nonlinear process monitoring, may not offer the most effective means for dealing with these nonlinear processes. This paper proposes a new hybrid linear-nonlinear statistical modeling approach for nonlinear process monitoring by closely integrating linear principal component analysis (PCA) and nonlinear KPCA using a serial model structure, which we refer to as serial PCA (SPCA). Specifically, PCA is first applied to extract PCs as linear features, and to decompose the data into the PC subspace and residual subspace (RS). Then, KPCA is performed in the RS to extract the nonlinear PCs as nonlinear features. Two monitoring statistics are constructed for fault detection, based on both the linear and nonlinear features extracted by the proposed SPCA. To effectively perform fault identification after a fault is detected, an SPCA similarity factor method is built for fault recognition, which fuses both the linear and nonlinear features. Unlike PCA and KPCA, the proposed method takes into account both linear and nonlinear PCs simultaneously, and therefore, it can better exploit the underlying process's structure to enhance fault diagnosis performance. Two case studies involving a simulated nonlinear process and the benchmark Tennessee Eastman process demonstrate that the proposed SPCA approach is more effective than the existing state-of-the-art approach based on KPCA alone, in terms of nonlinear process fault detection and identification.
Nonlinear Behavior in Optical and Other Systems
1987-09-01
numerical analysis). Others will be devoted to ’state of the art ’ discussions of specific problems (e.g. nonlinear waveguides, Anderson localization). It is...Nonlinearity and Statistical Physics. Approximate Cost of Workshop: $5,312. STATE OF THE ART DEVELOPMfENTS IN NONLINEAR OPTICS Organizers: J. Moloney, A... Art Developments in Nonlinear Optics V. List of Preprints and Reprints with Abstracts ANTICIPATED WORKSHOPS 1987 - 1988 I. Workshop on Singularities
A nonlinear regression model-based predictive control algorithm.
Dubay, R; Abu-Ayyad, M; Hernandez, J M
2009-04-01
This paper presents a unique approach for designing a nonlinear regression model-based predictive controller (NRPC) for single-input-single-output (SISO) and multi-input-multi-output (MIMO) processes that are common in industrial applications. The innovation of this strategy is that the controller structure allows nonlinear open-loop modeling to be conducted while closed-loop control is executed every sampling instant. Consequently, the system matrix is regenerated every sampling instant using a continuous function providing a more accurate prediction of the plant. Computer simulations are carried out on nonlinear plants, demonstrating that the new approach is easily implemented and provides tight control. Also, the proposed algorithm is implemented on two real time SISO applications; a DC motor, a plastic injection molding machine and a nonlinear MIMO thermal system comprising three temperature zones to be controlled with interacting effects. The experimental closed-loop responses of the proposed algorithm were compared to a multi-model dynamic matrix controller (MPC) with improved results for various set point trajectories. Good disturbance rejection was attained, resulting in improved tracking of multi-set point profiles in comparison to multi-model MPC.
Passive dynamic controllers for nonlinear mechanical systems
NASA Technical Reports Server (NTRS)
Juang, Jer-Nan; Wu, Shih-Chin; Phan, Minh; Longman, Richard W.
1991-01-01
A methodology for model-independant controller design for controlling large angular motion of multi-body dynamic systems is outlined. The controlled system may consist of rigid and flexible components that undergo large rigid body motion and small elastic deformations. Control forces/torques are applied to drive the system and at the same time suppress the vibration due to flexibility of the components. The proposed controller consists of passive second-order systems which may be designed with little knowledge of the system parameter, even if the controlled system is nonlinear. Under rather general assumptions, the passive design assures that the closed loop system has guaranteed stability properties. Unlike positive real controller design, stabilization can be accomplished without direct velocity feedback. In addition, the second-order passive design allows dynamic feedback controllers with considerable freedom to tune for desired system response, and to avoid actuator saturation. After developing the basic mathematical formulation of the design methodology, simulation results are presented to illustrate the proposed approach to a flexible six-degree-of-freedom manipulator.
Adiabatic elimination in nonlinear dynamical systems
NASA Astrophysics Data System (ADS)
Lugiato, L. A.; Mandel, P.; Narducci, L. M.
1984-03-01
The problem of the adiabatic elimination of selected dynamical variables in the description of nonlinear systems is reconsidered, with emphasis on the identification of suitable criteria for the global validity of this procedure. The problem is analyzed in detail using as a guideline the one-mode homogeneously broadened laser model, with an injected signal and an arbitrary population difference for added flexibility. Five conditions for the global validity of the adiabatic limit are proposed, after consideration not only of the relative size of the time scales involved, but also of the magnitude of all parameters, of the physical variables, and of their fluctuations. From the analysis, it is considered evident that the main conclusions are model independent and not at all restricted to the specific features of the dynamical system selected as a test case.
Nonlinear dynamic analysis of flexible multibody systems
NASA Technical Reports Server (NTRS)
Bauchau, Olivier A.; Kang, Nam Kook
1991-01-01
Two approaches are developed to analyze the dynamic behavior of flexible multibody systems. In the first approach each body is modeled with a modal methodology in a local non-inertial frame of reference, whereas in the second approach, each body is modeled with a finite element methodology in the inertial frame. In both cases, the interaction among the various elastic bodies is represented by constraint equations. The two approaches were compared for accuracy and efficiency: the first approach is preferable when the nonlinearities are not too strong but it becomes cumbersome and expensive to use when many modes must be used. The second approach is more general and easier to implement but could result in high computation costs for a large system. The constraints should be enforced in a time derivative fashion for better accuracy and stability.
Constrained tracking control for nonlinear systems.
Khani, Fatemeh; Haeri, Mohammad
2017-09-01
This paper proposes a tracking control strategy for nonlinear systems without needing a prior knowledge of the reference trajectory. The proposed method consists of a set of local controllers with appropriate overlaps in their stability regions and an on-line switching strategy which implements these controllers and uses some augmented intermediate controllers to ensure steering the system states to the desired set points without needing to redesign the controller for each value of set point changes. The proposed approach provides smooth transient responses despite switching among the local controllers. It should be mentioned that the stability regions of the proposed controllers could be estimated off-line for a range of set-point changes. The efficiencies of the proposed algorithm are illustrated via two example simulations. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Inferring Nonlinear Neuronal Computation Based on Physiologically Plausible Inputs
McFarland, James M.; Cui, Yuwei; Butts, Daniel A.
2013-01-01
The computation represented by a sensory neuron's response to stimuli is constructed from an array of physiological processes both belonging to that neuron and inherited from its inputs. Although many of these physiological processes are known to be nonlinear, linear approximations are commonly used to describe the stimulus selectivity of sensory neurons (i.e., linear receptive fields). Here we present an approach for modeling sensory processing, termed the Nonlinear Input Model (NIM), which is based on the hypothesis that the dominant nonlinearities imposed by physiological mechanisms arise from rectification of a neuron's inputs. Incorporating such ‘upstream nonlinearities’ within the standard linear-nonlinear (LN) cascade modeling structure implicitly allows for the identification of multiple stimulus features driving a neuron's response, which become directly interpretable as either excitatory or inhibitory. Because its form is analogous to an integrate-and-fire neuron receiving excitatory and inhibitory inputs, model fitting can be guided by prior knowledge about the inputs to a given neuron, and elements of the resulting model can often result in specific physiological predictions. Furthermore, by providing an explicit probabilistic model with a relatively simple nonlinear structure, its parameters can be efficiently optimized and appropriately regularized. Parameter estimation is robust and efficient even with large numbers of model components and in the context of high-dimensional stimuli with complex statistical structure (e.g. natural stimuli). We describe detailed methods for estimating the model parameters, and illustrate the advantages of the NIM using a range of example sensory neurons in the visual and auditory systems. We thus present a modeling framework that can capture a broad range of nonlinear response functions while providing physiologically interpretable descriptions of neural computation. PMID:23874185
A constructive approach for nonlinear system identification using multilayer perceptrons.
Choi, J Y; Van Landingham, H F; Bingulac, S
1996-01-01
This paper combines a conventional method of multivariable system identification with a dynamic multi-layer perceptron (MLP) to achieve a constructive method of nonlinear system identification. The class of nonlinear systems is assumed to operate nominally around an equilibrium point in the neighborhood of which a linearized model exists to represent the system, although normal operation is not limited to the linear region. The result is an accurate discrete-time nonlinear model, extended from a MIMO linear model, which captures the nonlinear behavior of the system.
Central suboptimal H ∞ control design for nonlinear polynomial systems
NASA Astrophysics Data System (ADS)
Basin, Michael V.; Shi, Peng; Calderon-Alvarez, Dario
2011-05-01
This article presents the central finite-dimensional H ∞ regulator for nonlinear polynomial systems, which is suboptimal for a given threshold γ with respect to a modified Bolza-Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, the article reduces the original H ∞ control problem to the corresponding optimal H 2 control problem, using this technique proposed in Doyle et al. [Doyle, J.C., Glover, K., Khargonekar, P.P., and Francis, B.A. (1989), 'State-space Solutions to Standard H 2 and H ∞ Control Problems', IEEE Transactions on Automatic Control, 34, 831-847]. This article yields the central suboptimal H ∞ regulator for nonlinear polynomial systems in a closed finite-dimensional form, based on the optimal H 2 regulator obtained in Basin and Calderon-Alvarez [Basin, M.V., and Calderon-Alvarez, D. (2008b), 'Optimal Controller for Uncertain Stochastic Polynomial Systems', Journal of the Franklin Institute, 345, 293-302]. Numerical simulations are conducted to verify performance of the designed central suboptimal regulator for nonlinear polynomial systems against the central suboptimal H ∞ regulator available for the corresponding linearised system.
NASA Astrophysics Data System (ADS)
Zhang, Qian; Wang, Qunjing; Li, Guoli
2016-05-01
This article deals with the identification of nonlinear model and Nonlinear Predictive Functional Controller (NPFC) design based on the Hammerstein structure for the turntable servo system. As a mechanism with multi-mass rotational system, nonlinearities significantly influence the system operation, especially when the turntable is in the states of zero-crossing distortion or rapid acceleration/deceleration, etc. The field data from identification experiments are processed by Comprehensive Learning Particle Swarm Optimization (CLPSO). As a result, Hammerstein model can be derived to describe the input-output relationship globally, considering all the linear and nonlinear factors of the turntable system. Cross validation results demonstrate good correspondence between the real equipment and the identified model. In the second part of this manuscript, a nonlinear control strategy based on the genetic algorithm and predictive control is developed. The global nonlinear predictive controller is carried out by two steps: (i) build the linear predictive functional controller with state space equations for the linear subsystem of Hammerstein model, and (ii) optimize the global control variable by minimizing the cost function through genetic algorithm. On the basis of distinguish model for turntable and the effectiveness of NPFC, the good performance of tracking ability is achieved in the simulation results.
SSNN toolbox for non-linear system identification
NASA Astrophysics Data System (ADS)
Luzar, Marcel; Czajkowski, Andrzej
2015-11-01
The aim of this paper is to develop and design a State Space Neural Network toolbox for a non-linear system identification with an artificial state-space neural networks, which can be used in a model-based robust fault diagnosis and control. Such toolbox is implemented in the MATLAB environment and it uses some of its predefined functions. It is designed in the way that any non-linear multi-input multi-output system is identified and represented in the classical state-space form. The novelty of the proposed approach is that the final result of the identification process is the state, input and output matrices, not only the neural network parameters. Moreover, the toolbox is equipped with the graphical user interface, which makes it useful for the users not familiar with the neural networks theory.
Sparse identification for nonlinear optical communication systems: SINO method.
Sorokina, Mariia; Sygletos, Stylianos; Turitsyn, Sergei
2016-12-26
We introduce low complexity machine learning method method (based on lasso regression, which promotes sparsity, to identify the interaction between symbols in different time slots and to select the minimum number relevant perturbation terms that are employed) for nonlinearity mitigation. The immense intricacy of the problem calls for the development of "smart" methodology, simplifying the analysis without losing the key features that are important for recovery of transmitted data. The proposed sparse identification method for optical systems (SINO) allows to determine the minimal (optimal) number of degrees of freedom required for adaptive mitigation of detrimental nonlinear effects. We demonstrate successful application of the SINO method both for standard fiber communication links (over 3 dB gain) and for few-mode spatial-division-multiplexing systems.
Discrete state space modeling and control of nonlinear unknown systems.
Savran, Aydogan
2013-11-01
A novel procedure for integrating neural networks (NNs) with conventional techniques is proposed to design industrial modeling and control systems for nonlinear unknown systems. In the proposed approach, a new recurrent NN with a special architecture is constructed to obtain discrete-time state-space representations of nonlinear dynamical systems. It is referred as the discrete state-space neural network (DSSNN). In the DSSNN, the outputs of the hidden layer neurons of the DSSNN represent the system's (pseudo) state. The inputs are fed to output neurons and the delayed outputs of the hidden layer neurons are fed to their inputs via adjustable weights. The discrete state space model of the actual system is directly obtained by training the DSSNN with the input-output data. A training procedure based on the back-propagation through time (BPTT) algorithm is developed. The Levenberg-Marquardt (LM) method with a trust region approach is used to update the DSSNN weights. Linear state space models enable to use well developed conventional analysis and design techniques. Thus, building a linear model of a system has primary importance in industrial applications. Thus, a suitable linearization procedure is proposed to derive the linear state space model from the nonlinear DSSNN representation. The controllability, observability and stability properties are examined. The state feedback controllers are designed with both the linear quadratic regulator (LQR) and the pole placement techniques. The regulator and servo control problems are both addressed. A full order observer is also designed to estimate the state variables. The performance of the proposed procedure is demonstrated by applying for both single-input single-output (SISO) and multiple-input multiple-output (MIMO) nonlinear control problems. © 2013 ISA. Published by Elsevier Ltd. All rights reserved.
On state representations of nonlinear implicit systems
NASA Astrophysics Data System (ADS)
Pereira da Silva, Paulo Sergio; Batista, Simone
2010-03-01
This work considers a semi-implicit system Δ, that is, a pair (S, y), where S is an explicit system described by a state representation ? , where x(t) ∈ ℝ n and u(t) ∈ ℝ m , which is subject to a set of algebraic constraints y(t) = h(t, x(t), u(t)) = 0, where y(t) ∈ ℝ l . An input candidate is a set of functions v = (v 1, …, v s ), which may depend on time t, on x, and on u and its derivatives up to a finite order. The problem of finding a (local) proper state representation ż = g(t, z, v) with input v for the implicit system Δ is studied in this article. The main result shows necessary and sufficient conditions for the solution of this problem, under mild assumptions on the class of admissible state representations of Δ. These solvability conditions rely on an integrability test that is computed from the explicit system S. The approach of this article is the infinite-dimensional differential geometric setting of Fliess, Lévine, Martin, and Rouchon (1999) ('A Lie-Bäcklund Approach to Equivalence and Flatness of Nonlinear Systems', IEEE Transactions on Automatic Control, 44(5), (922-937)).
Spatial nonlinearities: Cascading effects in the earth system
Peters, Debra P.C.; Pielke, R.A.; Bestelmeyer, B.T.; Allen, Craig D.; Munson-McGee, S.; Havstad, K. M.
2006-01-01
Nonlinear interactions and feedbacks associated with thresholds through time and across space are common features of biological, physical and materials systems. These spatial nonlinearities generate surprising behavior where dynamics at one scale cannot be easily predicted based on information obtained at finer or broader scales. These cascading effects often result in severe consequences for the environment and human welfare (i.e., catastrophes) that are expected to be particularly important under conditions of changes in climate and land use. In this chapter, we illustrate the usefulness of a general conceptual and mathematical framework for understanding and forecasting spatially nonlinear responses to global change. This framework includes cross-scale interactions, threshold behavior and feedback mechanisms. We focus on spatial nonlinearities produced by fine-scale processes that cascade through time and across space to influence broad spatial extents. Here we describe the spread of catastrophic events in the context of our cross-disciplinary framework using examples from biology (wildfires, desertification, infectious diseases) and engineering (structural failures) and discuss the consequences of applying these ideas to forecasting future dynamics under a changing global environment.
Asymmetric Heat Conduction in Nonlinear Systems
NASA Astrophysics Data System (ADS)
Hu, Bambi
2008-12-01
Heat conduction is an old yet important problem. Since Fourier introduced the law bearing his name two hundred years ago, a first-principle derivation of this law from statistical mechanics is still lacking. Worse still, the validity of this law in low dimensions, and the necessary and sufficient conditions for its validity are still far from clear. In this talk I'll give a review of recent works done on this subject. I'll also report our latest work on asymmetric heat conduction in nonlinear systems. The study of heat condution is not only of theoretical interest but also of practical interest. The study of electric conduction has led to the invention of such important electric devices such as electric diodes and transistors. The study of heat conduction may also lead to the invention of thermal diodes and transistors in the future. Note from Publisher: This article contains the abstract only.
Bifurcations and Patterns in Nonlinear Dissipative Systems
Guenter Ahlers
2005-05-27
This project consists of experimental investigations of heat transport, pattern formation, and bifurcation phenomena in non-linear non-equilibrium fluid-mechanical systems. These issues are studies in Rayleigh-B\\'enard convection, using both pure and multicomponent fluids. They are of fundamental scientific interest, but also play an important role in engineering, materials science, ecology, meteorology, geophysics, and astrophysics. For instance, various forms of convection are important in such diverse phenomena as crystal growth from a melt with or without impurities, energy production in solar ponds, flow in the earth's mantle and outer core, geo-thermal stratifications, and various oceanographic and atmospheric phenomena. Our work utilizes computer-enhanced shadowgraph imaging of flow patterns, sophisticated digital image analysis, and high-resolution heat transport measurements.
High-sensitivity damage detection based on enhanced nonlinear dynamics
NASA Astrophysics Data System (ADS)
Epureanu, Bogdan I.; Yin, Shih-Hsun; Derriso, Mark M.
2004-07-01
One of the most important aspects of detecting damage in the work-frame of structural health monitoring is increasing the sensitivity of the monitored feature to the presence, location, and extent of damage. Distinct from previous techniques of obtaining information about the monitored structure - such as measuring frequency response functions - the approach proposed herein is based on an active interrogation of the system. This interrogation approach allows for the embedding of the monitored system within a larger system by means of a nonlinear feedback excitation. The dynamics of the larger system is then analyzed in state space, and the shape of the attractor of its dynamics is used as a complex geometric feature which is very sensitive to damage. The proposed approach is implemented for monitoring the structural integrity of a panel forced by transverse loads and undergoing limit cycle oscillations and chaos. The nonlinear von Karman plate theory is used to obtain a model for the panel combined with a nonlinear feedback excitation. The presence of damage is modeled as a loss of stiffness in a portion of the plate. The sensitivity of the proposed approach to parametric changes is shown to be an effective tool in detecting damages.
High-sensitivity damage detection based on enhanced nonlinear dynamics
NASA Astrophysics Data System (ADS)
Epureanu, Bogdan I.; Yin, Shih-Hsun; Derriso, Mark M.
2005-04-01
One of the most important aspects of detecting damage in the framework of structural health monitoring is increasing the sensitivity of the monitored feature to the presence, location, and extent of damage. Distinct from previous techniques of obtaining information about the monitored structure—such as measuring frequency response functions—the approach proposed herein is based on an active interrogation of the system. This interrogation approach allows for the embedding of the monitored system within a larger system by means of a nonlinear feedback excitation. The dynamics of the larger system is then analyzed in state space, and the shape of the attractor of its dynamics is used as a complex geometric feature which is very sensitive to damage. The proposed approach is implemented for monitoring the structural integrity of a panel forced by transverse loads and undergoing limit cycle oscillations and chaos. The nonlinear von Karman plate theory is used to obtain a model for the panel combined with a nonlinear feedback excitation. The presence of damage is modeled as loss of stiffness of various levels in a portion of the plate at various locations. The sensitivity of the proposed approach to parametric changes is shown to be an effective tool in detecting damages. An earlier version was presented at the SPIE 11th International Symposium on Smart Structures and Materials.
Nonvolatile Memory Based on Nonlinear Magnetoelectric Effects
NASA Astrophysics Data System (ADS)
Shen, Jianxin; Cong, Junzhuang; Chai, Yisheng; Shang, Dashan; Shen, Shipeng; Zhai, Kun; Tian, Ying; Sun, Young
2016-08-01
The magnetoelectric effects in multiferroics have a great potential in creating next-generation memory devices. We use an alternative concept of nonvolatile memory based, on a type of nonlinear magnetoelectric effects showing a butterfly-shaped hysteresis loop. The principle is to utilize the states of the magnetoelectric coefficient, instead of magnetization, electric polarization, or resistance, to store binary information. Our experiments in a device made of the PMN-PT/Terfenol-D multiferroic heterostructure clearly demonstrate that the sign of the magnetoelectric coefficient can be repeatedly switched between positive and negative by applying electric fields, confirming the feasibility of this principle. This kind of nonvolatile memory has outstanding practical virtues such as simple structure, easy operation in writing and reading, low power, fast speed, and diverse materials available.
Nonlinear system identification with applications to space weather prediction
NASA Astrophysics Data System (ADS)
Palanthandalam-Madapusi, Harish J.
2007-02-01
System identification is the process of constructing empirical mathematical models of dynamcal systems using measured data. Since data represents a key link between mathematical principles and physical processes, system identification is an important research area that can benefit all disciplines. In this dissertation, we develop identification methods for Hammerstein-Wiener models, which are model structures based on the interconnection of linear dynamics and static nonlinearities. These identification methods identify models in state-space form and use known basis functions to represent the unknown nonlinear maps. Next, we use these methods to identify periodically- switching Hammerstein-Wiener models for predicting magnetic-field fluctuation on the surface of the Earth, 30 to 90 minutes into the future. These magnetic- field fluctuations caused by the solar wind (ejections of charged plasma from the surface of the Sun) can damage critical systems aboard satellites and drive currents in power grids that can overwhelm and damage transformers. By predicting magnetic-field fluctuations on the Earth, we obtain advance warning of future disturbances. Furthermore, to predict solar wind conditions 27 days in advance, we use solar wind measurements and image measurements to construct nonlinear time-series models. We propose a class of radial basis functions to represent the nonlinear maps, which have fewer parameters that need to be tuned by the user. Additionally, we develop an identification algorithm that simultaneously identifies the state space matrices of an unknown model and reconstructs the unknown input, using output measurements and known inputs. For this purpose, we formulate the concept of input and state observability, that is, conditions under which both the unknown input and initial state of a known model can be determined from output measurements. We provide necessary and sufficient conditions for input and state observability in discrete-time systems.
Nonlinear Programming for Large, Sparse Systems
1976-08-01
REFERENCES [1] J. Abadie, "Application of the GRG algorithm to optimal control problems," in: J. Abadie, ed., Integer and nonlinear programming (North... Optimization Laboratory Department of Operations DDG OC 13 1976 St an f or d 143qt] : 1University - 0 Stanford California 94305 NONLINEAR PROGRAMVING FOR...characterized by having n-m "nonbasic" variables equal to their upper or lower bound. With nonlinear problems we cannot expect an optimal solution to
NASA Technical Reports Server (NTRS)
Balas, M. J.
1980-01-01
This paper presents a theory of nonlinear state observers for nonlinear and bilinear distributed parameter systems. Convergence results are proved for these observers. Linear feedback control derived from such state observers is applied to the distributed parameter system and conditions are presented for closed-loop stability. The emphasis is on finite dimensional state observers and controllers (which can be implemented with on-line computers) and conditions for their successful operation with infinite dimensional distributed parameter systems.
Nonlinear behavior in small neural systems
NASA Astrophysics Data System (ADS)
Wheeler, Diek Winters
This work addresses the nonlinear behavior of one or two model neurons under the influence of different stimuli, whether they be forms of chaos control or varieties of added noise. This is a step towards the ultimate objective of exploring the notion that a neural system might utilize a mechanism such as a memory-searching chaotic attractor to locate and retrieve stable-memory limit cycles. The biological realism of the Hopfield neuron models is discussed, and the concept of an ``effective'' neuron is introduced. The dynamical effects of adding inertial/inductance terms to an effective-neuron system are presented along with arguments for the biological relevance of such terms. A two neuron system with one or two inertial terms added is shown to exhibit chaos. The chaos is confirmed by Lyapunov exponents, power spectra, and phase-space plots. The effects of multiplicative and additive noise on the dynamics of a two effective-neuron system are investigated. One of the neurons possesses an added inertial term so the system is able to generate chaotic dynamics. The multiplicative noise is added to the connection parameter J 11, and the additive noise is added to the equation for U 2 like an external driving force. Using J11 as a bifurcation parameter, the system is examined as it passes from limit cycle dynamics to chaotic dynamics. Both types of noise are found to lower the bifurcation point with respect to its deterministic value, and both cause the dynamics to expand in phase space. For equivalent levels of noise, additive noise is found to have a stronger effect on the dynamics than multiplicative noise. The bifurcation points are explored by means of ensembles of the largest Lyapunov exponents derived from the stochastic dynamics. A brief overview is presented of the current state of control theory in chaotic systems. One control method, Hübler's [74] technique of using aperiodic forces to drive nonlinear oscillators to resonance, is analyzed. The technique is
An extended harmonic balance method based on incremental nonlinear control parameters
NASA Astrophysics Data System (ADS)
Khodaparast, Hamed Haddad; Madinei, Hadi; Friswell, Michael I.; Adhikari, Sondipon; Coggon, Simon; Cooper, Jonathan E.
2017-02-01
A new formulation for calculating the steady-state responses of multiple-degree-of-freedom (MDOF) non-linear dynamic systems due to harmonic excitation is developed. This is aimed at solving multi-dimensional nonlinear systems using linear equations. Nonlinearity is parameterised by a set of 'non-linear control parameters' such that the dynamic system is effectively linear for zero values of these parameters and nonlinearity increases with increasing values of these parameters. Two sets of linear equations which are formed from a first-order truncated Taylor series expansion are developed. The first set of linear equations provides the summation of sensitivities of linear system responses with respect to non-linear control parameters and the second set are recursive equations that use the previous responses to update the sensitivities. The obtained sensitivities of steady-state responses are then used to calculate the steady state responses of non-linear dynamic systems in an iterative process. The application and verification of the method are illustrated using a non-linear Micro-Electro-Mechanical System (MEMS) subject to a base harmonic excitation. The non-linear control parameters in these examples are the DC voltages that are applied to the electrodes of the MEMS devices.
Noise and nonlinearities in digital magnetic recording systems
NASA Astrophysics Data System (ADS)
Xing, Xinzhi
1998-11-01
Various types of noise and nonlinearities in digital magnetic recording systems are investigated in this dissertation. Measurement techniques and analyzing methods are developed to understand each phenomenon. The nonlinearities due to the replay process using MR sensors are studied in Chapter 4. The nonlinearities are determined by comparing the measured signal with that obtained from a linear analysis. A characterization method of transition noise is developed in Chapter 5. Approximating transition noise by several leading 'modes' allows the noise parameters to be determined experimentally. Chapter 6 covers the investigation of disk substrate texture induced noise. The noise mechanism and characteristics are systematically studied. An analytical noise correlation function that directly relates the noise with the fluctuations of the textured disk surface is also developed in this chapter. An error rate model including colored and nonstationary noise is developed to further understand the impact of noise on system performance in Chapter 7. Noise with different characteristics is shown to influence the system performance differently. In addition, the influence of texture noise is examined in term of each noise parameter based upon the noise model developed in Chapter 6. Finally, in Chapter 8, the effect of finite write field rise time on recording performance is studied. Recording performance predicted by a simplified analytical model is compared with the measurements. It is shown that a slow flux rise time causes a degraded field gradient during writing, which results in a broader written transition, a larger NLTS, and noisier transition boundaries.
Robot arm force control through system linearization by nonlinear feedback
NASA Technical Reports Server (NTRS)
Tarn, T. J.; Bejczy, A. K.; Yun, Xiaoping
1988-01-01
Based on a differential geometric feedback linearization technique for nonlinear time-varying systems, a dynamic force control method for robot arms is developed. It uses active force-moment measurements at the robot wrist. The controller design fully incorporate the robot-arm dynamics and is so general that it can be reduced to pure position control, hybrid position/force control, pure force control. The controller design is independent of the tasks to be performed. Computer simulations show that the controller improves the position error by a factor of ten in cases in which position errors generate force measurements. A theorem on linearization of time-varying system is also presented.
Autonomous navigation system using a fuzzy adaptive nonlinear H∞ filter.
Outamazirt, Fariz; Li, Fu; Yan, Lin; Nemra, Abdelkrim
2014-09-19
Although nonlinear H∞ (NH∞) filters offer good performance without requiring assumptions concerning the characteristics of process and/or measurement noises, they still require additional tuning parameters that remain fixed and that need to be determined through trial and error. To address issues associated with NH∞ filters, a new SINS/GPS sensor fusion scheme known as the Fuzzy Adaptive Nonlinear H∞ (FANH∞) filter is proposed for the Unmanned Aerial Vehicle (UAV) localization problem. Based on a real-time Fuzzy Inference System (FIS), the FANH∞ filter continually adjusts the higher order of the Taylor development thorough adaptive bounds and adaptive disturbance attenuation , which significantly increases the UAV localization performance. The results obtained using the FANH∞ navigation filter are compared to the NH∞ navigation filter results and are validated using a 3D UAV flight scenario. The comparison proves the efficiency and robustness of the UAV localization process using the FANH∞ filter.
Nonlinear dynamic analysis for coupled vehicle-bridge vibration system on nonlinear foundation
NASA Astrophysics Data System (ADS)
Zhou, Shihua; Song, Guiqiu; Wang, Rongpeng; Ren, Zhaohui; Wen, Bangchun
2017-03-01
In this paper, the nonlinear dynamics of a parametrically excited coupled vehicle-bridge vibration system (CVBVS) is investigated, and the coupled system is subjected to a time-dependent transverse load including a constant value together with a harmonic time-variant component. The dynamic equations of the CVBVS are established by using the generalized Lagrange's equation. With the Galerkin truncation method, a set of nonlinear ordinary differential equations are derived by discretizing the continuous governing equation. The influences of parametric excitation with nonlinear support stiffness, mass ratio, excitation amplitude and position relation on the dynamic behaviors are studied for the interaction between vehicle and the bridge. The analysis results indicate that the nonlinear dynamic characteristics are strongly attributed to the interaction of the coupled system. Nonlinear support stiffness of foundation and mass ratio can lead to complex dynamic behaviors such as jump discontinuous phenomenon, periodic, quasi-periodic and chaotic motions. Vibration amplitude increases depending on the position, where the maximum vibration displacement does not occur at the center of the bridge. The excitation amplitude has an obvious influence on the nonlinear dynamic behaviors and the increase of the excitation amplitude makes the vibration strengthen. The bifurcation diagram and 3-D frequency spectrum are used to analyze the complex nonlinear dynamic behaviors of the CVBVS. The presented results can provide an insight to the understanding of the vibration characteristics of the coupled vehicle-bridge vibration system in engineering.
Error-based adaptive non-linear control and regions of feasibility
NASA Technical Reports Server (NTRS)
Teel, Andrew R.
1992-01-01
The nonlinear adaptive algorithm of Kanellakopoulos et al. (1991) was modified to produce an error-based algorithm. This permits global stabilizability for a large subset of pure-feedback nonlinear systems. The algorithm was demonstrated on the single-input stabilization problem, but extends easily to the multiple input tracking problems.
Nonlinear System Of Equations For Multicomponent Analysis Of Artificial Food Coloring
NASA Astrophysics Data System (ADS)
Santosa, I. E.; Budiasih, L. K.
2010-12-01
In multicomponent analysis of artificial food coloring (AFC), nonlinear relation of the absorbance and the concentration forms a nonlinear system of equations. The Newton's method based algorithm has been used to calculate individual AFC concentration in the mixture of two AFCs. The absorbance was measured using a spectrophotometer at two different wavelengths.
NASA Astrophysics Data System (ADS)
Dai, L.; Han, L.
2011-12-01
The multiple-periodicity, nonlinearity and transitional characteristics of nonlinear dynamic systems subjected to external excitations are studied in this research. Diagnoses of the number and changing multiple-periodicities of Duffing's systems are performed with implementation of the Periodicity Ratio (PR). The multiple-periodicity diagram is generated such that the periodicities and nonlinearity of the systems with respect to the system parameters can be graphically studied. The stability and convergence of the systems are investigated. The results of the research show that the number of period of periodicity of the systems increases continuously when certain system parameters increase. Transitional characteristics of the systems are also investigated. Both Lyapunov Exponents and Periodicity Ratio are implemented to diagnose the transitional routes of the systems. New symmetrical transition characters from periodicity to quasi-periodicity and chaos are displayed in terms of PR values. Comparing to Lyapunov Exponents, the Periodicity Ratio discloses more detailed and accurate transition information.
Limit cycle analysis of active disturbance rejection control system with two nonlinearities.
Wu, Dan; Chen, Ken
2014-07-01
Introduction of nonlinearities to active disturbance rejection control algorithm might have high control efficiency in some situations, but makes the systems with complex nonlinearity. Limit cycle is a typical phenomenon that can be observed in the nonlinear systems, usually causing failure or danger of the systems. This paper approaches the problem of the existence of limit cycles of a second-order fast tool servo system using active disturbance rejection control algorithm with two fal nonlinearities. A frequency domain approach is presented by using describing function technique and transfer function representation to characterize the nonlinear system. The derivations of the describing functions for fal nonlinearities and treatment of two nonlinearities connected in series are given to facilitate the limit cycles analysis. The effects of the parameters of both the nonlinearity and the controller on the limit cycles are presented, indicating that the limit cycles caused by the nonlinearities can be easily suppressed if the parameters are chosen carefully. Simulations in the time domain are performed to assess the prediction accuracy based on the describing function.
Vibration analysis of harmonically excited non-linear system using the method of multiple scales
NASA Astrophysics Data System (ADS)
Moon, Byung-Young; Kang, Beom-Soo
2003-05-01
An analytical method is presented for evaluation of the steady state periodic behavior of non-linear systems. This method is based on the substructure synthesis formulation and a multiple scales procedure, which is applied to the analysis of non-linear responses. A complex non-linear system is divided into substructures, of which equations are approximately transformed to modal co-ordinates including non-linear term under the reasonable procedure. Then, the equations are synthesized into the overall system and the solution of the non-linear system can be obtained. Based on the method of multiple scales, the proposed procedure reduces the size of large-degree-of-freedom problem in solving the non-linear equations. Feasibility and advantages of the proposed method are illustrated by the application of the analytic procedure to the non-linear rotating machine system as a large mechanical structure system. Results obtained are reported to be an efficient approach with respect to non-linear response prediction when compared with other conventional methods.
Data-Driven H∞ Control for Nonlinear Distributed Parameter Systems.
Luo, Biao; Huang, Tingwen; Wu, Huai-Ning; Yang, Xiong
2015-11-01
The data-driven H∞ control problem of nonlinear distributed parameter systems is considered in this paper. An off-policy learning method is developed to learn the H∞ control policy from real system data rather than the mathematical model. First, Karhunen-Loève decomposition is used to compute the empirical eigenfunctions, which are then employed to derive a reduced-order model (ROM) of slow subsystem based on the singular perturbation theory. The H∞ control problem is reformulated based on the ROM, which can be transformed to solve the Hamilton-Jacobi-Isaacs (HJI) equation, theoretically. To learn the solution of the HJI equation from real system data, a data-driven off-policy learning approach is proposed based on the simultaneous policy update algorithm and its convergence is proved. For implementation purpose, a neural network (NN)- based action-critic structure is developed, where a critic NN and two action NNs are employed to approximate the value function, control, and disturbance policies, respectively. Subsequently, a least-square NN weight-tuning rule is derived with the method of weighted residuals. Finally, the developed data-driven off-policy learning approach is applied to a nonlinear diffusion-reaction process, and the obtained results demonstrate its effectiveness.
Extending satisficing control strategy to slowly varying nonlinear systems
NASA Astrophysics Data System (ADS)
Binazadeh, T.; Shafiei, M. H.
2013-04-01
Based on the satisficing control strategy, a novel approach to design a stabilizing control law for nonlinear time varying systems with slowly varying parameters (slowly varying systems) is presented. The satisficing control strategy has been originally introduced for time-invariant systems; however, this technique does not have any stability proof for time varying systems. In this paper, first, a parametric version of the satisficing control strategy is developed. Then, by considering the time as a frozen parameter, the parametric satisficing control strategy is utilized. Finally, a theorem is presented which suggested a stabilizing satisficing control law for the slowly varying control systems. Moreover, in this theorem, the maximum admissible rate of change of the system dynamics is evaluated. The efficiency of the proposed approach is demonstrated by a computer simulation.
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.
Nonlinear phase noise in coherent optical OFDM transmission systems.
Zhu, Xianming; Kumar, Shiva
2010-03-29
We derive an analytical formula to estimate the variance of nonlinear phase noise caused by the interaction of amplified spontaneous emission (ASE) noise with fiber nonlinearity such as self-phase modulation (SPM), cross-phase modulation (XPM), and four-wave mixing (FWM) in coherent orthogonal frequency division multiplexing (OFDM) systems. The analytical results agree very well with numerical simulations, enabling the study of the nonlinear penalties in long-haul coherent OFDM systems without extensive numerical simulation. Our results show that the nonlinear phase noise induced by FWM is significantly larger than that induced by SPM and XPM, which is in contrast to traditional WDM systems where ASE-FWM interaction is negligible in quasi-linear systems. We also found that fiber chromatic dispersion can reduce the nonlinear phase noise. The variance of the total phase noise increases linearly with the bit rate, and does not depend significantly on the number of subcarriers for systems with moderate fiber chromatic dispersion.
Develop advanced nonlinear signal analysis topographical mapping system
NASA Technical Reports Server (NTRS)
Jong, Jen-Yi
1993-01-01
The SSME has been undergoing extensive flight certification and developmental testing, which involves some 250 health monitoring measurements. Under the severe temperature pressure, and dynamic environments sustained during operation, numerous major component failures have occurred, resulting in extensive engine hardware damage and scheduling losses. To enhance SSME safety and reliability, detailed analysis and evaluation of the measurements signal are mandatory to assess its dynamic characteristics and operational condition. Efficient and reliable signal detection techniques will reduce catastrophic system failure risks and expedite the evaluation of both flight and ground test data, and thereby reduce launch turn-around time. The basic objective of this contract are threefold: (1) Develop and validate a hierarchy of innovative signal analysis techniques for nonlinear and nonstationary time-frequency analysis. Performance evaluation will be carried out through detailed analysis of extensive SSME static firing and flight data. These techniques will be incorporated into a fully automated system. (2) Develop an advanced nonlinear signal analysis topographical mapping system (ATMS) to generate a Compressed SSME TOPO Data Base (CSTDB). This ATMS system will convert tremendous amounts of complex vibration signals from the entire SSME test history into a bank of succinct image-like patterns while retaining all respective phase information. A high compression ratio can be achieved to allow the minimal storage requirement, while providing fast signature retrieval, pattern comparison, and identification capabilities. (3) Integrate the nonlinear correlation techniques into the CSTDB data base with compatible TOPO input data format. Such integrated ATMS system will provide the large test archives necessary for a quick signature comparison. This study will provide timely assessment of SSME component operational status, identify probable causes of malfunction, and indicate
Develop advanced nonlinear signal analysis topographical mapping system
NASA Technical Reports Server (NTRS)
1994-01-01
The Space Shuttle Main Engine (SSME) has been undergoing extensive flight certification and developmental testing, which involves some 250 health monitoring measurements. Under the severe temperature, pressure, and dynamic environments sustained during operation, numerous major component failures have occurred, resulting in extensive engine hardware damage and scheduling losses. To enhance SSME safety and reliability, detailed analysis and evaluation of the measurements signal are mandatory to assess its dynamic characteristics and operational condition. Efficient and reliable signal detection techniques will reduce catastrophic system failure risks and expedite the evaluation of both flight and ground test data, and thereby reduce launch turn-around time. The basic objective of this contract are threefold: (1) develop and validate a hierarchy of innovative signal analysis techniques for nonlinear and nonstationary time-frequency analysis. Performance evaluation will be carried out through detailed analysis of extensive SSME static firing and flight data. These techniques will be incorporated into a fully automated system; (2) develop an advanced nonlinear signal analysis topographical mapping system (ATMS) to generate a Compressed SSME TOPO Data Base (CSTDB). This ATMS system will convert tremendous amount of complex vibration signals from the entire SSME test history into a bank of succinct image-like patterns while retaining all respective phase information. High compression ratio can be achieved to allow minimal storage requirement, while providing fast signature retrieval, pattern comparison, and identification capabilities; and (3) integrate the nonlinear correlation techniques into the CSTDB data base with compatible TOPO input data format. Such integrated ATMS system will provide the large test archives necessary for quick signature comparison. This study will provide timely assessment of SSME component operational status, identify probable causes of
Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality
NASA Technical Reports Server (NTRS)
Acikmese, Ahmet Behcet; Corless, Martin
2004-01-01
We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.
Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality
NASA Technical Reports Server (NTRS)
Acikmese, Ahmet Behcet; Corless, Martin
2004-01-01
We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.
Dynamics of nonlinear dissipative systems in the vicinity of resonance
NASA Astrophysics Data System (ADS)
Plaksiy, K. Y.; Mikhlin, Y. V.
2015-01-01
The behavior of nonlinear dissipative 2-DOF mechanical systems in the vicinity of resonance is studied in this paper. Namely, the free resonance vibrations of a spring-mass-pendulum system and the forced resonance vibrations of a 2-DOF dissipative system containing a nonlinear absorber are considered. A reduced system stated with respect to the system energy, the arctangent of the vibration amplitudes ratio, and the phase difference, is obtained and analyzed. The nonlinear normal mode approach is used in this analysis. Conditions for vibration energy localization are discussed.
Input-to-state stable nonlinear filtering for a class of continuous-time delayed nonlinear systems
NASA Astrophysics Data System (ADS)
Ahn, Choon Ki
2013-06-01
This paper investigates the input-to-state stable (ISS) nonlinear filtering problem for a class of continuous-time delayed nonlinear systems with external disturbance. A new delay-dependent nonlinear ISS filter is established through available measurements to estimate the states of delayed nonlinear systems, such that the filtering error system is both exponentially and input-to-state stable for any bounded external disturbance. The design of the nonlinear ISS filter for these nonlinear systems is achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed filter.
Reduced Order Models Based on Linear and Nonlinear Aerodynamic Impulse Responses
NASA Technical Reports Server (NTRS)
Silva, Walter A.
1999-01-01
This paper discusses a method for the identification and application of reduced-order models based on linear and nonlinear aerodynamic impulse responses. The Volterra theory of nonlinear systems and an appropriate kernel identification technique are described. Insight into the nature of kernels is provided by applying the method to the nonlinear Riccati equation in a non-aerodynamic application. The method is then applied to a nonlinear aerodynamic model of an RAE 2822 supercritical airfoil undergoing plunge motions using the CFL3D Navier-Stokes flow solver with the Spalart-Allmaras turbulence model. Results demonstrate the computational efficiency of the technique.
Tools for Nonlinear Control Systems Design
NASA Technical Reports Server (NTRS)
Sastry, S. S.
1997-01-01
This is a brief statement of the research progress made on Grant NAG2-243 titled "Tools for Nonlinear Control Systems Design", which ran from 1983 till December 1996. The initial set of PIs on the grant were C. A. Desoer, E. L. Polak and myself (for 1983). From 1984 till 1991 Desoer and I were the Pls and finally I was the sole PI from 1991 till the end of 1996. The project has been an unusually longstanding and extremely fruitful partnership, with many technical exchanges, visits, workshops and new avenues of investigation begun on this grant. There were student visits, long term.visitors on the grant and many interesting joint projects. In this final report I will only give a cursory description of the technical work done on the grant, since there was a tradition of annual progress reports and a proposal for the succeeding year. These progress reports cum proposals are attached as Appendix A to this report. Appendix B consists of papers by me and my students as co-authors sorted chronologically. When there are multiple related versions of a paper, such as a conference version and journal version they are listed together. Appendix C consists of papers by Desoer and his students as well as 'solo' publications by other researchers supported on this grant similarly chronologically sorted.
Quantised consensus of multi-agent systems with nonlinear dynamics
NASA Astrophysics Data System (ADS)
Zhu, Yunru; Zheng, Yuanshi; Wang, Long
2015-08-01
This paper studies the consensus problem of first-order and second-order multi-agent systems with nonlinear dynamics and quantised interactions. Continuous-time and impulsive control inputs are designed for the multi-agent systems on the logarithmic quantised relative state measurements of agents, respectively. By using nonsmooth analysis tools, we get some sufficient conditions for the consensus of multi-agent systems under the continuous-time inputs. Compared with continuous-time control inputs, impulsive distributed control inputs just use the state variables of the systems at discrete-time instances. Based on impulsive control theory, we prove that the multi-agent systems can reach consensus by choosing proper control gains and impulsive intervals. The simulation results are given to verify the effectiveness of the theoretical results.
A System Identification and Change Detection Methodology for Stochastic Nonlinear Dynamic Systems
Yun, Hae-Bum; Masri, Sami F.; Caffrey, John P.
2008-07-08
In this paper a component-level detection methodology for system identification and change detection is discussed. The methodology is based on non-parametric, data-driven, stochastic system identification classifications using statistical pattern recognition techniques. In order to validate the methodology discussed in this paper an experimental study was performed using a complex nonlinear magneto-rheological (MR) damper. The results of this study show that the proposed methodology is very promising to detect interpret changes in critical structural components such as nonlinear springs joints as well as various types of dampers.
Identification of systems containing nonlinear stiffnesses using backbone curves
NASA Astrophysics Data System (ADS)
Londoño, Julián M.; Cooper, Jonathan E.; Neild, Simon A.
2017-02-01
This paper presents a method for the dynamic identification of structures containing discrete nonlinear stiffnesses. The approach requires the structure to be excited at a single resonant frequency, enabling measurements to be made in regimes of large displacements where nonlinearities are more likely to be significant. Measured resonant decay data is used to estimate the system backbone curves. Linear natural frequencies and nonlinear parameters are identified using these backbone curves assuming a form for the nonlinear behaviour. Numerical and experimental examples, inspired by an aerospace industry test case study, are considered to illustrate how the method can be applied. Results from these models demonstrate that the method can successfully deliver nonlinear models able to predict the response of the test structure nonlinear dynamics.
A Survey of Repetitive Control for Nonlinear Systems
NASA Astrophysics Data System (ADS)
Quan, Quan; Cai, Kai-Yuan
2010-10-01
In aerospace engineering and industry, control tasks are often of a periodic nature, while repetitive control is especially suitable for tracking and rejection of periodic exogenous signals. Because of limited research effort on nonlinear systems, we give a survey of repetitive control for nonlinear systems in this paper. First, a brief introduction of repetitive control is presented. Then, after giving a brief overview of repetitive control for linear systems, this paper summarizes design methods and existing problems of repetitive control for nonlinear systems in detail. Lastly, relationships between repetitive control and other control schemes are analyzed to recognize repetitive control from different aspects more insightfully.
System Identification for Nonlinear Control Using Neural Networks
NASA Technical Reports Server (NTRS)
Stengel, Robert F.; Linse, Dennis J.
1990-01-01
An approach to incorporating artificial neural networks in nonlinear, adaptive control systems is described. The controller contains three principal elements: a nonlinear inverse dynamic control law whose coefficients depend on a comprehensive model of the plant, a neural network that models system dynamics, and a state estimator whose outputs drive the control law and train the neural network. Attention is focused on the system identification task, which combines an extended Kalman filter with generalized spline function approximation. Continual learning is possible during normal operation, without taking the system off line for specialized training. Nonlinear inverse dynamic control requires smooth derivatives as well as function estimates, imposing stringent goals on the approximating technique.
Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems
NASA Astrophysics Data System (ADS)
Tryoen, J.; Le Maître, O.; Ndjinga, M.; Ern, A.
2010-09-01
This paper deals with stochastic spectral methods for uncertainty propagation and quantification in nonlinear hyperbolic systems of conservation laws. We consider problems with parametric uncertainty in initial conditions and model coefficients, whose solutions exhibit discontinuities in the spatial as well as in the stochastic variables. The stochastic spectral method relies on multi-resolution schemes where the stochastic domain is discretized using tensor-product stochastic elements supporting local polynomial bases. A Galerkin projection is used to derive a system of deterministic equations for the stochastic modes of the solution. Hyperbolicity of the resulting Galerkin system is analyzed. A finite volume scheme with a Roe-type solver is used for discretization of the spatial and time variables. An original technique is introduced for the fast evaluation of approximate upwind matrices, which is particularly well adapted to local polynomial bases. Efficiency and robustness of the overall method are assessed on the Burgers and Euler equations with shocks.
Subspace-based identification of a nonlinear spacecraft in the time and frequency domains
NASA Astrophysics Data System (ADS)
Noël, J. P.; Marchesiello, S.; Kerschen, G.
2014-02-01
The objective of the present paper is to address the identification of a strongly nonlinear satellite structure. To this end, two nonlinear subspace identification methods formulated in the time and frequency domains are exploited, referred to as the TNSI and FNSI methods, respectively. The modal parameters of the underlying linear structure and the coefficients of the nonlinearities will be estimated by these two approaches based on periodic random measurements. Their respective merits will also be discussed in terms of both accuracy and computational efficiency and the use of stabilisation diagrams in nonlinear system identification will be introduced. The application of interest is the SmallSat spacecraft developed by EADS-Astrium, which possesses an impact-type nonlinear device consisting of eight mechanical stops limiting the motion of an inertia wheel mounted on an elastomeric interface. This application is challenging for several reasons including the non-smooth nature of the nonlinearities, high modal density and high non-proportional damping.
Asymptotic Stability of Interconnected Passive Non-Linear Systems
NASA Technical Reports Server (NTRS)
Isidori, A.; Joshi, S. M.; Kelkar, A. G.
1999-01-01
This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.
An Entropy-Based Approach to Nonlinear Stability
NASA Technical Reports Server (NTRS)
Merriam, Marshal L.
1989-01-01
Many numerical methods used in computational fluid dynamics (CFD) incorporate an artificial dissipation term to suppress spurious oscillations and control nonlinear instabilities. The same effect can be accomplished by using upwind techniques, sometimes augmented with limiters to form Total Variation Diminishing (TVD) schemes. An analysis based on numerical satisfaction of the second law of thermodynamics allows many such methods to be compared and improved upon. A nonlinear stability proof is given for discrete scalar equations arising from a conservation law. Solutions to such equations are bounded in the L sub 2 norm if the second law of thermodynamics is satisfied in a global sense over a periodic domain. It is conjectured that an analogous statement is true for discrete equations arising from systems of conservation laws. Analysis and numerical experiments suggest that a more restrictive condition, a positive entropy production rate in each cell, is sufficient to exclude unphysical phenomena such as oscillations and expansion shocks. Construction of schemes which satisfy this condition is demonstrated for linear and nonlinear wave equations and for the one-dimensional Euler equations.
High-throughput vibrational cytometry based on nonlinear Raman microspectroscopy
NASA Astrophysics Data System (ADS)
Arora, R.; Petrov, G. I.; Yakovlev, V. V.
2010-02-01
Flow cytometry is a technology that allows a single cell or particle to be measured for a variety of characteristics, determined by looking at their properties while they flow in a liquid stream. High speed of flow and huge number of objects to be analyzed imposed some strict criteria on which methods can be used for analysis. All the known commercial instruments are currently using light scattering for particle sizing and fluorescence detection for chemical recognition. However, vibrational spectroscopy is the only non-invasive optical spectroscopy tool, which has proven to provide chemically-specific information about the interrogated sample. It is proposed that vibrational spectroscopy, based on nonlinear Raman scattering can be used to serve as an analytical tool for cytometry by providing rapid and accurate chemical recognition of flowing materials. To achieve a desired speed (>10,000 cell/particles per second), we have substantially upgraded our previous system for nonlinear Raman microspectroscopy. By increasing the size of the excitation volume to the size of a cell and by keeping the incident intensity at the same level, a dramatic increase of the nonlinear Raman signal is achieved. This allows high-quality vibrational spectra to be acquired within 10-100 microsecond from a single yeast cell without any observable damage to the irradiated cell. This is four orders of magnitude better than any previous attempts involving Raman microspectroscopy.
Optimal spatiotemporal reduced order modeling for nonlinear dynamical systems
NASA Astrophysics Data System (ADS)
LaBryer, Allen
Proposed in this dissertation is a novel reduced order modeling (ROM) framework called optimal spatiotemporal reduced order modeling (OPSTROM) for nonlinear dynamical systems. The OPSTROM approach is a data-driven methodology for the synthesis of multiscale reduced order models (ROMs) which can be used to enhance the efficiency and reliability of under-resolved simulations for nonlinear dynamical systems. In the context of nonlinear continuum dynamics, the OPSTROM approach relies on the concept of embedding subgrid-scale models into the governing equations in order to account for the effects due to unresolved spatial and temporal scales. Traditional ROMs neglect these effects, whereas most other multiscale ROMs account for these effects in ways that are inconsistent with the underlying spatiotemporal statistical structure of the nonlinear dynamical system. The OPSTROM framework presented in this dissertation begins with a general system of partial differential equations, which are modified for an under-resolved simulation in space and time with an arbitrary discretization scheme. Basic filtering concepts are used to demonstrate the manner in which residual terms, representing subgrid-scale dynamics, arise with a coarse computational grid. Models for these residual terms are then developed by accounting for the underlying spatiotemporal statistical structure in a consistent manner. These subgrid-scale models are designed to provide closure by accounting for the dynamic interactions between spatiotemporal macroscales and microscales which are otherwise neglected in a ROM. For a given resolution, the predictions obtained with the modified system of equations are optimal (in a mean-square sense) as the subgrid-scale models are based upon principles of mean-square error minimization, conditional expectations and stochastic estimation. Methods are suggested for efficient model construction, appraisal, error measure, and implementation with a couple of well-known time
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.
Possibility of measuring weak noise in nonlinear systems
NASA Astrophysics Data System (ADS)
Surovyatkina, Elena D.
2004-05-01
The possibility of measuring weak noise in nonlinear systems on the basis of the phenomenon of prebifurcation noise amplification is proposed. This phenomenon is shortly outlined with special emphasis on the transition from linear regime to the regime of nonlinear saturation of fluctuation amplification. Estimates of the fluctuation variance are obtained both for the linear (away from the bifurcation threshold) and for the nonlinear regime (in the vicinity of the bifurcation threshold). These estimates have proved to be efficient for two simple bifurcation models: period doubling bifurcation and bifurcation of spontaneous symmetry breaking. Theoretical estimates have proved to be in good agreement with the results of numerical simulation. It is shown, that in the saturation regime, fluctuation variance is proportional to the square root of external noise variance, whereas in linear regime, fluctuation variance is proportional to noise variance. The approach to weak noise measuring is based on comparison of maximal fluctuation variance at the bifurcation threshold with variance away from that threshold. The applicability of this approach is limited by the necessity to perform rather long-term observations.
Optical limiter based on two-dimensional nonlinear photonic crystals
NASA Astrophysics Data System (ADS)
Belabbas, Amirouche; Lazoul, Mohamed
2016-04-01
The aim behind this work is to investigate the capabilities of nonlinear photonic crystals to achieve ultra-fast optical limiters based on third order nonlinear effects. The purpose is to combine the actions of nonlinear effects with the properties of photonic crystals in order to activate the photonic band according to the magnitude of the nonlinear effects, themselves a function of incident laser power. We are interested in designing an optical limiter based nonlinear photonic crystal operating around 1064 nm and its second harmonic at 532 nm. Indeed, a very powerful solid-state laser that can blind or destroy optical sensors and is widely available and easy to handle. In this work, we perform design and optimization by numerical simulations to determine the better structure for the nonlinear photonic crystal to achieve compact and efficient integrated optical limiter. The approach consists to analyze the band structures in Kerr-nonlinear two-dimensional photonic crystals as a function of the optical intensity. We confirm that these bands are dynamically red-shifted with regard to the bands observed in linear photonic crystals or in the case of weak nonlinear effects. The implemented approach will help to understand such phenomena as intensitydriven optical limiting with Kerr-nonlinear photonic crystals.
On the benefit of DMT modulation in nonlinear VLC systems.
Qian, Hua; Cai, Sunzeng; Yao, Saijie; Zhou, Ting; Yang, Yang; Wang, Xudong
2015-02-09
In a visible light communication (VLC) system, the nonlinear characteristic of the light emitting diode (LED) in transmitter is a limiting factor of system performance. Modern modulation signals with large peak-to-power-ratio (PAPR) suffers uneven distortion. The nonlinear response directly impacts the intensity modulation and direct detection VLC system with pulse-amplitude modulation (PAM). The amplitude of the PAM signal is distorted unevenly and large signal is vulnerable to noise. Orthogonal linear transformations, such as discrete multi-tone (DMT) modulation, can spread the nonlinear effects evenly to each data symbol, thus perform better than PAM signals. In this paper, we provide theoretical analysis on the benefit of DMT modulation in nonlinear VLC system. We show that the DMT modulation is a better choice than the PAM modulation for the VLC system as the DMT modulation is more robust against nonlinearity. We also show that the post-distortion nonlinear elimination method, which is applied at the receiver, can be a reliable solution to the nonlinear VLC system. Simulation results show that the post-distortion greatly improves the system performance for the DMT modulation.
Linear theory for filtering nonlinear multiscale systems with model error
Berry, Tyrus; Harlim, John
2014-01-01
In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online, as part of a filtering procedure
NASA Astrophysics Data System (ADS)
Wang, C. Y.; Jiao, X. H.
2015-10-01
This paper is devoted to discuss arbitrarily switching control problem for a class of nonlinearly parameterised nonlinear switched systems. Compared with the existing results, improvements are that a systematic procedure is given for an explicit construction of a common smooth adaptive controller independent of the switching signals. Meanwhile, the developed design method can be extended to the adaptive arbitrarily switching stabilisation problem for a class of cascade switched nonlinear systems. The theoretical analysis is presented for the Lyapunov stability of the resulting closed-loop switched system and the convergence of the original switched system states at the equilibrium under arbitrary switching. Moreover, the effectiveness and feasibility of the developed method are demonstrated by both a numerical example and a chemical system.
Microwave Oscillators Based on Nonlinear WGM Resonators
NASA Technical Reports Server (NTRS)
Maleki, Lute; Matsko, Andrey; Savchenkov, Anatoliy; Strekalov, Dmitry
2006-01-01
Optical oscillators that exploit resonantly enhanced four-wave mixing in nonlinear whispering-gallery-mode (WGM) resonators are under investigation for potential utility as low-power, ultra-miniature sources of stable, spectrally pure microwave signals. There are numerous potential uses for such oscillators in radar systems, communication systems, and scientific instrumentation. The resonator in an oscillator of this type is made of a crystalline material that exhibits cubic Kerr nonlinearity, which supports the four-photon parametric process also known as four-wave mixing. The oscillator can be characterized as all-optical in the sense that the entire process of generation of the microwave signal takes place within the WGM resonator. The resonantly enhanced four-wave mixing yields coherent, phase-modulated optical signals at frequencies governed by the resonator structure. The frequency of the phase-modulation signal, which is in the microwave range, equals the difference between the frequencies of the optical signals; hence, this frequency is also governed by the resonator structure. Hence, further, the microwave signal is stable and can be used as a reference signal. The figure schematically depicts the apparatus used in a proof-of-principle experiment. Linearly polarized pump light was generated by an yttrium aluminum garnet laser at a wavelength of 1.32 microns. By use of a 90:10 fiber-optic splitter and optical fibers, some of the laser light was sent into a delay line and some was transmitted to one face of glass coupling prism, that, in turn, coupled the laser light into a crystalline CaF2 WGM disk resonator that had a resonance quality factor (Q) of 6x10(exp 9). The output light of the resonator was collected via another face of the coupling prism and a single-mode optical fiber, which transmitted the light to a 50:50 fiber-optic splitter. One output of this splitter was sent to a slow photodiode to obtain a DC signal for locking the laser to a particular
A Quasi-ARX Neural Network with Switching Mechanism to Adaptive Control of Nonlinear Systems
NASA Astrophysics Data System (ADS)
Wang, Lan; Cheng, Yu; Hu, Jinglu
This paper introduces an improved quasi-ARX neural network and discusses its application to adaptive control of nonlinear systems. A switching mechanism is employed to improve the performance of the quasi-ARX neural network prediction model which has linear and nonlinear parts. An adaptive controller for a nonlinear system is established based on the proposed prediction model and some stability analysis of the control system is shown. Simulations are given to show the effectiveness of the proposed method both on stability and accuracy.
NASA Astrophysics Data System (ADS)
Zhai, Jun-Yong
2014-03-01
This article addresses the problem of global finite-time output feedback stabilisation for a class of nonlinear systems in nontriangular form with an unknown output function. Since the output function is not precisely known, traditional observers based on the output is not implementable. We first design a state observer and use the observer states to construct a controller to globally stabilise the nominal system without the perturbing nonlinearities. Then, we apply the homogeneous domination approach to design a scaled homogeneous observer and controller with an appropriate choice of gain to render the nonlinear system globally finite-time stable.
Stability Analysis and Stabilization of Nonlinear Systems via Locally Defined Density Functions
NASA Astrophysics Data System (ADS)
Masubuchi, Izumi
This paper considers local stability analysis of nonlinear systems with deriving a positively invariant set based on the Rantzer's stability theory by using density functions. We define a notion of locally defined density functions around an equilibrium that give monotonously increasing positive measures near the equilibrium of a nonlinear system. Under certain assumptions, it is shown that some level set of a locally defined density function is a positively invariant set where almost all of the system trajectories converge to the equilibrium. We also mention an SOS (sum-of-squares) formulation for synthesis of a nonlinear gain via locally defined density functions.
Semi-global decentralised output feedback stabilisation for a class of uncertain nonlinear systems
NASA Astrophysics Data System (ADS)
Zhai, Jun-yong; Zha, Wen-ting; Fei, Shu-min
2013-06-01
This paper discusses the problem of semi-global decentralised output feedback control for a class of uncertain nonlinear systems. Based on the ideas of the homogeneous systems theory and the adding a power integrator technique, we first design a homogeneous observer and an output feedback control law for each nominal subsystem without the nonlinearities. Then, using the homogeneous domination approach, we relax the linear growth condition to a polynomial one and construct decentralised stabilisers to render the nonlinear system semi-globally asymptotically stable. Two simulation examples are provided to show the effectiveness of the control scheme.
Analysis and design of robust decentralized controllers for nonlinear systems
Schoenwald, D.A.
1993-07-01
Decentralized control strategies for nonlinear systems are achieved via feedback linearization techniques. New results on optimization and parameter robustness of non-linear systems are also developed. In addition, parametric uncertainty in large-scale systems is handled by sensitivity analysis and optimal control methods in a completely decentralized framework. This idea is applied to alleviate uncertainty in friction parameters for the gimbal joints on Space Station Freedom. As an example of decentralized nonlinear control, singular perturbation methods and distributed vibration damping are merged into a control strategy for a two-link flexible manipulator.
Control design for a class of nonlinear parameter varying systems
NASA Astrophysics Data System (ADS)
Cai, Xiushan; Liu, Yang; Zhang, Wei
2015-07-01
Stabilisation for a class of one-sided Lipschitz nonlinear parameter varying systems is dealt with in this paper. First, the nonlinear parameter varying system is represented as a subsystem of a differential inclusion. Sufficient conditions for exponential stabilisation for the differential inclusion are given by solving linear matrix inequalities. Then a continuous control law is designed to stabilise the differential inclusion. It leads to stabilising the nonlinear parameter varying system. Finally, a simulation example is presented to show the validity and advantages of the proposed method.
NASA Astrophysics Data System (ADS)
Enokida, Ryuta; Takewaki, Izuru; Stoten, David
2014-12-01
The problem of control system design can be conceptualised as identifying an input signal to a plant (the system to be controlled) so that the corresponding output matches that of a pre-defined reference signal. Primarily, this problem is solved via well-known techniques based upon the principle of feedback design, an essential component for ensuring stability and robustness of the controlled system. However, feedforward design techniques also have a large part to play, whereby (in the absence of feedback control and assuming that the plant is stable) a model of the plant dynamics can be used to modify the reference signal so that the resultant feedforward input signal generates a plant output signal that is sufficiently close to the original reference signal. The principal objective of this paper is to introduce a new nonlinear control method, called nonlinear signal-based control (NSBC) that can be executed as an on-line technique of feedforward compensation (used synonymously here with the phrase 'input identification') and an off-line technique of feedback compensation. NSBC determines the feedforward input signal to the plant by using an error signal, determined from the difference between the output signals from a linear model of the plant and from the nonlinear plant, under the same input signal. The efficacy of NSBC is examined via numerical examples using Matlab/Simulink and compared with alternative well-known methods based upon inverse transfer function compensation and also the method of high gain feedback control. NSBC was found to provide the most accurate input identification in all the examined cases of linear or nonlinear single-input, single-output and single-input, multi-output (SIMO) systems. Furthermore, in problems of structural and earthquake engineering, NSBC was also found to be particularly effective in estimating the original ground motion from a nonlinear SIMO system and its response.
NASA Astrophysics Data System (ADS)
Wang, Zuo-Cai; Xin, Yu; Ren, Wei-Xin
2016-08-01
This paper proposes a new nonlinear joint model updating method for shear type structures based on the instantaneous characteristics of the decomposed structural dynamic responses. To obtain an accurate representation of a nonlinear system's dynamics, the nonlinear joint model is described as the nonlinear spring element with bilinear stiffness. The instantaneous frequencies and amplitudes of the decomposed mono-component are first extracted by the analytical mode decomposition (AMD) method. Then, an objective function based on the residuals of the instantaneous frequencies and amplitudes between the experimental structure and the nonlinear model is created for the nonlinear joint model updating. The optimal values of the nonlinear joint model parameters are obtained by minimizing the objective function using the simulated annealing global optimization method. To validate the effectiveness of the proposed method, a single-story shear type structure subjected to earthquake and harmonic excitations is simulated as a numerical example. Then, a beam structure with multiple local nonlinear elements subjected to earthquake excitation is also simulated. The nonlinear beam structure is updated based on the global and local model using the proposed method. The results show that the proposed local nonlinear model updating method is more effective for structures with multiple local nonlinear elements. Finally, the proposed method is verified by the shake table test of a real high voltage switch structure. The accuracy of the proposed method is quantified both in numerical and experimental applications using the defined error indices. Both the numerical and experimental results have shown that the proposed method can effectively update the nonlinear joint model.
NASA Astrophysics Data System (ADS)
Long, Lijun; Zhao, Jun
2013-03-01
This article investigates the problem of global stabilisation for a class of switched nonlinear systems with unknown control coefficients by output feedback. Full state measurements are unavailable. We first show that via a coordinate transformation, the unknown control coefficients are lumped together and the original switched nonlinear system is transformed into a new switched nonlinear system for which control design becomes feasible. Second, for the new switched nonlinear system, based on backstepping, we design output-feedback controllers for subsystems and construct a common Lyapunov function, which rely on the designed state observer, to guarantee asymptotic stability of the closed-loop system under arbitrary switchings. Finally, as an application of the proposed design method, global stabilisation of a mass-spring-damper system is achieved by output feedback.
Computational studies of nonlinear dispersive plasma systems
NASA Astrophysics Data System (ADS)
Qian, Xin
Plasma systems with dispersive waves are ubiquitous. Dispersive waves have the property that their wave velocity depends on the wave number of the wave. These waves show up in weakly as well as strongly coupled plasmas, and play a significant role in the underlying plasma dynamics. Dispersive waves bring new challenges to the computer simulation of nonlinear phenomena. The goal of this thesis is to discuss two computational studies of plasma phenomena, one drawn from strongly coupled complex or dusty plasmas, and the other from weakly coupled hydrogen plasmas. In the realm of dusty plasmas, we focus on the problem of three-dimensional (3D) Mach cones which we study by means of Molecular Dynamics (MD) simulations, assuming that the dust particles interact via a Yukawa potential. While laboratory and MD simulations have explored thoroughly the properties of Mach cones in 2D, elucidating the important role of dispersive waves in the formation of multiple cones, the simulations presented in this thesis represent the first 3D MD studies of Mach cones in strongly coupled dusty plasmas. These results have qualitative similarities with experimental observations on 3D Mach cones from the PK-3 plus project, which studies complex plasmas under microgravity conditions aboard the International Space station. In the realm of weakly coupled plasmas, we present results on the application of non-oscillatory central schemes to Hall MHD reconnection problems, in which the presence of dispersive whistler waves presents a formidable challenge for numerical algorithms that rely on explicit time-stepping schemes. In particular, we focus on the semi-discrete central formulation of Kurganov and Tadmor (2000), which has the advantage that it allow for larger time steps, and with significantly smaller numerical viscosity, than fully discrete schemes. We implement the Hall MHD equations through the CentPACK software package that implements the Kurganov-Tadmor formulation for a wide range of
NASA Astrophysics Data System (ADS)
Errouissi, Rachid; Yang, Jun; Chen, Wen-Hua; Al-Durra, Ahmed
2016-08-01
In this paper, a robust nonlinear generalised predictive control (GPC) method is proposed by combining an integral sliding mode approach. The composite controller can guarantee zero steady-state error for a class of uncertain nonlinear systems in the presence of both matched and unmatched disturbances. Indeed, it is well known that the traditional GPC based on Taylor series expansion cannot completely reject unknown disturbance and achieve offset-free tracking performance. To deal with this problem, the existing approaches are enhanced by avoiding the use of the disturbance observer and modifying the gain function of the nonlinear integral sliding surface. This modified strategy appears to be more capable of achieving both the disturbance rejection and the nominal prescribed specifications for matched disturbance. Simulation results demonstrate the effectiveness of the proposed approach.
Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems
Rodriguez-Fernandez, Maria; Egea, Jose A; Banga, Julio R
2006-01-01
Background We consider the problem of parameter estimation (model calibration) in nonlinear dynamic models of biological systems. Due to the frequent ill-conditioning and multi-modality of many of these problems, traditional local methods usually fail (unless initialized with very good guesses of the parameter vector). In order to surmount these difficulties, global optimization (GO) methods have been suggested as robust alternatives. Currently, deterministic GO methods can not solve problems of realistic size within this class in reasonable computation times. In contrast, certain types of stochastic GO methods have shown promising results, although the computational cost remains large. Rodriguez-Fernandez and coworkers have presented hybrid stochastic-deterministic GO methods which could reduce computation time by one order of magnitude while guaranteeing robustness. Our goal here was to further reduce the computational effort without loosing robustness. Results We have developed a new procedure based on the scatter search methodology for nonlinear optimization of dynamic models of arbitrary (or even unknown) structure (i.e. black-box models). In this contribution, we describe and apply this novel metaheuristic, inspired by recent developments in the field of operations research, to a set of complex identification problems and we make a critical comparison with respect to the previous (above mentioned) successful methods. Conclusion Robust and efficient methods for parameter estimation are of key importance in systems biology and related areas. The new metaheuristic presented in this paper aims to ensure the proper solution of these problems by adopting a global optimization approach, while keeping the computational effort under reasonable values. This new metaheuristic was applied to a set of three challenging parameter estimation problems of nonlinear dynamic biological systems, outperforming very significantly all the methods previously used for these benchmark
Nonlinear mechanics of graphene membranes and related systems
NASA Astrophysics Data System (ADS)
De Alba, Roberto
Micro- and nano-mechanical resonators with low mass and high vibrational frequency are often studied for applications in mass and force detection where they can offer unparalleled precision. They are also excellent systems with which to study nonlinear phenomena and fundamental physics due to the numerous routes through which they can couple to each other or to external systems. In this work we study the structural, thermal, and nonlinear properties of various micro-mechanical systems. First, we present a study of graphene-coated silicon nitride membranes; the resulting devices demonstrate the high quality factors of silicon nitride as well as the useful electrical and optical properties of graphene. We then study nonlinear mechanics in pure graphene membranes, where all vibrational eigenmodes are coupled to one another through the membrane tension. This effect enables coherent energy transfer from one mechanical mode to another, in effect creating a graphene mechanics-based frequency mixer. In another experiment, we measure the resonant frequency of a graphene membrane over a wide temperature range, 80K - 550K, to determine whether or not it demonstrates the negative thermal expansion coefficient predicted by prevailing theories; our results indicate that this coefficient is positive at low temperatures - possibly due to polymer contaminants on the graphene surface - and negative above room temperature. Lastly, we study optically-induced self-oscillation in metal-coated silicon nitride nanowires. These structures exhibit self-oscillation at extremely low laser powers ( 1muW incident on the nanowire), and we use this photo-thermal effect to counteract the viscous air-damping that normally inhibits micro-mechanical motion.
A new nonlinear model for analyzing the behaviour of carbon nanotube-based resonators
NASA Astrophysics Data System (ADS)
Farokhi, Hamed; Païdoussis, Michael P.; Misra, Arun K.
2016-09-01
The present study develops a new size-dependent nonlinear model for the analysis of the behaviour of carbon nanotube-based resonators. In particular, based on modified couple stress theory, the fully nonlinear equations of motion of the carbon nanotube-based resonator are derived using Hamilton's principle, taking into account both the longitudinal and transverse displacements. Molecular dynamics simulation is then performed in order to verify the validity of the developed size-dependent continuum model at the nano scale. The nonlinear partial differential equations of motion of the system are discretized by means of the Galerkin technique, resulting in a high-dimensional reduced-order model of the system. The pseudo-arclength continuation technique is employed to examine the nonlinear resonant behaviour of the carbon nanotube-based resonator. A new universal pull-in formula is also developed for predicting the occurrence of the static pull-in and validated using numerical simulations.
Fuzzy fractional order sliding mode controller for nonlinear systems
NASA Astrophysics Data System (ADS)
Delavari, H.; Ghaderi, R.; Ranjbar, A.; Momani, S.
2010-04-01
In this paper, an intelligent robust fractional surface sliding mode control for a nonlinear system is studied. At first a sliding PD surface is designed and then, a fractional form of these networks PDα, is proposed. Fast reaching velocity into the switching hyperplane in the hitting phase and little chattering phenomena in the sliding phase is desired. To reduce the chattering phenomenon in sliding mode control (SMC), a fuzzy logic controller is used to replace the discontinuity in the signum function at the reaching phase in the sliding mode control. For the problem of determining and optimizing the parameters of fuzzy sliding mode controller (FSMC), genetic algorithm (GA) is used. Finally, the performance and the significance of the controlled system two case studies (robot manipulator and coupled tanks) are investigated under variation in system parameters and also in presence of an external disturbance. The simulation results signify performance of genetic-based fuzzy fractional sliding mode controller.
Phenomenological modeling of nonlinear holograms based on metallic geometric metasurfaces.
Ye, Weimin; Li, Xin; Liu, Juan; Zhang, Shuang
2016-10-31
Benefiting from efficient local phase and amplitude control at the subwavelength scale, metasurfaces offer a new platform for computer generated holography with high spatial resolution. Three-dimensional and high efficient holograms have been realized by metasurfaces constituted by subwavelength meta-atoms with spatially varying geometries or orientations. Metasurfaces have been recently extended to the nonlinear optical regime to generate holographic images in harmonic generation waves. Thus far, there has been no vector field simulation of nonlinear metasurface holograms because of the tremendous computational challenge in numerically calculating the collective nonlinear responses of the large number of different subwavelength meta-atoms in a hologram. Here, we propose a general phenomenological method to model nonlinear metasurface holograms based on the assumption that every meta-atom could be described by a localized nonlinear polarizability tensor. Applied to geometric nonlinear metasurfaces, we numerically model the holographic images formed by the second-harmonic waves of different spins. We show that, in contrast to the metasurface holograms operating in the linear optical regime, the wavelength of incident fundamental light should be slightly detuned from the fundamental resonant wavelength to optimize the efficiency and quality of nonlinear holographic images. The proposed modeling provides a general method to simulate nonlinear optical devices based on metallic metasurfaces.
Correlation techniques to determine model form in robust nonlinear system realization/identification
NASA Technical Reports Server (NTRS)
Stry, Greselda I.; Mook, D. Joseph
1991-01-01
The fundamental challenge in identification of nonlinear dynamic systems is determining the appropriate form of the model. A robust technique is presented which essentially eliminates this problem for many applications. The technique is based on the Minimum Model Error (MME) optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature is the ability to identify nonlinear dynamic systems without prior assumption regarding the form of the nonlinearities, in contrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. Model form is determined via statistical correlation of the MME optimal state estimates with the MME optimal model error estimates. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length.
Control synthesis of continuous-time T-S fuzzy systems with local nonlinear models.
Dong, Jiuxiang; Wang, Youyi; Yang, Guang-Hong
2009-10-01
This paper is concerned with the problem of designing fuzzy controllers for a class of nonlinear dynamic systems. The considered nonlinear systems are described by T-S fuzzy models with nonlinear local models, and the fuzzy models have fewer fuzzy rules than conventional T-S fuzzy models with local linear models. A new fuzzy control scheme with local nonlinear feedbacks is proposed, and the corresponding control synthesis conditions are given in terms of solutions to a set of linear matrix inequalities (LMIs). In contrast to the existing methods for fuzzy control synthesis, the new proposed control design method is based on fewer fuzzy rules and less computational burden. Moreover, the local nonlinear feedback laws in the new fuzzy controllers are also helpful in achieving good control effects. Numerical examples are given to illustrate the effectiveness of the proposed method.
Input Forces Estimation for Nonlinear Systems by Applying a Square-Root Cubature Kalman Filter.
Song, Xuegang; Zhang, Yuexin; Liang, Dakai
2017-10-10
This work presents a novel inverse algorithm to estimate time-varying input forces in nonlinear beam systems. With the system parameters determined, the input forces can be estimated in real-time from dynamic responses, which can be used for structural health monitoring. In the process of input forces estimation, the Runge-Kutta fourth-order algorithm was employed to discretize the state equations; a square-root cubature Kalman filter (SRCKF) was employed to suppress white noise; the residual innovation sequences, a priori state estimate, gain matrix, and innovation covariance generated by SRCKF were employed to estimate the magnitude and location of input forces by using a nonlinear estimator. The nonlinear estimator was based on the least squares method. Numerical simulations of a large deflection beam and an experiment of a linear beam constrained by a nonlinear spring were employed. The results demonstrated accuracy of the nonlinear algorithm.
Frequency domain stability analysis of nonlinear active disturbance rejection control system.
Li, Jie; Qi, Xiaohui; Xia, Yuanqing; Pu, Fan; Chang, Kai
2015-05-01
This paper applies three methods (i.e., root locus analysis, describing function method and extended circle criterion) to approach the frequency domain stability analysis of the fast tool servo system using nonlinear active disturbance rejection control (ADRC) algorithm. Root locus qualitative analysis shows that limit cycle is generated because the gain of the nonlinear function used in ADRC varies with its input. The parameters in the nonlinear function are adjustable to suppress limit cycle. In the process of root locus analysis, the nonlinear function is transformed based on the concept of equivalent gain. Then, frequency domain description of the nonlinear function via describing function is presented and limit cycle quantitative analysis including estimating prediction error is presented, which virtually and theoretically demonstrates that the describing function method cannot guarantee enough precision in this case. Furthermore, absolute stability analysis based on extended circle criterion is investigated as a complement.
Simple saturated designs for ANCBC systems and extension to feedforward nonlinear systems
NASA Astrophysics Data System (ADS)
Ye, Huawen; Gui, Weihua
2012-12-01
This article re-examines the robust stabilisation of the asymptotically null-controllable with bounded controls (ANCBC) systems, and extends the established algorithm to a wide class of feedforward nonlinear systems whose nominal dynamics contains both multiple integrators and multiple oscillators. Based on the notion of 'converging-input bounded-state' (CIBS) rather than 'small-input small-state' (SISS), the computation burden in Sussmann et al. (Sussmann, H.J., Sontag, E.D., and Yang, Y. (1994), 'A General Result on the Stabilization of Linear Systems using Bounded Controls', IEEE Transactions on Automatic Control, 39, 2411-2425) is reduced and a class of simple saturated control laws is presented for the CIBS stabilisation of ANCBC systems. Then, by combining the technique of dealing with higher-order terms, the algorithm for ANCBC systems is extended to feedforward nonlinear systems.
Filtering nonlinear dynamical systems with linear stochastic models
NASA Astrophysics Data System (ADS)
Harlim, J.; Majda, A. J.
2008-06-01
An important emerging scientific issue is the real time filtering through observations of noisy signals for nonlinear dynamical systems as well as the statistical accuracy of spatio-temporal discretizations for filtering such systems. From the practical standpoint, the demand for operationally practical filtering methods escalates as the model resolution is significantly increased. For example, in numerical weather forecasting the current generation of global circulation models with resolution of 35 km has a total of billions of state variables. Numerous ensemble based Kalman filters (Evensen 2003 Ocean Dyn. 53 343-67 Bishop et al 2001 Mon. Weather Rev. 129 420-36 Anderson 2001 Mon. Weather Rev. 129 2884-903 Szunyogh et al 2005 Tellus A 57 528-45 Hunt et al 2007 Physica D 230 112-26) show promising results in addressing this issue; however, all these methods are very sensitive to model resolution, observation frequency, and the nature of the turbulent signals when a practical limited ensemble size (typically less than 100) is used. In this paper, we implement a radical filtering approach to a relatively low (40) dimensional toy model, the L-96 model (Lorenz 1996 Proc. on Predictability (ECMWF, 4-8 September 1995) pp 1-18) in various chaotic regimes in order to address the 'curse of ensemble size' for complex nonlinear systems. Practically, our approach has several desirable features such as extremely high computational efficiency, filter robustness towards variations of ensemble size (we found that the filter is reasonably stable even with a single realization) which makes it feasible for high dimensional problems, and it is independent of any tunable parameters such as the variance inflation coefficient in an ensemble Kalman filter. This radical filtering strategy decouples the problem of filtering a spatially extended nonlinear deterministic system to filtering a Fourier diagonal system of parametrized linear stochastic differential equations (Majda and Grote
Li, Bing-Xuan; Wei, Yong; Huang, Cheng-Hui; Zhuang, Feng-Jiang; Zhang, Ge; Guo, Guo-Cong
2014-01-01
In the present paper the authors report a research on testing the nonlinear optical performance of optical materials in visible and infrared band. Based on the second order nonlinear optic principle and the photoelectric signal detection technology, the authors have proposed a new testing scheme in which a infrared OPO laser and a method for separating the beams arising from frequency matching and the light produced by other optical effects were used. The OPO laser is adopted as light source to avoid the error of measurement caused by absorption because the double frequency signal of the material is in the transmittance band Our research work includes testing system composition, operational principle and experimental method. The experimental results of KTP, KDP, AGS tested by this method were presented. In the experiment several new infrared non-linear materials were found. This method possesses the merits of good stability and reliability, high sensitivity, simple operation and good reproducibility, which can effectively make qualitative and semi-quantitative test for optical material's nonlinear optical properties from visible to infrared. This work provides an important test -method for the research on second order nonlinear optical materials in visible, infrared and ultraviolet bands.
Simple nonlinear systems and navigating catastrophes
NASA Astrophysics Data System (ADS)
Harré, Michael S.; Atkinson, Simon R.; Hossain, Liaquat
2013-06-01
Tipping points are a common occurrence in complex adaptive systems. In such systems feedback dynamics strongly influence equilibrium points and they are one of the principal concerns of research in this area. Tipping points occur as small changes in system parameters result in disproportionately large changes in the global properties of the system. In order to show how tipping points might be managed we use the Maximum Entropy (MaxEnt) method developed by Jaynes to find the fixed points of an economic system in two different ways. In the first, economic agents optimise their choices based solely on their personal benefits. In the second they optimise the total benefits of the system, taking into account the effects of all agent's actions. The effect is to move the game from a recently introduced dual localised Lagrangian problem to that of a single global Lagrangian. This leads to two distinctly different but related solutions where localised optimisation provides more flexibility than global optimisation. This added flexibility allows an economic system to be managed by adjusting the relationship between macro parameters, in this sense such manipulations provide for the possibility of "steering" an economy around potential disasters.
Chang, Yeong-Chan
2005-12-01
This paper addresses the problem of designing adaptive fuzzy-based (or neural network-based) robust controls for a large class of uncertain nonlinear time-varying systems. This class of systems can be perturbed by plant uncertainties, unmodeled perturbations, and external disturbances. Nonlinear H(infinity) control technique incorporated with adaptive control technique and VSC technique is employed to construct the intelligent robust stabilization controller such that an H(infinity) control is achieved. The problem of the robust tracking control design for uncertain robotic systems is employed to demonstrate the effectiveness of the developed robust stabilization control scheme. Therefore, an intelligent robust tracking controller for uncertain robotic systems in the presence of high-degree uncertainties can easily be implemented. Its solution requires only to solve a linear algebraic matrix inequality and a satisfactorily transient and asymptotical tracking performance is guaranteed. A simulation example is made to confirm the performance of the developed control algorithms.
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.
Neuro-fuzzy identification applied to fault detection in nonlinear systems
NASA Astrophysics Data System (ADS)
Blázquez, L. Felipe; de Miguel, Luis J.; Aller, Fernando; Perán, José R.
2011-10-01
This article describes a fault detection method, based on the parity equations approach, to be applied to nonlinear systems. The input-output nonlinear model of the plant, used in the method, has been obtained by a neural fuzzy inference architecture and its learning algorithm. The proposed method is able to detect small abrupt faults, even in systems with unknown nonlinearities. This method has been applied to a real industrial pilot plant, and good performance has been obtained for the experimental case of fault detection in the level sensor of a level control process in the said industrial pilot plant.
NASA Astrophysics Data System (ADS)
Hassan, Absar U.; Hodaei, Hossein; Miri, Mohammad-Ali; Khajavikhan, Mercedeh; Christodoulides, Demetrios N.
2015-12-01
A system of two coupled semiconductor-based resonators is studied when lasing around an exceptional point. We show that the presence of nonlinear saturation effects can have important ramifications on the transition behavior of this system. In sharp contrast with linear PT -symmetric configurations, nonlinear processes are capable of reversing the order in which the symmetry breaking occurs. Yet, even in the nonlinear regime, the resulting non-Hermitian states still retain the structural form of the corresponding linear eigenvectors expected above and below the phase-transition point. The conclusions of our analysis are in agreement with experimental data.
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.
Self-characterization of linear and nonlinear adaptive optics systems
NASA Astrophysics Data System (ADS)
Hampton, Peter J.; Conan, Rodolphe; Keskin, Onur; Bradley, Colin; Agathoklis, Pan
2008-01-01
We present methods used to determine the linear or nonlinear static response and the linear dynamic response of an adaptive optics (AO) system. This AO system consists of a nonlinear microelectromechanical systems deformable mirror (DM), a linear tip-tilt mirror (TTM), a control computer, and a Shack-Hartmann wavefront sensor. The system is modeled using a single-input-single-output structure to determine the one-dimensional transfer function of the dynamic response of the chain of system hardware. An AO system has been shown to be able to characterize its own response without additional instrumentation. Experimentally determined models are given for a TTM and a DM.
Robust adaptive dynamic programming and feedback stabilization of nonlinear systems.
Jiang, Yu; Jiang, Zhong-Ping
2014-05-01
This paper studies the robust optimal control design for a class of uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (RADP). The objective is to fill up a gap in the past literature of adaptive dynamic programming (ADP) where dynamic uncertainties or unmodeled dynamics are not addressed. A key strategy is to integrate tools from modern nonlinear control theory, such as the robust redesign and the backstepping techniques as well as the nonlinear small-gain theorem, with the theory of ADP. The proposed RADP methodology can be viewed as an extension of ADP to uncertain nonlinear systems. Practical learning algorithms are developed in this paper, and have been applied to the controller design problems for a jet engine and a one-machine power system.
Future directions of nonlinear dynamics in physical and biological systems
Christiansen, P.L.; Eilbeck, J.C.; Parmentier, R.D.
1992-01-01
Early in 1990 a scientific committee was formed for the purpose of organizing a high-level scientific meeting on Future Directions of Nonlinear Dynamics in Physical and Biological Systems, in honor of Alwyn Scott's 60th birthday (December 25, 1991). As preparations for the meeting proceeded, they were met with an unusually broad-scale and high level of enthusiasm on the part of the international nonlinear science community, resulting in a participation by 168 scientists from 23 different countries in the conference, which was held July 23 to August 1 1992. The contributions to this present volume have been grouped into the following chapters: (1) Integrability, solitons and coherent structures; (2) Nonlinear evolution equations and diffusive systems; (3) Chaotic and stochastic dynamics; (4) Classical and quantum lattices and fields; (5) Superconductivity and superconducting devices; (6) Nonlinear optics; (7) Davydov solitons and biomolecular dynamics; and (8) Biological systems and Neurophysics.
3-D Mesh Generation Nonlinear Systems
Christon, M. A.; Dovey, D.; Stillman, D. W.; Hallquist, J. O.; Rainsberger, R. B
1994-04-07
INGRID is a general-purpose, three-dimensional mesh generator developed for use with finite element, nonlinear, structural dynamics codes. INGRID generates the large and complex input data files for DYNA3D, NIKE3D, FACET, and TOPAZ3D. One of the greatest advantages of INGRID is that virtually any shape can be described without resorting to wedge elements, tetrahedrons, triangular elements or highly distorted quadrilateral or hexahedral elements. Other capabilities available are in the areas of geometry and graphics. Exact surface equations and surface intersections considerably improve the ability to deal with accurate models, and a hidden line graphics algorithm is included which is efficient on the most complicated meshes. The primary new capability is associated with the boundary conditions, loads, and material properties required by nonlinear mechanics programs. Commands have been designed for each case to minimize user effort. This is particularly important since special processing is almost always required for each load or boundary condition.
Entropy-Based Approach To Nonlinear Stability
NASA Technical Reports Server (NTRS)
Merriam, Marshal L.
1991-01-01
NASA technical memorandum suggests schemes for numerical solution of differential equations of flow made more accurate and robust by invoking second law of thermodynamics. Proposes instead of using artificial viscosity to suppress such unphysical solutions as spurious numerical oscillations and nonlinear instabilities, one should formulate equations so that rate of production of entropy within each cell of computational grid be nonnegative, as required by second law.
Chen, Mou; Ge, Shuzhi Sam; How, Bernard Voon Ee
2010-05-01
In this paper, robust adaptive neural network (NN) control is investigated for a general class of uncertain multiple-input-multiple-output (MIMO) nonlinear systems with unknown control coefficient matrices and input nonlinearities. For nonsymmetric input nonlinearities of saturation and deadzone, variable structure control (VSC) in combination with backstepping and Lyapunov synthesis is proposed for adaptive NN control design with guaranteed stability. In the proposed adaptive NN control, the usual assumption on nonsingularity of NN approximation for unknown control coefficient matrices and boundary assumption between NN approximation error and control input have been eliminated. Command filters are presented to implement physical constraints on the virtual control laws, then the tedious analytic computations of time derivatives of virtual control laws are canceled. It is proved that the proposed robust backstepping control is able to guarantee semiglobal uniform ultimate boundedness of all signals in the closed-loop system. Finally, simulation results are presented to illustrate the effectiveness of the proposed adaptive NN control.
Breakpoint Tuning in DCT-Based Nonlinear Layered Video Codecs
NASA Astrophysics Data System (ADS)
Cuenca, Pedro; Orozco-Barbosa, Luis; Delicado, Francisco; Garrido, Antonio
2004-12-01
Many studies have been conducted to evaluate the benefits of using layered video coding schemes as a means to improve the robustness of video communications systems. In this paper, we study a frame-aware nonlinear layering scheme for the transport of a DCT-based video over packet-switched networks. This scheme takes into account the relevance of the different elements of the video sequence composing the encoded video sequence. Throughout a detailed study over a large set of video streams, we show that by properly tuning the encoding parameters, it is feasible to gracefully degrade or even maintain the video quality while reducing the amount of data representing the video sequence. We then provide the major guidelines to properly tune up the encoding parameters allowing us to set the basis towards the development of more robust video communications systems.
A globalization procedure for solving nonlinear systems of equations
NASA Astrophysics Data System (ADS)
Shi, Yixun
1996-09-01
A new globalization procedure for solving a nonlinear system of equationsF(x)D0 is proposed based on the idea of combining Newton step and the steepest descent step WITHIN each iteration. Starting with an arbitrary initial point, the procedure converges either to a solution of the system or to a local minimizer off(x)D1/2F(x)TF(x). Each iteration is chosen to be as close to a Newton step as possible and could be the Newton step itself. Asymptotically the Newton step will be taken in each iteration and thus the convergence is quadratic. Numerical experiments yield positive results. Further generalizations of this procedure are also discussed in this paper.
Parameter and Structure Inference for Nonlinear Dynamical Systems
NASA Technical Reports Server (NTRS)
Morris, Robin D.; Smelyanskiy, Vadim N.; Millonas, Mark
2006-01-01
A great many systems can be modeled in the non-linear dynamical systems framework, as x = f(x) + xi(t), where f() is the potential function for the system, and xi is the excitation noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We show that using the Bayesian Information Criteria (BIC) to rank models, and the beam search technique, that we can accurately determine the structure of simple non-linear dynamical system models, and the structure of the coupling between non-linear dynamical systems where the individual systems are known. This last case has important ecological applications.
NASA Astrophysics Data System (ADS)
Liu, Yurong; Alsaadi, Fuad E.; Yin, Xiaozhou; Wang, Yamin
2015-02-01
In this paper, we are concerned with the robust H∞ filtering problem for a class of nonlinear discrete time-delay stochastic systems. The system under consideration involves parameter uncertainties, stochastic disturbances, time-varying delays and sector nonlinearities. Both missing measurements and randomly occurring nonlinearities are described via the binary switching sequences satisfying a conditional probability distribution, and the nonlinearities are assumed to be sector bounded. The problem addressed is the design of a full-order filter such that, for all admissible uncertainties, nonlinearities and time-delays, the dynamics of the filtering error is constrained to be robustly exponentially stable in the mean square, and a prescribed ? disturbance rejection attenuation level is also guaranteed. By using the Lyapunov stability theory and some new techniques, sufficient conditions are first established to ensure the existence of the desired filtering parameters. Then, the explicit expression of the desired filter gains is described in terms of the solution to a linear matrix inequality. Finally, a numerical example is exploited to show the usefulness of the results derived.
Direct Gaze Estimation Based on Nonlinearity of EOG.
Manabe, Hiroyuki; Fukumoto, Masaaki; Yagi, Tohru
2015-06-01
Electrooculography (EOG) is one of the measures used to estimate the direction of a person's gaze; however, conventional EOG techniques suffer from a drift issue which makes it difficult to extract an accurate absolute eye angle. The technique proposed here is based on the nonlinearity of the EOG and offers a practical solution to this problem. It estimates the absolute eye angles before and after a saccade, which cancels the offset due to the drift. Additionally, it does not require any effort from the user or any target, but instead uses only the difference of the EOGs. Experiments with five subjects confirm that the proposed technique can estimate the absolute eye angle with an error of less than 4(°). They also show improvements are achieved with several options such as weighting and multiple saccades. The technique will contribute to practical EOG-based interaction systems.
Finite-time H∞ filtering for non-linear stochastic systems
NASA Astrophysics Data System (ADS)
Hou, Mingzhe; Deng, Zongquan; Duan, Guangren
2016-09-01
This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.
Li, Yongming; Tong, Shaocheng; Li, Tieshan
2015-01-01
In this paper, an adaptive fuzzy decentralized output feedback control design is presented for a class of interconnected nonlinear pure-feedback systems. The considered nonlinear systems contain unknown nonlinear uncertainties and the states are not necessary to be measured directly. Fuzzy logic systems are employed to approximate the unknown nonlinear functions, and then a fuzzy state observer is designed and the estimations of the immeasurable state variables are obtained. Based on the adaptive backstepping dynamic surface control design technique, an adaptive fuzzy decentralized output feedback control scheme is developed. It is proved that all the variables of the resulting closed-loop system are semi-globally uniformly ultimately bounded, and also that the observer and tracking errors are guaranteed to converge to a small neighborhood of the origin. Some simulation results and comparisons with the existing results are provided to illustrate the effectiveness and merits of the proposed approach.
Zhong, Xiangnan; He, Haibo; Zhang, Huaguang; Wang, Zhanshan
2014-12-01
In this paper, we develop and analyze an optimal control method for a class of discrete-time nonlinear Markov jump systems (MJSs) with unknown system dynamics. Specifically, an identifier is established for the unknown systems to approximate system states, and an optimal control approach for nonlinear MJSs is developed to solve the Hamilton-Jacobi-Bellman equation based on the adaptive dynamic programming technique. We also develop detailed stability analysis of the control approach, including the convergence of the performance index function for nonlinear MJSs and the existence of the corresponding admissible control. Neural network techniques are used to approximate the proposed performance index function and the control law. To demonstrate the effectiveness of our approach, three simulation studies, one linear case, one nonlinear case, and one single link robot arm case, are used to validate the performance of the proposed optimal control method.
Coherent nonlinear structures in ITG-Zonal flow system
NASA Astrophysics Data System (ADS)
Singh, Rameswar; Singh, Raghvendra; Kaw, Predhiman; Diamond, Patrick H.
2013-10-01
Nonlinear stationary structure formation in the coupled ion temperature gradient (ITG) - Zonal flow system is investigated. The ITG turbulence is described by a wave-kinetic equation for the action density of ITG mode and the longer scale zonal mode is described by a dynamical equation for the m = n = 0 component of the potential. In a moving frame, two populations of trappped and untrapped drift wave trajectories are shown to exist. This novel effect leads to formation of nonlinear stationary structures. It is shown that the ITG turbulence can self-consistently sustain coherent, radialy propagating modulation envelope structures such as solitons, shocks, nonlinear wave trains, etc.
Quantum-criticality-induced strong Kerr nonlinearities in optomechanical systems
Lü, Xin-You; Zhang, Wei-Min; Ashhab, Sahel; Wu, Ying; Nori, Franco
2013-01-01
We investigate a hybrid electro-optomechanical system that allows us to realize controllable strong Kerr nonlinearities even in the weak-coupling regime. We show that when the controllable electromechanical subsystem is close to its quantum critical point, strong photon-photon interactions can be generated by adjusting the intensity (or frequency) of the microwave driving field. Nonlinear optical phenomena, such as the appearance of the photon blockade and the generation of nonclassical states (e.g., Schrödinger cat states), are demonstrated in the weak-coupling regime, making the observation of strong Kerr nonlinearities feasible with currently available optomechanical technology. PMID:24126279
Design and evaluation of a fast Fourier transform-based nonlinear dielectric spectrometer
NASA Astrophysics Data System (ADS)
Treo, Ernesto F.; Felice, Carmelo J.
2009-11-01
Nonlinear dielectric spectroscopy of micro-organism is carried out by applying a moderate electrical field to an aqueous sample through two metal electrodes. Several ad hoc nonlinear spectrometers were proposed in the literature. However, these designs barely compensated the nonlinear distortion derived from the electrode-electrolyte interfaces (EEI). Moreover, the contribution of the suspension is masked by the effect of the nonlinearity introduced by the electrode contacts. Conversely, the nonlinear capability of a commercial tetrapolar analyzer has not been fully investigated. In this paper a new nonlinear tetrapolar spectrometer is proposed based on a commercial linear apparatus and ad hoc control and signal processing software. The system was evaluated with discrete electronic phantoms and showed that it can measure nonlinear properties of aqueous suspension independently of the presence of EEI (ANOVA test, p >0.001). It was also tested with real aqueous samples. The harmonics observed in the current that circulates through the sample reveals useful information about the transfer function of the sample. The total harmonic distortion was computed for linear mediums. Values lower than -60 dB suggest that the system has enough capability to perform nonlinear microbiological analysis. Design specifications, sources of interference, and equipment's limitations are discussed.
Design and evaluation of a fast Fourier transform-based nonlinear dielectric spectrometer.
Treo, Ernesto F; Felice, Carmelo J
2009-11-01
Nonlinear dielectric spectroscopy of micro-organism is carried out by applying a moderate electrical field to an aqueous sample through two metal electrodes. Several ad hoc nonlinear spectrometers were proposed in the literature. However, these designs barely compensated the nonlinear distortion derived from the electrode-electrolyte interfaces (EEI). Moreover, the contribution of the suspension is masked by the effect of the nonlinearity introduced by the electrode contacts. Conversely, the nonlinear capability of a commercial tetrapolar analyzer has not been fully investigated. In this paper a new nonlinear tetrapolar spectrometer is proposed based on a commercial linear apparatus and ad hoc control and signal processing software. The system was evaluated with discrete electronic phantoms and showed that it can measure nonlinear properties of aqueous suspension independently of the presence of EEI (ANOVA test, p>0.001). It was also tested with real aqueous samples. The harmonics observed in the current that circulates through the sample reveals useful information about the transfer function of the sample. The total harmonic distortion was computed for linear mediums. Values lower than -60 dB suggest that the system has enough capability to perform nonlinear microbiological analysis. Design specifications, sources of interference, and equipment's limitations are discussed.
Applications of nonlinear system identification to structural health monitoring.
Farrar, C. R.; Sohn, H.; Robertson, A. N.
2004-01-01
The process of implementing a damage detection strategy for aerospace, civil and mechanical engineering infrastructure is referred to as structural health monitoring (SHM). In many cases damage causes a structure that initially behaves in a predominantly linear manner to exhibit nonlinear response when subject to its operating environment. The formation of cracks that subsequently open and close under operating loads is an example of such damage. The damage detection process can be significantly enhanced if one takes advantage of these nonlinear effects when extracting damage-sensitive features from measured data. This paper will provide an overview of nonlinear system identification techniques that are used for the feature extraction process. Specifically, three general approaches that apply nonlinear system identification techniques to the damage detection process are discussed. The first two approaches attempt to quantify the deviation of the system from its initial linear characteristics that is a direct result of damage. The third approach is to extract features from the data that are directly related to the specific nonlinearity associated with the damaged condition. To conclude this discussion, a summary of outstanding issues associated with the application of nonlinear system identification techniques to the SHM problem is presented.
Fault-tolerant control for a class of non-linear systems with dead-zone
NASA Astrophysics Data System (ADS)
Chen, Mou; Jiang, Bin; Guo, William W.
2016-05-01
In this paper, a fault-tolerant control scheme is proposed for a class of single-input and single-output non-linear systems with the unknown time-varying system fault and the dead-zone. The non-linear state observer is designed for the non-linear system using differential mean value theorem, and the non-linear fault estimator that estimates the unknown time-varying system fault is developed. On the basis of the designed fault estimator, the observer-based fault-tolerant tracking control is then developed using the backstepping technique for non-linear systems with the dead-zone. The stability of the whole closed-loop system is rigorously proved via Lyapunov analysis and the satisfactory tracking control performance is guaranteed in the presence of the unknown time-varying system fault and the dead-zone. Numerical simulation results are presented to illustrate the effectiveness of the proposed backstepping fault-tolerant control scheme for non-linear systems.
Non-linear system identification in flow-induced vibration
Spanos, P.D.; Zeldin, B.A.; Lu, R.
1996-12-31
The paper introduces a method of identification of non-linear systems encountered in marine engineering applications. The non-linearity is accounted for by a combination of linear subsystems and known zero-memory non-linear transformations; an equivalent linear multi-input-single-output (MISO) system is developed for the identification problem. The unknown transfer functions of the MISO system are identified by assembling a system of linear equations in the frequency domain. This system is solved by performing the Cholesky decomposition of a related matrix. It is shown that the proposed identification method can be interpreted as a {open_quotes}Gram-Schmidt{close_quotes} type of orthogonal decomposition of the input-output quantities of the equivalent MISO system. A numerical example involving the identification of unknown parameters of flow (ocean wave) induced forces on offshore structures elucidates the applicability of the proposed method.
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network
NASA Astrophysics Data System (ADS)
Goto, Hayato
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via its bifurcation with a slowly varying parameter. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing. To distinguish them, we refer to the present approach as bifurcation-based adiabatic quantum computation. Our numerical simulation results suggest that quantum superposition and quantum fluctuation work effectively to find optimal solutions.
Simulation program of nonlinearities applied to telecommunication systems
NASA Technical Reports Server (NTRS)
Thomas, C.
1979-01-01
In any satellite communication system, the problems of distorsion created by nonlinear devices or systems must be considered. The subject of this paper is the use of the Fast Fourier Transform (F.F.T.) in the prediction of the intermodulation performance of amplifiers, mixers, filters. A nonlinear memory-less model is chosen to simulate amplitude and phase nonlinearities of the device in the simulation program written in FORTRAN 4. The experimentally observed nonlinearity parameters of a low noise 3.7-4.2 GHz amplifier are related to the gain and phase coefficients of Fourier Service Series. The measured results are compared with those calculated from the simulation in the cases where the input signal is composed of two, three carriers and noise power density.
Nonlinear Dynamics and Chaotic Motions in Feedback Controlled Elastic Systems.
1985-08-01
mechanical oscillator ", "On slowly varying oscillations ", "Knotted Orbits and bifurcation sequences in periodically forced oscillations ", "Dynamics of a...each P.I. 2.1 Analytical Studies of Feedback Controlled Oscillators (P.J. Holmes, S. Wiggins (Grad. Student)) 2.1.1 Bifurcation studies. Local and...global bifurcation studies of nonlinear oscillators subject to linear and nonlinear feedback have been completed. The systems treated have the form x
NASA Astrophysics Data System (ADS)
Tavassoli, Vahid
This thesis studies and mathematically models nonlinear interactions among channels of modern high bit rate (amplitude/) phase modulated optical systems. First, phase modulated analogue systems are studied and a differential receiving method is suggested with experimental validation. The main focus of the rest of the thesis is on digital advanced modulation format systems. Cross-talk due to fiber Kerr nonlinearity in two-format hybrid systems as well as 16-QAM systems is mathematically modelled and verified by simulation for different system parameters. A comparative study of differential receivers and coherent receivers is also given for hybrid systems. The model is based on mathematically proven assumptions and provides an intuitive analytical understanding of nonlinear cross-talk in such systems.
Energy and Transmissibility in Nonlinear Viscous Base Isolators
NASA Astrophysics Data System (ADS)
Markou, Athanasios A.; Manolis, George D.
2016-09-01
High damping rubber bearings (HDRB) are the most commonly used base isolators in buildings and are often combined with other systems, such as sliding bearings. Their mechanical behaviour is highly nonlinear and dependent on a number of factors. At first, a physical process is suggested here to explain the empirical formula introduced by J.M. Kelly in 1991, where the dissipated energy of a HDRB under cyclic testing, at constant frequency, is proportional to the amplitude of the shear strain, raised to a power of approximately 1.50. This physical process is best described by non-Newtonian fluid behaviour, originally developed by F.H. Norton in 1929 to describe creep in steel at high-temperatures. The constitutive model used includes a viscous term, that depends on the absolute value of the velocity, raised to a non-integer power. The identification of a three parameter Kelvin model, the simplest possible system with nonlinear viscosity, is also suggested here. Furthermore, a more advanced model with variable damping coefficient is implemented to better model in this complex mechanical process. Next, the assumption of strain-rate dependence in their rubber layers under cyclic loading is examined in order to best interpret experimental results on the transmission of motion between the upper and lower surfaces of HDRB. More specifically, the stress-relaxation phenomenon observed with time in HRDB can be reproduced numerically, only if the constitutive model includes a viscous term, that depends on the absolute value of the velocity raised to a non-integer power, i. e., the Norton fluid previously mentioned. Thus, it becomes possible to compute the displacement transmissibility function between the top and bottom surfaces of HDRB base isolator systems and to draw engineering-type conclusions, relevant to their design under time-harmonic loads.
Nonperturbative analytical approximate solutions in intrinsically nonlinear systems
NASA Astrophysics Data System (ADS)
Kindall, Kevin Gaylynn
The basis for obtaining analytical approximations in this dissertation is a new nonperturbative iterative approach that preserves the intrinsic nonlinearity of the system. The traditional method for approaching nonlinear equations has been the small amplitude approximation of classical perturbation theory. However, it is becoming increasingly evident that intrinsic nonlinearity or persistence of the interaction is a primary feature of the solutions for the nonlinear equations that have been solved. Although perturbation theory may be useful in certain physical domains, it is a domain which excludes the effects of the persistent interaction, since perturbation theory nullifies any intrinsically nonlinear property. The method of solution used here proceeds by analogy to the well-known result that second order, linear ordinary differential equations can be transformed to a Riccati equation by a change in dependent variable. An analogous transformation for nonlinear partial differential equations leads to a set of integro- differential equations for which the basic structure is Riccati. Approximations are introduced in the integral part of the integro-differential equation which allow for systematic iteration while making no expansion in powers of the coupling constant. Two sets of differential equations are examined: the Maxwell-Bloch set and the Rossler set. The importance of the former lies in its importance to the phenomenon of optical bistability. The latter represents the minimal set necessary to display chaos. In each case, their intrinsic nonlinearity is demonstrated, and nonperturbative approximate solutions are constructed.
Geometric framework for phase synchronization in coupled noisy nonlinear systems
NASA Astrophysics Data System (ADS)
Balakrishnan, J.
2006-03-01
A geometric approach is introduced for understanding the phenomenon of phase synchronization in coupled nonlinear systems in the presence of additive noise. We show that the emergence of cooperative behavior through a change of stability via a Hopf bifurcation entails the spontaneous appearance of a gauge structure in the system, arising from the evolution of the slow dynamics, but induced by the fast variables. The conditions for the oscillators to be synchronised in phase are obtained. The role of weak noise appears to be to drive the system towards a more synchronized behavior. Our analysis provides a framework to explain recent experimental observations on noise-induced phase synchronization in coupled nonlinear systems.
Epackachi, S.; Esmaili, O.; Mirghaderi, S. R.; Taheri, A. A.
2008-07-08
Tehran tower is a 56 story reinforced concrete tall building consisting of three wings with identical plan dimensions each approximately 48 meters by 22 meters. The three wings are at 120 degree from each other and have no expansions/seismic Joints. This paper contains the consideration of the retrofitting of the Tehran tower based on the findings of an exhaustive investigation of the nonlinear performance evaluation efforts. It has tried to show the procedure followed, methodologies utilized, and the results obtained for life-safety and collapse-prevention evaluation of the building. More over the weak zones of the structure due to analysis results are introduced and appropriate retrofit technique for satisfaction related life-safety and collapse-prevention criteria is presented. Actually in this project to improve the local behavior of coupling panels which are located regularly in main walls and definitely have been recognized as the most vulnerable structural elements, making use of steel plates which are connected to concrete members by chemical anchors has been used as the best retrofitting method for this case. Therefore in the final section of this paper it has been tried to explain the professional practical method utilized to perform the mentioned retrofitting project.
NASA Astrophysics Data System (ADS)
Epackachi, S.; Esmaili, O.; Mirghaderi, S. R.; Taheri, A. A.
2008-07-01
Tehran tower is a 56 story reinforced concrete tall building consisting of three wings with identical plan dimensions each approximately 48 meters by 22 meters. The three wings are at 120 degree from each other and have no expansions/seismic Joints. This paper contains the consideration of the retrofitting of the Tehran tower based on the findings of an exhaustive investigation of the nonlinear performance evaluation efforts. It has tried to show the procedure followed, methodologies utilized, and the results obtained for life-safety and collapse-prevention evaluation of the building. More over the weak zones of the structure due to analysis results are introduced and appropriate retrofit technique for satisfaction related life-safety and collapse-prevention criteria is presented. Actually in this project to improve the local behavior of coupling panels which are located regularly in main walls and definitely have been recognized as the most vulnerable structural elements, making use of steel plates which are connected to concrete members by chemical anchors has been used as the best retrofitting method for this case. Therefore in the final section of this paper it has been tried to explain the professional practical method utilized to perform the mentioned retrofitting project.
Nonlinear model updating applied to the IMAC XXXII Round Robin benchmark system
NASA Astrophysics Data System (ADS)
Kurt, Mehmet; Moore, Keegan J.; Eriten, Melih; McFarland, D. Michael; Bergman, Lawrence A.; Vakakis, Alexander F.
2017-05-01
We consider the application of a new nonlinear model updating strategy to a computational benchmark system. The approach relies on analyzing system response time series in the frequency-energy domain by constructing both Hamiltonian and forced and damped frequency-energy plots (FEPs). The system parameters are then characterized and updated by matching the backbone branches of the FEPs with the frequency-energy wavelet transforms of experimental and/or computational time series. The main advantage of this method is that no nonlinearity model is assumed a priori, and the system model is updated solely based on simulation and/or experimental measured time series. By matching the frequency-energy plots of the benchmark system and its reduced-order model, we show that we are able to retrieve the global strongly nonlinear dynamics in the frequency and energy ranges of interest, identify bifurcations, characterize local nonlinearities, and accurately reconstruct time series. We apply the proposed methodology to a benchmark problem, which was posed to the system identification community prior to the IMAC XXXII (2014) and XXXIII (2015) Conferences as a "Round Robin Exercise on Nonlinear System Identification". We show that we are able to identify the parameters of the non-linear element in the problem with a priori knowledge about its position.
Nonlinear Krylov acceleration for CFD-based aeroelasticity
NASA Astrophysics Data System (ADS)
Feng, Z.; Soulaı¨Mani, A.; Saad, Y.
2009-01-01
A nonlinear computational aeroelasticity model based on the Euler equations of compressible flows and the linear elastodynamic equations for structures is developed. The Euler equations are solved on dynamic meshes using the ALE kinematic description. Thus, the mesh constitutes another field governed by pseudo-elastodynamic equations. The three fields are discretized using proper finite element formulations which satisfy the geometric conservation law. A matcher module is incorporated for the purpose of pairing the grids on the fluid-structure interface and for transferring the loads and displacements between the fluid and structure solvers. Two solution strategies (Gauss-Seidel and Schur-complement) for solving the non-linear aeroelastic system are discussed. By using second-order time discretization scheme, we are able to utilize large time steps in the computations. The numerical results on the AGARD 445.6 aeroelastic wing compare well with the experimental results and show that the Schur-complement coupling algorithm is more robust than the Gauss-Seidel algorithm for relatively large oscillation amplitudes.
NASA Astrophysics Data System (ADS)
Ming, Yi; Li, Hui-Min; Ding, Ze-Jun
2016-03-01
Thermal rectification and negative differential thermal conductance were realized in harmonic chains in this work. We used the generalized Caldeira-Leggett model to study the heat flow. In contrast to most previous studies considering only the linear system-bath coupling, we considered the nonlinear system-bath coupling based on recent experiment [Eichler et al., Nat. Nanotech. 6, 339 (2011), 10.1038/nnano.2011.71]. When the linear coupling constant is weak, the multiphonon processes induced by the nonlinear coupling allow more phonons transport across the system-bath interface and hence the heat current is enhanced. Consequently, thermal rectification and negative differential thermal conductance are achieved when the nonlinear couplings are asymmetric. However, when the linear coupling constant is strong, the umklapp processes dominate the multiphonon processes. Nonlinear coupling suppresses the heat current. Thermal rectification is also achieved. But the direction of rectification is reversed compared to the results of weak linear coupling constant.
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.
Scalable analysis of nonlinear systems using convex optimization
NASA Astrophysics Data System (ADS)
Papachristodoulou, Antonis
In this thesis, we investigate how convex optimization can be used to analyze different classes of nonlinear systems at various scales algorithmically. The methodology is based on the construction of appropriate Lyapunov-type certificates using sum of squares techniques. After a brief introduction on the mathematical tools that we will be using, we turn our attention to robust stability and performance analysis of systems described by Ordinary Differential Equations. A general framework for constrained systems analysis is developed, under which stability of systems with polynomial, non-polynomial vector fields and switching systems, as well estimating the region of attraction and the L2 gain can be treated in a unified manner. We apply our results to examples from biology and aerospace. We then consider systems described by Functional Differential Equations (FDEs), i.e., time-delay systems. Their main characteristic is that they are infinite dimensional, which complicates their analysis. We first show how the complete Lyapunov-Krasovskii functional can be constructed algorithmically for linear time-delay systems. Then, we concentrate on delay-independent and delay-dependent stability analysis of nonlinear FDEs using sum of squares techniques. An example from ecology is given. The scalable stability analysis of congestion control algorithms for the Internet is investigated next. The models we use result in an arbitrary interconnection of FDE subsystems, for which we require that stability holds for arbitrary delays, network topologies and link capacities. Through a constructive proof, we develop a Lyapunov functional for FAST---a recently developed network congestion control scheme---so that the Lyapunov stability properties scale with the system size. We also show how other network congestion control schemes can be analyzed in the same way. Finally, we concentrate on systems described by Partial Differential Equations. We show that axially constant perturbations of
Esfandiari, Kasra; Abdollahi, Farzaneh; Talebi, Heidar Ali
2015-10-01
This paper presents a tracking control methodology for a class of uncertain nonlinear systems subject to input saturation constraint and external disturbances. Unlike most previous approaches on saturated systems, which assumed affine nonlinear systems, in this paper, tracking control problem is solved for uncertain nonaffine nonlinear systems with input saturation. To deal with the saturation constraint, an auxiliary system is constructed and a modified tracking error is defined. Then, by employing implicit function theorem, mean value theorem, and modified tracking error, updating rules are derived based on the well-known back-propagation (BP) algorithm, which has been proven to be the most relevant updating rule to control problems. However, most of the previous approaches on BP algorithm suffer from lack of stability analysis. By injecting a damping term to the standard BP algorithm, uniformly ultimately boundedness of all the signals of the closed-loop system is ensured via Lyapunov's direct method. Furthermore, the presented approach employs nonlinear in parameter neural networks. Hence, the proposed scheme is applicable to systems with higher degrees of nonlinearity. Using a high-gain observer to reconstruct the states of the system, an output feedback controller is also presented. Finally, the simulation results performed on a Duffing-Holmes chaotic system, a generalized pendulum-type system, and a numerical system are presented to demonstrate the effectiveness of the suggested state and output feedback control schemes.
Prediction and simulation errors in parameter estimation for nonlinear systems
NASA Astrophysics Data System (ADS)
Aguirre, Luis A.; Barbosa, Bruno H. G.; Braga, Antônio P.
2010-11-01
This article compares the pros and cons of using prediction error and simulation error to define cost functions for parameter estimation in the context of nonlinear system identification. To avoid being influenced by estimators of the least squares family (e.g. prediction error methods), and in order to be able to solve non-convex optimisation problems (e.g. minimisation of some norm of the free-run simulation error), evolutionary algorithms were used. Simulated examples which include polynomial, rational and neural network models are discussed. Our results—obtained using different model classes—show that, in general the use of simulation error is preferable to prediction error. An interesting exception to this rule seems to be the equation error case when the model structure includes the true model. In the case of error-in-variables, although parameter estimation is biased in both cases, the algorithm based on simulation error is more robust.
Method and system for non-linear motion estimation
NASA Technical Reports Server (NTRS)
Lu, Ligang (Inventor)
2011-01-01
A method and system for extrapolating and interpolating a visual signal including determining a first motion vector between a first pixel position in a first image to a second pixel position in a second image, determining a second motion vector between the second pixel position in the second image and a third pixel position in a third image, determining a third motion vector between one of the first pixel position in the first image and the second pixel position in the second image, and the second pixel position in the second image and the third pixel position in the third image using a non-linear model, determining a position of the fourth pixel in a fourth image based upon the third motion vector.
Nonlinear analysis of rotor-bearing systems using component mode synthesis
NASA Technical Reports Server (NTRS)
Nelson, H. D.; Meacham, W. L.; Fleming, D. P.; Kascak, A. F.
1982-01-01
The method of component mode synthesis is developed to determine the forced response of nonlinear, multishaft, rotor-bearing systems. The formulation allows for simulation of system response due to blade loss, distributed unbalance, base shock, maneuver loads, and specified fixed frame forces. The motion of each rotating component of the system is described by superposing constraint modes associated with boundary coordinates and constrained precessional modes associated with internal coordinates. The precessional modes are truncated for each component and the reduced component equations are assembled with the nonlinear supports and interconnections to form a set of nonlinear system equations of reduced order. These equations are then numerically integrated to obtain the system response. A computer program, which is presently restricted to single shaft systems, has been written and results are presented for transient system response associated with blade loss dynamics with squeeze film dampers, and with interference rubs.
A new method for observing the running states of a single-variable nonlinear system.
Meng, Yu; Chen, Hong; Chen, Cheng
2015-03-01
In order to timely grasp a single variable nonlinear system running states, a new method called Scatter Point method is put forward in this paper. It can be used to observe or monitor the running states of a single variable nonlinear system in real-time. In this paper, the definition of the method is given at first, and then its working principle is expounded theoretically, after this, some physical experiments based on Chua's nonlinear system are conducted. At the same time, many scatter point graphs are measured by a general analog oscilloscope. The motion, number, and distribution of these scatter points shown on the oscilloscope screen can directly reflect the current states of the tested system. The experimental results further confirm that the method is effective and practical, in which the system running states are not easily lost. In addition, this method is not only suitable for single variable systems but also for multivariable systems.
IDENTIFICATION OF NONLINEARITIES IN AN 8-DOF SYSTEM THROUGH SPECTRAL FEEDBACK
B. ARCAND; J. WAIT
2000-08-01
The accurate detection and characterization of nonlinearities associated with damage in structural systems is an area of vibration analysis that is being widely researched. In this paper, nonlinear behavior is considered a potential indicator of damage. Most conventional damage detection methods, such as those based on resonant frequencies and mode shapes, do not accurately identify the location and extent of nonlinearities present in a given structural system. As an extension of previous work at LANL, an effort is made to validate a damage detection method proposed by Adams. This method states that the frequency response function (FRF) matrix obtained from a low-level vibration test approximates the underlying linear FRF matrix of the system. The nonlinear systems' responses to high level excitation are combined with the linear FRF in a classic feedback loop to obtain the contributions of nonlinear internal forces. The temporal and spatial characteristics of the nonlinearities present in a structural system are identified. An 8-DOF system is used as a test case to validate the aforementioned method. Results of the tests and important issues concerning the method are presented.
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.
NASA Astrophysics Data System (ADS)
Gao, Fangzheng; Wu, Yuqiang; Yu, Xin
2016-12-01
In this paper, the problem of global stabilisation by state feedback is investigated for a class of stochastic high-order nonlinear systems with both high-order and low-order nonlinearities, to which the existing control methods are inapplicable. Based on the generalised stochastic Lyapunov theorem, and by skillfully using the method of adding a power integrator, a continuous state feedback controller is successfully constructed, which can guarantee the global asymptotic stability in probability of the resulting closed-loop system in the sense of weak solution, and also is able to lead to an interesting result of finite-time stabilisation under appropriate conditions. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed approach.
Cumulants of heat transfer across nonlinear quantum systems
NASA Astrophysics Data System (ADS)
Li, Huanan; Agarwalla, Bijay Kumar; Li, Baowen; Wang, Jian-Sheng
2013-12-01
We consider thermal conduction across a general nonlinear phononic junction. Based on two-time observation protocol and the nonequilibrium Green's function method, heat transfer in steady-state regimes is studied, and practical formulas for the calculation of the cumulant generating function are obtained. As an application, the general formalism is used to study anharmonic effects on fluctuation of steady-state heat transfer across a single-site junction with a quartic nonlinear on-site pinning potential. An explicit nonlinear modification to the cumulant generating function exact up to the first order is given, in which the Gallavotti-Cohen fluctuation symmetry is found still valid. Numerically a self-consistent procedure is introduced, which works well for strong nonlinearity.
Predictability of extremes in non-linear hierarchically organized systems
NASA Astrophysics Data System (ADS)
Kossobokov, V. G.; Soloviev, A.
2011-12-01
Understanding the complexity of non-linear dynamics of hierarchically organized systems progresses to new approaches in assessing hazard and risk of the extreme catastrophic events. In particular, a series of interrelated step-by-step studies of seismic process along with its non-stationary though self-organized behaviors, has led already to reproducible intermediate-term middle-range earthquake forecast/prediction technique that has passed control in forward real-time applications during the last two decades. The observed seismic dynamics prior to and after many mega, great, major, and strong earthquakes demonstrate common features of predictability and diverse behavior in course durable phase transitions in complex hierarchical non-linear system of blocks-and-faults of the Earth lithosphere. The confirmed fractal nature of earthquakes and their distribution in space and time implies that many traditional estimations of seismic hazard (from term-less to short-term ones) are usually based on erroneous assumptions of easy tractable analytical models, which leads to widespread practice of their deceptive application. The consequences of underestimation of seismic hazard propagate non-linearly into inflicted underestimation of risk and, eventually, into unexpected societal losses due to earthquakes and associated phenomena (i.e., collapse of buildings, landslides, tsunamis, liquefaction, etc.). The studies aimed at forecast/prediction of extreme events (interpreted as critical transitions) in geophysical and socio-economical systems include: (i) large earthquakes in geophysical systems of the lithosphere blocks-and-faults, (ii) starts and ends of economic recessions, (iii) episodes of a sharp increase in the unemployment rate, (iv) surge of the homicides in socio-economic systems. These studies are based on a heuristic search of phenomena preceding critical transitions and application of methodologies of pattern recognition of infrequent events. Any study of rare
NASA Astrophysics Data System (ADS)
Katayama, Hitoshi
2014-09-01
Design of reduced-order observer-based output feedback consensus controllers for nonlinear sampled-data multi-agent systems of strict-feedback form is considered based on nonlinear sampled-data control and consensus control theories. As a practical application of the proposed design method, output feedback consensus control for sampled-data fully actuated ships is also discussed.
Performance evaluation of nonlinear weighted T-system
NASA Astrophysics Data System (ADS)
Benfekir, A.; Hamaci, S.; Boimond, J.-L.; Labadi, K.
2013-10-01
This article deals with the analysis of discrete event systems which can be modelled by timed event graphs with multipliers (TEGMs). These graphs are an extension of weighted T-systems studied in the Petri net literature. These models do not admit a linear representation in (min, +) algebra. This nonlinearity is due to the presence of weights on arcs. To mitigate this problem of nonlinearity and to apply some basic results used to analyse the performances of linear systems in dioid algebra, we propose a linearisation method of mathematical model reflecting the behaviour of a TEGM in order to obtain a (min, +) linear model.
Recent results of nonlinear estimators applied to hereditary systems.
NASA Technical Reports Server (NTRS)
Schiess, J. R.; Roland, V. R.; Wells, W. R.
1972-01-01
An application of the extended Kalman filter to delayed systems to estimate the state and time delay is presented. Two nonlinear estimators are discussed and the results compared with those of the Kalman filter. For all the filters considered, the hereditary system was treated with the delay in the pure form and by using Pade approximations of the delay. A summary of the convergence properties of the filters studied is given. The results indicate that the linear filter applied to the delayed system performs inadequately while the nonlinear filters provide reasonable estimates of both the state and the parameters.
Recent results of nonlinear estimators applied to hereditary systems.
NASA Technical Reports Server (NTRS)
Schiess, J. R.; Roland, V. R.; Wells, W. R.
1972-01-01
An application of the extended Kalman filter to delayed systems to estimate the state and time delay is presented. Two nonlinear estimators are discussed and the results compared with those of the Kalman filter. For all the filters considered, the hereditary system was treated with the delay in the pure form and by using Pade approximations of the delay. A summary of the convergence properties of the filters studied is given. The results indicate that the linear filter applied to the delayed system performs inadequately while the nonlinear filters provide reasonable estimates of both the state and the parameters.
Convex aggregative modelling of infinite memory nonlinear systems
NASA Astrophysics Data System (ADS)
Wachel, Paweł
2016-08-01
The convex aggregation technique is applied for modelling general class of nonlinear systems with unknown structure and infinite memory. The finite sample size properties of the algorithm are formally established and compared to the standard least-squares counterpart of the method. The proposed algorithm demonstrates its advantages when the a-priori knowledge and the measurement data are both scarce, that is, when the information about the actual system structure is unknown or uncertain and the measurement set is small and disturbed by a noise. Numerical experiments illustrate application and practical benefits of the method for various nonlinear systems.
Nonlinear analysis for image stabilization in IR imaging system
NASA Astrophysics Data System (ADS)
Xie, Zhan-lei; Lu, Jin; Luo, Yong-hong; Zhang, Mei-sheng
2009-07-01
In order to acquire stabilization image for IR imaging system, an image stabilization system is required. Linear method is often used in current research on the system and a simple PID controller can meet the demands of common users. In fact, image stabilization system is a structure with nonlinear characters such as structural errors, friction and disturbances. In up-grade IR imaging system, although conventional PID controller is optimally designed, it cannot meet the demands of higher accuracy and fast responding speed when disturbances are present. To get high-quality stabilization image, nonlinear characters should be rejected. The friction and gear clearance are key factors and play an important role in the image stabilization system. The friction induces static error of system. When the system runs at low speed, stick-slip and creeping induced by friction not only decrease resolution and repeating accuracy, but also increase the tracking error and the steady state error. The accuracy of the system is also limited by gear clearance, and selfexcited vibration is brought on by serious clearance. In this paper, effects of different nonlinear on image stabilization precision are analyzed, including friction and gear clearance. After analyzing the characters and influence principle of the friction and gear clearance, a friction model is established with MATLAB Simulink toolbox, which is composed of static friction, Coulomb friction and viscous friction, and the gear clearance non-linearity model is built, providing theoretical basis for the future engineering practice.
Pulse-Shaping-Based Nonlinear Microscopy: Development and Applications
NASA Astrophysics Data System (ADS)
Flynn, Daniel Christopher
The combination of optical microscopy and ultrafast spectroscopy make the spatial characterization of chemical kinetics on the femtosecond time scale possible. Commercially available octave-spanning Ti:Sapphire oscillators with sub-8 fs pulse durations can drive a multitude of nonlinear transitions across a significant portion of the visible spectrum with minimal average power. Unfortunately, dispersion from microscope objectives broadens pulse durations, decreases temporal resolution and lowers the peak intensities required for driving nonlinear transitions. In this dissertation, pulse shaping is used to compress laser pulses after the microscope objective. By using a binary genetic algorithm, pulse-shapes are designed to enable selective two-photon excitation. The pulse-shapes are demonstrated in two-photon fluorescence of live COS-7 cells expressing GFP-variants mAmetrine and tdTomato. The pulse-shaping approach is applied to a new multiphoton fluorescence resonance energy transfer (FRET) stoichiometry method that quantifies donor and acceptor molecules in complex, as well as the ratio of total donor to acceptor molecules. Compared to conventional multi-photon imaging techniques that require laser tuning or multiple laser systems to selectively excite individual fluorophores, the pulse-shaping approach offers rapid selective multifluorphore imaging at biologically relevant time scales. By splitting the laser beam into two beams and building a second pulse shaper, a pulse-shaping-based pump-probe microscope is developed. The technique offers multiple imaging modalities, such as excited state absorption (ESA), ground state bleach (GSB), and stimulated emission (SE), enhancing contrast of structures via their unique quantum pathways without the addition of contrast agents. Pulse-shaping based pump-probe microscopy is demonstrated for endogenous chemical-contrast imaging of red blood cells. In the second section of this dissertation, ultrafast spectroscopic
Nonlinear observer designs for fuel cell power systems
NASA Astrophysics Data System (ADS)
Gorgun, Haluk
A fuel cell is an electrochemical device that combines hydrogen and oxygen, with the aid of electro-catalysts, to produce electricity. A fuel cell consists of a negatively charged anode, a positively charged cathode and an electrolyte, which transports protons or ions. A low temperature fuel cell has an electrical potential of about 0.7 Volt when generating a current density of 300--500 mA/cm2. Practical fuel cell power systems will require a combination of several cells in series (a stack) to satisfy the voltage requirements of specific applications. Fuel cells are suitable for a potentially wide variety of applications, from stationary power generation in the range of hundreds of megawatts to portable electronics in the range of a couple of watts. Efficient operation of a fuel cell system requires advanced feedback control designs. Reliable measurements from the system are necessary to implement such designs. However, most of the commercially available sensors do not operate properly in the reformate and humidified gas streams in fuel cell systems. Sensors working varying degrees of success are too big and costly, and sensors that are potentially low cost are not reliable or do not have the required life time [28]. Observer designs would eliminate sensor needs for measurements, and make feedback control implementable. Since the fuel cell system dynamics are highly nonlinear, observer design is not an easy task. In this study we aim to develop nonlinear observer design methods applicable to fuel cell systems. In part I of the thesis we design an observer to estimate the hydrogen partial pressure in the anode channel. We treat inlet partial pressure as an unknown slowly varying parameter and develop an adaptive observer that employs a nonlinear voltage injection term. However in this design Fuel Processing System (FPS) dynamics are not modelled, and their effect on the anode dynamics are treated as plant uncertainty. In part II of the thesis we study the FPS
Linear homotopy solution of nonlinear systems of equations in geodesy
NASA Astrophysics Data System (ADS)
Paláncz, Béla; Awange, Joseph L.; Zaletnyik, Piroska; Lewis, Robert H.
2010-01-01
A fundamental task in geodesy is solving systems of equations. Many geodetic problems are represented as systems of multivariate polynomials. A common problem in solving such systems is improper initial starting values for iterative methods, leading to convergence to solutions with no physical meaning, or to convergence that requires global methods. Though symbolic methods such as Groebner bases or resultants have been shown to be very efficient, i.e., providing solutions for determined systems such as 3-point problem of 3D affine transformation, the symbolic algebra can be very time consuming, even with special Computer Algebra Systems (CAS). This study proposes the Linear Homotopy method that can be implemented easily in high-level computer languages like C++ and Fortran that are faster than CAS by at least two orders of magnitude. Using Mathematica, the power of Homotopy is demonstrated in solving three nonlinear geodetic problems: resection, GPS positioning, and affine transformation. The method enlarging the domain of convergence is found to be efficient, less sensitive to rounding of numbers, and has lower complexity compared to other local methods like Newton-Raphson.
Stability properties of nonlinear dynamical systems and evolutionary stable states
NASA Astrophysics Data System (ADS)
Gleria, Iram; Brenig, Leon; Rocha Filho, Tarcísio M.; Figueiredo, Annibal
2017-03-01
In this paper we address the problem of stability in a general class of non-linear systems. We establish a link between the concepts of asymptotic stable interior fixed points of square Quasi-Polynomial systems and evolutionary stable states, a property of some payoff matrices arising from evolutionary games.
Observer Design for a Class of MIMO Nonlinear Systems (Preprint)
2006-06-01
without control), because it covers an important class of dynamic systems such as the Van der Pol equation and Duffing oscillator [5], [13] — both of...1992. [5] J. Guckenheimer and P. Holmes, Nonlinear oscillations , dynamical systems, and bifurcations of vector fields, Springer, NY, 1983. [6] A
A bias identification and state estimation methodology for nonlinear systems
NASA Technical Reports Server (NTRS)
Caglayan, A. K.; Lancraft, R. E.
1983-01-01
A computational algorithm for the identification of input and output biases in discrete-time nonlinear stochastic systems is derived by extending the separate bias estimation results for linear systems to the extended Kalman filter formulation. The merits of the approach are illustrated by identifying instrument biases using a terminal configured vehicle simulation.
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.
NASA Technical Reports Server (NTRS)
Gunderson, R. W.; George, J. H.
1974-01-01
Two approaches are investigated for obtaining estimates on the error between approximate and exact solutions of dynamic systems. The first method is primarily useful if the system is nonlinear and of low dimension. The second requires construction of a system of v-functions but is useful for higher dimensional systems, either linear or nonlinear.
NASA Technical Reports Server (NTRS)
Gunderson, R. W.; George, J. H.
1974-01-01
Two approaches are investigated for obtaining estimates on the error between approximate and exact solutions of dynamic systems. The first method is primarily useful if the system is nonlinear and of low dimension. The second requires construction of a system of v-functions but is useful for higher dimensional systems, either linear or nonlinear.
A new method for the control of discrete nonlinear dynamic systems using neural networks.
Adetona, O; Garcia, E; Keel, L H
2000-01-01
A new controller design method for nonaffine nonlinear dynamic systems is presented in this paper. An identified neural network model of the nonlinear plant is used in the proposed method. The method is based on a new control law that is developed for any discrete deterministic time-invariant nonlinear dynamic system in a subregion Phi(x) of an asymptotically stable equilibrium point of the plant. The performance of the control law is not necessarily dependent on the distance between the current state of the plant and the equilibrium state if the nonlinear dynamic system satisfies some mild requirements in Phi(x). The control law is simple to implement and is based on a novel linearization of the input-output model of the plant at each instant in time. It can be used to control both minimum phase and nonminimum phase nonaffine nonlinear plants. Extensive empirical studies have confirmed that the control law can be used to control a relatively general class of highly nonlinear multiinput-multioutput (MIMO) plants.
Nonlinear Modes in Finite-Dimensional PT-Symmetric Systems
NASA Astrophysics Data System (ADS)
Zezyulin, D. A.; Konotop, V. V.
2012-05-01
By rearrangements of waveguide arrays with gain and losses one can simulate transformations among parity-time (PT-) symmetric systems not affecting their pure real linear spectra. Subject to such transformations, however, the nonlinear properties of the systems undergo significant changes. On an example of an array of four waveguides described by the discrete nonlinear Schrödinger equation with dissipation and gain, we show that the equivalence of the underlying linear spectra does not imply similarity of the structure or stability of the nonlinear modes in the arrays. Even the existence of one-parametric families of nonlinear modes is not guaranteed by the PT symmetry of a newly obtained system. In addition, the stability is not directly related to the PT symmetry: stable nonlinear modes exist even when the spectrum of the linear array is not purely real. We use a graph representation of PT-symmetric networks allowing for a simple illustration of linearly equivalent networks and indicating their possible experimental design.
Nonlinear frequency conversion effect in a one-dimensional graphene-based photonic crystal
NASA Astrophysics Data System (ADS)
Wicharn, S.; Buranasiri, P.
2015-07-01
In this research, the nonlinear frequency conversion effect based on four-wave mixing (FWM) principle in a onedimensional graphene-based photonics crystal (1D-GPC) has been investigated numerically. The 1D-GPC structure is composed of two periodically alternating material layers, which are graphene-silicon dioxide bilayer system and silicon membrane. Since, the third-order nonlinear susceptibility χ(3) of bilayer system is hundred time higher than pure silicon dioxide layer, so the enhancement of FWM response can be achieved inside the structure with optimizing photon energy being much higher than a chemical potential level (μ) of graphene sheet. In addition, the conversion efficiencies of 1DGPC structure are compared with chalcogenide based photonic structure for showing that 1D-GPC structure can enhance nonlinear effect by a factor of 100 above the chalcogenide based structure with the same structure length.
Nonlinear system guidance in the presence of transmission zero dynamics
NASA Technical Reports Server (NTRS)
Meyer, G.; Hunt, L. R.; Su, R.
1995-01-01
An iterative procedure is proposed for computing the commanded state trajectories and controls that guide a possibly multiaxis, time-varying, nonlinear system with transmission zero dynamics through a given arbitrary sequence of control points. The procedure is initialized by the system inverse with the transmission zero effects nulled out. Then the 'steady state' solution of the perturbation model with the transmission zero dynamics intact is computed and used to correct the initial zero-free solution. Both time domain and frequency domain methods are presented for computing the steady state solutions of the possibly nonminimum phase transmission zero dynamics. The procedure is illustrated by means of linear and nonlinear examples.
From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity
NASA Astrophysics Data System (ADS)
Okuyama, Manaka; Takahashi, Kazutaka
2016-08-01
Using shortcuts to adiabaticity, we solve the time-dependent Schrödinger equation that is reduced to a classical nonlinear integrable equation. For a given time-dependent Hamiltonian, the counterdiabatic term is introduced to prevent nonadiabatic transitions. Using the fact that the equation for the dynamical invariant is equivalent to the Lax equation in nonlinear integrable systems, we obtain the counterdiabatic term exactly. The counterdiabatic term is available when the corresponding Lax pair exists and the solvable systems are classified in a unified and systematic way. Multisoliton potentials obtained from the Korteweg-de Vries equation and isotropic X Y spin chains from the Toda equations are studied in detail.
NASA Technical Reports Server (NTRS)
Gunderson, R. W.
1975-01-01
A comparison principle based on a Kamke theorem and Lipschitz conditions is presented along with its possible applications and modifications. It is shown that the comparison lemma can be used in the study of such areas as classical stability theory, higher order trajectory derivatives, Liapunov functions, boundary value problems, approximate dynamic systems, linear and nonlinear systems, and bifurcation analysis.
Guidance of Nonlinear Nonminimum-Phase Dynamic Systems
NASA Technical Reports Server (NTRS)
Devasia, Santosh
1996-01-01
The research work has advanced the inversion-based guidance theory for: systems with non-hyperbolic internal dynamics; systems with parameter jumps; and systems where a redesign of the output trajectory is desired. A technique to achieve output tracking for nonminimum phase linear systems with non-hyperbolic and near non-hyperbolic internal dynamics was developed. This approach integrated stable inversion techniques, that achieve exact-tracking, with approximation techniques, that modify the internal dynamics to achieve desirable performance. Such modification of the internal dynamics was used (a) to remove non-hyperbolicity which is an obstruction to applying stable inversion techniques and (b) to reduce large preactuation times needed to apply stable inversion for near non-hyperbolic cases. The method was applied to an example helicopter hover control problem with near non-hyperbolic internal dynamics for illustrating the trade-off between exact tracking and reduction of preactuation time. Future work will extend these results to guidance of nonlinear non-hyperbolic systems. The exact output tracking problem for systems with parameter jumps was considered. Necessary and sufficient conditions were derived for the elimination of switching-introduced output transient. While previous works had studied this problem by developing a regulator that maintains exact tracking through parameter jumps (switches), such techniques are, however, only applicable to minimum-phase systems. In contrast, our approach is also applicable to nonminimum-phase systems and leads to bounded but possibly non-causal solutions. In addition, for the case when the reference trajectories are generated by an exosystem, we developed an exact-tracking controller which could be written in a feedback form. As in standard regulator theory, we also obtained a linear map from the states of the exosystem to the desired system state, which was defined via a matrix differential equation.
Accelerator-feasible N -body nonlinear integrable system
NASA Astrophysics Data System (ADS)
Danilov, V.; Nagaitsev, S.
2014-12-01
Nonlinear N -body integrable Hamiltonian systems, where N is an arbitrary number, have attracted the attention of mathematical physicists for the last several decades, following the discovery of some number of these systems. This paper presents a new integrable system, which can be realized in facilities such as particle accelerators. This feature makes it more attractive than many of the previous such systems with singular or unphysical forces.