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. PMID:26285223
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. PMID:18255659
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.
Reduced bases for nonlinear structural dynamic systems: A comparative study
NASA Astrophysics Data System (ADS)
Lülf, Fritz Adrian; Tran, Duc-Minh; Ohayon, Roger
2013-07-01
The presented work provides an overview of some commonly used approaches for generating reduced bases for discrete nonlinear dynamic systems. It investigates the performance and the robustness of these bases if they are applied in a reduction-by-projection procedure on different test cases. The bases are created from the Linear Normal Modes, the Ritz-vectors, the Proper and the Smooth Orthogonal Decomposition method, the A Priori Reduction, the Centroidal Voronoi Tessellation and the Local Equivalent Linear Stiffness Method. Second-Order Terms and an Enhanced Proper Orthogonal Decomposition formulation are included as variants. The test cases are small dimensional, locally or entirely nonlinear system subjected to a harmonic or an impulse force excitation. The double objective of this numerical study is, first, to determine which bases are most adequate for a given combination of nonlinearity and excitation and, second, to which extend the bases exhibit an inherent robustness if the parameterisation of the excitation is changed. A specific multicriteria decision analysis score is developed to assess the bases' performance. As a major result, a strong dependence of the performance of the bases on the type of excitation is established and thus some bases become more adequate for a certain situation than others. Also a lack of robustness for all considered bases can be observed. This situation improves in most cases if the basis is generated with the most critical values of the parameter.
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.
Hybrid time-frequency domain equalization for LED nonlinearity mitigation in OFDM-based VLC systems.
Li, Jianfeng; Huang, Zhitong; Liu, Xiaoshuang; Ji, Yuefeng
2015-01-12
A novel hybrid time-frequency domain equalization scheme is proposed and experimentally demonstrated to mitigate the white light emitting diode (LED) nonlinearity in visible light communication (VLC) systems based on orthogonal frequency division multiplexing (OFDM). We handle the linear and nonlinear distortion separately in a nonlinear OFDM system. The linear part is equalized in frequency domain and the nonlinear part is compensated by an adaptive nonlinear time domain equalizer (N-TDE). The experimental results show that with only a small number of parameters the nonlinear equalizer can efficiently mitigate the LED nonlinearity. With the N-TDE the modulation index (MI) and BER performance can be significantly enhanced. PMID:25835706
General purpose nonlinear system solver based on Newton-Krylov method.
Energy Science and Technology Software Center (ESTSC)
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].
Simulation-based optimal Bayesian experimental design for nonlinear systems
Huan, Xun; Marzouk, Youssef M.
2013-01-01
The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general mathematical framework and an algorithmic approach for optimal experimental design with nonlinear simulation-based models; in particular, we focus on finding sets of experiments that provide the most information about targeted sets of parameters. Our framework employs a Bayesian statistical setting, which provides a foundation for inference from noisy, indirect, and incomplete data, and a natural mechanism for incorporating heterogeneous sources of information. An objective function is constructed from information theoretic measures, reflecting expected information gain from proposed combinations of experiments. Polynomial chaos approximations and a two-stage Monte Carlo sampling method are used to evaluate the expected information gain. Stochastic approximation algorithms are then used to make optimization feasible in computationally intensive and high-dimensional settings. These algorithms are demonstrated on model problems and on nonlinear parameter inference problems arising in detailed combustion kinetics.
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.
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
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
NASA Astrophysics Data System (ADS)
Li, Heng; Ren, Changzhi; Song, Libin; Wu, Jun
2014-07-01
The direct drive tracking system of Telescope is one multivariable, nonlinear and strong coupling complex mechanical control system which is disturbed by some nonlinear disturbance such torque ripple, wind disturbance during the tracking process. the traditional PID control cannot fundamentally solved the contradiction between static and dynamic performance, tracking data and disturbance .This paper explores a kind of CMAC with nonlinear PID parallel composite control method for dual redundant telescope tracing servo system. The simulation result proves that combined algorithm based on CMAC and PID realizes the servo system without overshoot and accelerates the response of the system. What's more, CMAC feedforward control improves anti-disturbance ability and the control precision of the servo system.
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. PMID:23757525
Leveraging nonlinear saturation-based phenomena in an L-shaped vibration energy harvesting system
NASA Astrophysics Data System (ADS)
Harne, R. L.; Sun, A.; Wang, K. W.
2016-02-01
Trees exploit intriguing mechanisms such as multimodal frequency distributions and nonlinearities to distribute and dampen the aerodynamically-induced vibration energies to which they are subjected. In dynamical systems, these mechanisms are comparable to internal resonance phenomena. In recent years, researchers have harnessed strong nonlinearities, including internal resonance, to induce energetic dynamics that enhance performance of vibration energy harvesting systems. For trees, the internal resonance-like dynamics are evidently useful to dampen swaying motions in spite of the high variation associated with excitation and structural parameters. Yet for dynamic systems, studies show narrow operating regimes which exhibit internal resonance-based behaviors; this additionally suggests that the energetic dynamics may be susceptible to deactivation if stochastic inputs corrupt ideal excitation properties. To address these issues and to investigate whether the underlying motivation of exploiting internal resonance-induced saturation dynamics is truly justified, this research evaluates the opportunities enabled by exploiting nonlinear, multimodal motions in an L-shaped energy harvester platform. The system dynamics are probed analytically, numerically, and experimentally for comprehensive insights on the versatility of internal resonance-based behaviors for energy harvesting. It is found that although activating the high amplitude nonlinear dynamics to enhance power generation is robust to significant additive noise in the harmonic excitations, parameter sensitivities may pose practical challenges in application. Discussion is provided on means to address such concerns and on future strategies that may favorably exploit nonlinearity and multimodal dynamics for robust energy harvesting performance.
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. PMID:25277626
Fuzzy rule base design using tabu search algorithm for nonlinear system modeling.
Bagis, Aytekin
2008-01-01
This paper presents an approach to fuzzy rule base design using tabu search algorithm (TSA) for nonlinear system modeling. TSA is used to evolve the structure and the parameter of fuzzy rule base. The use of the TSA, in conjunction with a systematic neighbourhood structure for the determination of fuzzy rule base parameters, leads to a significant improvement in the performance of the model. To demonstrate the effectiveness of the presented method, several numerical examples given in the literature are examined. The results obtained by means of the identified fuzzy rule bases are compared with those belonging to other modeling approaches in the literature. The simulation results indicate that the method based on the use of a TSA performs an important and very effective modeling procedure in fuzzy rule base design in the modeling of the nonlinear or complex systems. PMID:17945233
NASA Astrophysics Data System (ADS)
Liu, Derong; Huang, Yuzhu; Wang, Ding; Wei, Qinglai
2013-09-01
In this paper, an observer-based optimal control scheme is developed for unknown nonlinear systems using adaptive dynamic programming (ADP) algorithm. First, a neural-network (NN) observer is designed to estimate system states. Then, based on the observed states, a neuro-controller is constructed via ADP method to obtain the optimal control. In this design, two NN structures are used: a three-layer NN is used to construct the observer which can be applied to systems with higher degrees of nonlinearity and without a priori knowledge of system dynamics, and a critic NN is employed to approximate the value function. The optimal control law is computed using the critic NN and the observer NN. Uniform ultimate boundedness of the closed-loop system is guaranteed. The actor, critic, and observer structures are all implemented in real-time, continuously and simultaneously. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control scheme.
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
Nonlinear adaptive control systems design of BTT missile based on fully tuned RBF neural networks
NASA Astrophysics Data System (ADS)
Hu, Yunan; Jin, Yuqiang; Li, Jing
2003-09-01
Based on fully tuned RBF neural networks and backstepping control techniques, a novel nonlinear adaptive control scheme is proposed for missile control systems with a general set of uncertainties. The effect of the uncertainties is synthesized one term in the design procedure. Then RBF neural networks are used to eliminate its effect. The nonlinear adaptive controller is designed using backstepping control techniques. The control problem is resolved while the control coefficient matrix is unknown. The adaptive tuning rules for updating all of the parameters of the fully tuned RBF neural networks are firstly derived by the Lyapunov stability theorem. Finally, nonlinear 6-DOF numerical simulation results for a BTT missile model are presented to demonstrate the effectiveness of the proposed method.
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
Fernández de Cañete, J; Barreiro, A; García-Cerezo, A; García-Moral, I
2001-01-01
A stabilization method based on the input-output conicity criterion is presented. Conventional learning algorithms are applied to adjust the controller dynamics, and robust stability of the closed-loop system is guaranteed by modifying the training patterns which yield unstable behavior. The methodology developed expands the class of nonlinear systems to be controlled using neural control schemes, so that the stabilization of a broad class of neural-network-based control systems, even with unknown dynamics, is assured. Straightforwardness in the application of this method is evident in contrast to the Lyapunov function approach. PMID:18249978
Fault detection in non-linear systems based on type-2 fuzzy logic
NASA Astrophysics Data System (ADS)
Safarinejadian, Behrooz; Ghane, Parisa; Monirvaghefi, Hossein
2015-02-01
This paper presents a new method for fault detection (FD) based on interval type-2 fuzzy sets. The main idea is based on a confident span using interval type-2 fuzzy systems. An estimate for upper and lower bounds of output has been taken using the designing of an optimal fuzzy system through clustering. Finally the method has been tested in two non-linear systems, a two-tank with a fluid flow and pH neutralisation process, and it is compared with a well-known method named ANFIS. Furthermore, the mathematical model and the results of simulations prove the effectiveness, usefulness and applications of our new method.
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. PMID:23672740
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
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.
Nonparametric identification of nonlinear dynamic systems using a synchronisation-based method
NASA Astrophysics Data System (ADS)
Kenderi, Gábor; Fidlin, Alexander
2014-12-01
The present study proposes an identification method for highly nonlinear mechanical systems that does not require a priori knowledge of the underlying nonlinearities to reconstruct arbitrary restoring force surfaces between degrees of freedom. This approach is based on the master-slave synchronisation between a dynamic model of the system as the slave and the real system as the master using measurements of the latter. As the model synchronises to the measurements, it becomes an observer of the real system. The optimal observer algorithm in a least-squares sense is given by the Kalman filter. Using the well-known state augmentation technique, the Kalman filter can be turned into a dual state and parameter estimator to identify parameters of a priori characterised nonlinearities. The paper proposes an extension of this technique towards nonparametric identification. A general system model is introduced by describing the restoring forces as bilateral spring-dampers with time-variant coefficients, which are estimated as augmented states. The estimation procedure is followed by an a posteriori statistical analysis to reconstruct noise-free restoring force characteristics using the estimated states and their estimated variances. Observability is provided using only one measured mechanical quantity per degree of freedom, which makes this approach less demanding in the number of necessary measurement signals compared with truly nonparametric solutions, which typically require displacement, velocity and acceleration signals. Additionally, due to the statistical rigour of the procedure, it successfully addresses signals corrupted by significant measurement noise. In the present paper, the method is described in detail, which is followed by numerical examples of one degree of freedom (1DoF) and 2DoF mechanical systems with strong nonlinearities of vibro-impact type to demonstrate the effectiveness of the proposed technique.
NASA Astrophysics Data System (ADS)
Maboodi, M.; Khaki-Sedigh, A.; Camacho, E. F.
2015-08-01
In this paper, control performance assessment for a class of nonlinear systems modelled by autoregressive second-order Volterra series with a general linear additive disturbance is presented. The proposed approach employs the nonlinear generalised minimum variance (NGMV) controller concept. The Volterra series models provide a natural extension of a linear convolution model with the nonlinearity considered in an additive term. The polynomial operator form is used throughout this paper for the description of the system input-output model. The closed form formulation of NGMV controller for autoregressive second-order Volterra series is presented in a polynomial form then a control assessment criterion based on the NGMV control is given. Simulation results and comparison studies are used to show the effectiveness of the proposed approach for a class of nonlinear systems.
Deng, Hua; Li, Han-Xiong; Wu, Yi-Hu
2008-09-01
A new feedback-linearization-based neural network (NN) adaptive control is proposed for unknown nonaffine nonlinear discrete-time systems. An equivalent model in affine-like form is first derived for the original nonaffine discrete-time systems as feedback linearization methods cannot be implemented for such systems. Then, feedback linearization adaptive control is implemented based on the affine-like equivalent model identified with neural networks. Pretraining is not required and the weights of the neural networks used in adaptive control are directly updated online based on the input-output measurement. The dead-zone technique is used to remove the requirement of persistence excitation during the adaptation. With the proposed neural network adaptive control, stability and performance of the closed-loop system are rigorously established. Illustrated examples are provided to validate the theoretical findings. PMID:18779092
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.
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.
Kokil, Priyanka
2014-01-01
A linear matrix inequality (LMI) based criterion for the global asymptotic stability of discrete-time systems with multiple state-delays employing saturation nonlinearities is presented. Numerical examples highlighting the effectiveness of the proposed criterion are given.
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.
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. PMID:25312944
Embedded algorithms within an FPGA-based system to process nonlinear time series data
NASA Astrophysics Data System (ADS)
Jones, Jonathan D.; Pei, Jin-Song; Tull, Monte P.
2008-03-01
This paper presents some preliminary results of an ongoing project. A pattern classification algorithm is being developed and embedded into a Field-Programmable Gate Array (FPGA) and microprocessor-based data processing core in this project. The goal is to enable and optimize the functionality of onboard data processing of nonlinear, nonstationary data for smart wireless sensing in structural health monitoring. Compared with traditional microprocessor-based systems, fast growing FPGA technology offers a more powerful, efficient, and flexible hardware platform including on-site (field-programmable) reconfiguration capability of hardware. An existing nonlinear identification algorithm is used as the baseline in this study. The implementation within a hardware-based system is presented in this paper, detailing the design requirements, validation, tradeoffs, optimization, and challenges in embedding this algorithm. An off-the-shelf high-level abstraction tool along with the Matlab/Simulink environment is utilized to program the FPGA, rather than coding the hardware description language (HDL) manually. The implementation is validated by comparing the simulation results with those from Matlab. In particular, the Hilbert Transform is embedded into the FPGA hardware and applied to the baseline algorithm as the centerpiece in processing nonlinear time histories and extracting instantaneous features of nonstationary dynamic data. The selection of proper numerical methods for the hardware execution of the selected identification algorithm and consideration of the fixed-point representation are elaborated. Other challenges include the issues of the timing in the hardware execution cycle of the design, resource consumption, approximation accuracy, and user flexibility of input data types limited by the simplicity of this preliminary design. Future work includes making an FPGA and microprocessor operate together to embed a further developed algorithm that yields better
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.
An Ensemble-Based Smoother with Retrospectively Updated Weights for Highly Nonlinear Systems
NASA Technical Reports Server (NTRS)
Chin, T. M.; Turmon, M. J.; Jewell, J. B.; Ghil, M.
2006-01-01
Monte Carlo computational methods have been introduced into data assimilation for nonlinear systems in order to alleviate the computational burden of updating and propagating the full probability distribution. By propagating an ensemble of representative states, algorithms like the ensemble Kalman filter (EnKF) and the resampled particle filter (RPF) rely on the existing modeling infrastructure to approximate the distribution based on the evolution of this ensemble. This work presents an ensemble-based smoother that is applicable to the Monte Carlo filtering schemes like EnKF and RPF. At the minor cost of retrospectively updating a set of weights for ensemble members, this smoother has demonstrated superior capabilities in state tracking for two highly nonlinear problems: the double-well potential and trivariate Lorenz systems. The algorithm does not require retrospective adaptation of the ensemble members themselves, and it is thus suited to a streaming operational mode. The accuracy of the proposed backward-update scheme in estimating non-Gaussian distributions is evaluated by comparison to the more accurate estimates provided by a Markov chain Monte Carlo algorithm.
A new active variable stiffness suspension system using a nonlinear energy sink-based controller
NASA Astrophysics Data System (ADS)
Anubi, Olugbenga Moses; Crane, Carl D.
2013-10-01
This paper presents the active case of a variable stiffness suspension system. The central concept is based on a recently designed variable stiffness mechanism which consists of a horizontal control strut and a vertical strut. The horizontal strut is used to vary the load transfer ratio by actively controlling the location of the point of attachment of the vertical strut to the car body. The control algorithm, effected by a hydraulic actuator, uses the concept of nonlinear energy sink (NES) to effectively transfer the vibrational energy in the sprung mass to a control mass, thereby reducing the transfer of energy from road disturbance to the car body at a relatively lower cost compared to the traditional active suspension using the skyhook concept. The analyses and simulation results show that a better performance can be achieved by subjecting the point of attachment of a suspension system, to the chassis, to the influence of a horizontal NES system.
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. PMID:24808600
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. PMID:26404514
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
NASA Technical Reports Server (NTRS)
Meyer, George
1997-01-01
The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of way points through which the aircraft trajectory must pass. The way points typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory which satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multi-dimensional, multi-axis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of possible operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordinatization, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions must be smooth. The guidance algorithm is based on the inversion of the pure feedback approximations, which is followed by iterative corrections for the effects of zero dynamics. The paper describes the structure and modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.
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. PMID:25594991
An adaptive critic-based scheme for consensus control of nonlinear multi-agent systems
NASA Astrophysics Data System (ADS)
Heydari, Ali; Balakrishnan, S. N.
2014-12-01
The problem of decentralised consensus control of a network of heterogeneous nonlinear systems is formulated as an optimal tracking problem and a solution is proposed using an approximate dynamic programming based neurocontroller. The neurocontroller training comprises an initial offline training phase and an online re-optimisation phase to account for the fact that the reference signal subject to tracking is not fully known and available ahead of time, i.e., during the offline training phase. As long as the dynamics of the agents are controllable, and the communication graph has a directed spanning tree, this scheme guarantees the synchronisation/consensus even under switching communication topology and directed communication graph. Finally, an aerospace application is selected for the evaluation of the performance of the method. Simulation results demonstrate the potential of the scheme.
Aggregation-based fuzzy dual-mode control for nonlinear systems with mixed constraints
NASA Astrophysics Data System (ADS)
Wen, Jiwei; Liu, Fei
2012-05-01
A new receding horizon dual-mode control method is proposed for a class of discrete-time nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy models subject to mixed constraints including hard input constraint and soft state constraint. On the one hand, our receding horizon scheme is based upon an online optimisation that utilises optimised sequence plus local linear feedback. On the other hand, due to the consideration of computation burden, an amplitude decaying aggregation strategy is introduced to reduce the number of optimisation variables. The proposed controller is obtained using semi-definite programming, which can be easily solved by means of linear matrix inequalities. A numerical example is given to verify the feasibility and efficiency of the proposed method.
Dr. Katja Lindenberg
2005-11-20
During the one-year period 2004-2005 our work continued to focus on nonlinear noisy systems, with special attention to spatially extended systems. There is a history of many decades of research in the sciences and engineering on the behavior of noninear noisy systems, but only in the past ten years or so has a theoretical understanding of spatially extended systems begun to emerge. This has been the outcome of a symbiosis of numerical simulations not possible until recently, laboratory experiments, and new analytic methods.
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.
Neural network modeling of nonlinear systems based on Volterra series extension of a linear model
NASA Technical Reports Server (NTRS)
Soloway, Donald I.; Bialasiewicz, Jan T.
1992-01-01
A Volterra series approach was applied to the identification of nonlinear systems which are described by a neural network model. A procedure is outlined by which a mathematical model can be developed from experimental data obtained from the network structure. Applications of the results to the control of robotic systems are discussed.
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.
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. PMID:25720004
NASA Astrophysics Data System (ADS)
Smolders, K.; Volckaert, M.; Swevers, J.
2008-11-01
This paper presents a nonlinear model-based iterative learning control procedure to achieve accurate tracking control for nonlinear lumped mechanical continuous-time systems. The model structure used in this iterative learning control procedure is new and combines a linear state space model and a nonlinear feature space transformation. An intuitive two-step iterative algorithm to identify the model parameters is presented. It alternates between the estimation of the linear and the nonlinear model part. It is assumed that besides the input and output signals also the full state vector of the system is available for identification. A measurement and signal processing procedure to estimate these signals for lumped mechanical systems is presented. The iterative learning control procedure relies on the calculation of the input that generates a given model output, so-called offline model inversion. A new offline nonlinear model inversion method for continuous-time, nonlinear time-invariant, state space models based on Newton's method is presented and applied to the new model structure. This model inversion method is not restricted to minimum phase models. It requires only calculation of the first order derivatives of the state space model and is applicable to multivariable models. For periodic reference signals the method yields a compact implementation in the frequency domain. Moreover it is shown that a bandwidth can be specified up to which learning is allowed when using this inversion method in the iterative learning control procedure. Experimental results for a nonlinear single-input-single-output system corresponding to a quarter car on a hydraulic test rig are presented. It is shown that the new nonlinear approach outperforms the linear iterative learning control approach which is currently used in the automotive industry on durability test rigs.
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.
Chen, Zheng; Jagannathan, Sarangapani
2008-01-01
In this paper, we consider the use of nonlinear networks towards obtaining nearly optimal solutions to the control of nonlinear discrete-time (DT) systems. The method is based on least squares successive approximation solution of the generalized Hamilton-Jacobi-Bellman (GHJB) equation which appears in optimization problems. Successive approximation using the GHJB has not been applied for nonlinear DT systems. The proposed recursive method solves the GHJB equation in DT on a well-defined region of attraction. The definition of GHJB, pre-Hamiltonian function, HJB equation, and method of updating the control function for the affine nonlinear DT systems under small perturbation assumption are proposed. A neural network (NN) is used to approximate the GHJB solution. It is shown that the result is a closed-loop control based on an NN that has been tuned a priori in offline mode. Numerical examples show that, for the linear DT system, the updated control laws will converge to the optimal control, and for nonlinear DT systems, the updated control laws will converge to the suboptimal control. PMID:18269941
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.
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.
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.
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. PMID:27187937
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. PMID:18632390
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. PMID:24156668
Nonlinearity modelling of an on-board microwave photonics system based on Mach-Zehnder modulator
NASA Astrophysics Data System (ADS)
Zhu, Zi-hang; Zhao, Shang-hong; Yao, Zhou-shi; Tan, Qing-gui; Li, Yong-jun; Chu, Xing-chun; Wang, Xiang; Zhao, Gu-hao
2012-11-01
For the nonlinearity distortion problem of Mach-Zehnder modulator (MZM) applied in the on-board microwave photonics system, the situation for two input radio frequency (RF) signals with different frequencies and phases is discussed, and an exact analytical solution is derived with the method of expanding Bessel series and Graf addition theory. According to the analytical expression, the nonlinearity characteristics of the modulator can be precisely predicted, and the system performance can be optimized. The correctness of the analytical solution is approved by simulation results. Analytical results indicate that the nonlinearity distortion is suppressed as the decrease of modulation index, the increase of direct current bias phase shift and phase difference between two input RF signals. When the phase difference equals zero or π and the direct current bias phase shift is π/2, there are only odd-order distortion terms. When the phase difference equals zero or π and the direct current bias phase shift is π, there are only even-order distortion terms.
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 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.
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. PMID:25898325
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.
IMAGE-BASED VISUAL SERVOING FOR ROBOTIC SYSTEMS: A NONLINEAR LYAPUNOV-BASED CONTROL APPROACH
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 devel...
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.
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. PMID:23012525
SOS based robust H(∞) fuzzy dynamic output feedback control of nonlinear networked control systems.
Chae, Seunghwan; Nguang, Sing Kiong
2014-07-01
In this paper, a methodology for designing a fuzzy dynamic output feedback controller for discrete-time nonlinear networked control systems is presented where the nonlinear plant is modelled by a Takagi-Sugeno fuzzy model and the network-induced delays by a finite state Markov process. The transition probability matrix for the Markov process is allowed to be partially known, providing a more practical consideration of the real world. Furthermore, the fuzzy controller's membership functions and premise variables are not assumed to be the same as the plant's membership functions and premise variables, that is, the proposed approach can handle the case, when the premise of the plant are not measurable or delayed. The membership functions of the plant and the controller are approximated as polynomial functions, then incorporated into the controller design. Sufficient conditions for the existence of the controller are derived in terms of sum of square inequalities, which are then solved by YALMIP. Finally, a numerical example is used to demonstrate the validity of the proposed methodology. PMID:24108002
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. PMID:26357411
Nonlinear model for building-soil systems
McCallen, D.B.; Romstad, K.M.
1994-05-01
A finite-element based, numerical analysis methodology has been developed for the nonlinear analysis of building-soil systems. The methodology utilizes a reduced-order, nonlinear continuum model to represent the building, and the soil is represented with a simple nonlinear two-dimensional plane strain finite element. The foundation of the building is idealized as a rigid block and the interface between the soil and the foundation is modeled with an interface contract element. The objectives of the current paper are to provide the theoretical development of the system model, with particular emphasis on the modeling of the foundation-soil contact, and to demonstrate the special-purpose finite-element program that has been developed for nonlinear analysis of the building-soil system. Examples are included that compare the results obtained with the special-purpose program with the results of a general-purpose nonlinear finite-element program.
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)
Ko, Alex C. T.; Ridsdale, Andrew; Pegoraro, Adrian F.; Smith, Michael S. D.; Mostaço-Guidolin, Leila B.; Hewko, Mark D.; Kohlenberg, Elicia M.; Schattka, Bernie J.; Shiomi, Masashi; Stolow, Albert; Sowa, Michael G.
2009-02-01
Nonlinear optical (NLO) microscopy provides a minimally invasive optical method for fast molecular imaging at subcellular resolution with 3D sectioning capability in thick, highly scattering biological tissues. In the current study, we demonstrate the imaging of arterial tissue using a nonlinear optical microscope based on photonic crystal fiber and a single femto-second oscillator operating at 800nm. This NLO microscope system is capable of simultaneous imaging extracellular elastin/collagen structures and lipid distribution within aortic tissue obtained from coronary atherosclerosis-prone WHHLMI rabbits (Watanabe heritable hyperlipidemic rabbit-myocardial infarction) Clear pathological differences in arterial lumen surface were observed between healthy arterial tissue and atherosclerotic lesions through NLO imaging.
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.
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.
Chin, Sanghooon; Gonzalez-Herraez, Miguel; Thévenaz, Luc
2009-11-23
We experimentally demonstrate complete compensation of pulse broadening in an amplifier-based slow light system. The configuration of the delay line basically consists of two stages: a conventional Brillouin slow light system and a nonlinear regeneration element. Signal pulses experienced both time delay and temporal broadening through the Brillouin delay line and then the delayed pulses were delivered into a nonlinear optical loop mirror. Due to the nonlinear response of the transmission of the fiber loop, the inevitably broadened pulses were moderately compressed in the output of the loop, without loss in the capacity to delay the pulses. The overall result is that, for the maximum delay, the width of the pulse could be kept below the input width while the time delays introduced by the slow light element were preserved. Using this delay line, a signal pulse with duration of 27 ns at full width at half maximum was delayed up to 1.3-bits without suffering from signal distortion. PMID:19997435
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.
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.
Nonlinear dynamical systems analyzer
NASA Astrophysics Data System (ADS)
Coffey, Adrian S.; Johnson, Martin; Jones, Robin
1994-10-01
Computationally intensive algorithms are an ever more common requirement of modern signal processing. Following the work of Gentleman and Kung, McWhirter, Shepherd and Proudler suggested that certain matrix-orientated algorithms can be mapped onto systolic array architectures for adaptive linear signal processing. This has been extended by Broomhead et al. to the calculation of nonlinear predictive models and applied by Jones et al. to target identification and recognition. We shall show that predictive models are extremely sharp discriminators. Our chosen problem, if implemented as a systolic array, would require 3403 processors which would result in high through-put rate at excessive cost. We are developing an efficient sub-optimally implemented systolic array; one processor servicing more than one systolic node. We describe a prototype Heuristic Processor which computes a multi- dimensional, nonlinear, predictive model. It consists of a Radial Basis Function Network and a least squares optimizer using QR decomposition. The optimized solution of a set of simultaneous equations in 81 unknowns is calculated in 150 (mu) S. The QR section emulates a triangular systolic array by the novel use of an array of 40 mature silicon DSP chips costing under DOL100 each. The DSP chips operate in synchronism at a 50 MHz clock rate passing data to each other through multi-port memories on a dead-letter box principle; there are no memory access conflicts and only two-port and three-port memories are required. The processor provides 1-GFlop of computing power per cubic-foot of electronics for a component cost of approximately DOL15,000.
Canonical forms for nonlinear systems
NASA Technical Reports Server (NTRS)
Su, R.; Hunt, L. R.; Meyer, G.
1983-01-01
Necessary and sufficient conditions for transforming a nonlinear system to a controllable linear system have been established, and this theory has been applied to the automatic flight control of aircraft. These transformations show that the nonlinearities in a system are often not intrinsic, but are the result of unfortunate choices of coordinates in both state and control variables. Given a nonlinear system (that may not be transformable to a linear system), we construct a canonical form in which much of the nonlinearity is removed from the system. If a system is not transformable to a linear one, then the obstructions to the transformation are obvious in canonical form. If the system can be transformed (it is called a linear equivalent), then the canonical form is a usual one for a controllable linear system. Thus our theory of canonical forms generalizes the earlier transformation (to linear systems) results. Our canonical form is not unique, except up to solutions of certain partial differential equations we discuss. In fact, the important aspect of this paper is the constructive procedure we introduce to reach the canonical form. As is the case in many areas of mathematics, it is often easier to work with the canonical form than in arbitrary coordinate variables.
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.
HGO-based decentralised indirect adaptive fuzzy control for a class of large-scale nonlinear systems
NASA Astrophysics Data System (ADS)
Huang, Yi-Shao; Chen, Xiaoxin; Zhou, Shao-Wu; Yu, Ling-Li; Wang, Zheng-Wu
2012-06-01
In this article, a novel high gain observer (HGO)-based decentralised indirect adaptive fuzzy controller is developed for a class of uncertain affine large-scale nonlinear systems. By the combination of fuzzy logic systems and an HGO, the state variables are not required to be measurable. The proposed feedback and adaptation mechanisms guarantee that each subsystem is able to adaptively compensate for interconnections and disturbances with unknown bounds. It is ascertained using a singular perturbation method that all the signals of the closed-loop large-scale system stand uniformly ultimately bounded and the tracking errors converge to tunable neighbourhoods of the origin. Simulation results of correlated double inverted pendulums substantiate the effectiveness of the proposed controller.
NASA Astrophysics Data System (ADS)
Shukla, Amit; Bailey Van Kuren, Michael
2004-07-01
A neonatal transport cart is used by hospitals to transport critical infants. The ride during ground transportation generates severe vibrations which have been found to adversely affect the infant's physiological symptoms. This work is the first attempt to design a vibration isolation system using magneto-rheological fluid damper-based suspension system for the neonatal transport cart. In this paper the effect of various system and control parameters on the two-degree-of-freedom model are numerically studied for parametric bifurcation stability behavior. It is shown that system can undergo loss of stability via Hopf bifurcation and exhibit limit cycle oscillations which is counter to the goal of the proposed suspension design.
Image encryption based on nonlinear encryption system and public-key cryptography
NASA Astrophysics Data System (ADS)
Zhao, Tieyu; Ran, Qiwen; Chi, Yingying
2015-03-01
Recently, optical asymmetric cryptosystem (OACS) has became the focus of discussion and concern of researchers. Some researchers pointed out that OACS was not tenable because of misunderstanding the concept of asymmetric cryptosystem (ACS). We propose an improved cryptosystem using RSA public-key algorithm based on existing OACS and the new system conforms to the basic agreement of public key cryptosystem. At the beginning of the encryption process, the system will produce an independent phase matrix and allocate the input image, which also conforms to one-time pad cryptosystem. The simulation results show that the validity of the improved cryptosystem and the high robustness against attack scheme using phase retrieval technique.
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.
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.
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. PMID:26520069
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. PMID:18701368
Impulsive synchronization of networked nonlinear dynamical systems
NASA Astrophysics Data System (ADS)
Jiang, Haibo; Bi, Qinsheng
2010-06-01
In this Letter, we investigate the problem of impulsive synchronization of networked multi-agent systems, where each agent can be modeled as an identical nonlinear dynamical system. Firstly, an impulsive control protocol is designed for network with fixed topology based on the local information of agents. Then sufficient conditions are given to guarantee the synchronization of the networked nonlinear dynamical system by using algebraic graph theory and impulsive control theory. Furthermore, how to select the discrete instants and impulsive constants is discussed. The case that the topologies of the networks are switching is also considered. Numerical simulations show the effectiveness of our theoretical results.
Nonlinear input-output systems
NASA Technical Reports Server (NTRS)
Hunt, L. R.; Luksic, Mladen; Su, Renjeng
1987-01-01
Necessary and sufficient conditions that the nonlinear system dot-x = f(x) + ug(x) and y = h(x) be locally feedback equivalent to the controllable linear system dot-xi = A xi + bv and y = C xi having linear output are found. Only the single input and single output case is considered, however, the results generalize to multi-input and multi-output systems.
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.
NASA Astrophysics Data System (ADS)
Sznitko, Lech; Mysliwiec, Jaroslaw; Karpinski, Pawel; Palewska, Krystyna; Parafiniuk, Kacper; Bartkiewicz, Stanislaw; Rau, Ileana; Kajzar, Francois; Miniewicz, Andrzej
2011-07-01
In this paper, we present results of detailed studies on amplified spontaneous emission (ASE) and lasing achieved in a double-layer system consisted of a biopolymer based matrix loaded with 3-(1,1-dicyanoethenyl1)-1phenyl-4,5dihydro-1H-pyrazole organic nonlinear optical dye and photochromic polymer. The laser action was achieved via distributed feedback configuration with third order of Bragg scattering on surface relief grating generated in photochromic polymer. To excite the luminescence, we have used 6 ns pulses of Nd:YAG laser at 532 nm. The ASE and lasing thresholds were estimated to be 17 mJ/cm2 and 11 mJ/cm2, respectively.
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. PMID:25720005
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. PMID:24807443
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
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.
NASA Astrophysics Data System (ADS)
Pai, P. Frank
2011-10-01
Presented here is a new time-frequency signal processing methodology based on Hilbert-Huang transform (HHT) and a new conjugate-pair decomposition (CPD) method for characterization of nonlinear normal modes and parametric identification of nonlinear multiple-degree-of-freedom dynamical systems. Different from short-time Fourier transform and wavelet transform, HHT uses the apparent time scales revealed by the signal's local maxima and minima to sequentially sift components of different time scales. Because HHT does not use pre-determined basis functions and function orthogonality for component extraction, it provides more accurate time-varying amplitudes and frequencies of extracted components for accurate estimation of system characteristics and nonlinearities. CPD uses adaptive local harmonics and function orthogonality to extract and track time-localized nonlinearity-distorted harmonics without the end effect that destroys the accuracy of HHT at the two data ends. For parametric identification, the method only needs to process one steady-state response (a free undamped modal vibration or a steady-state response to a harmonic excitation) and uses amplitude-dependent dynamic characteristics derived from perturbation analysis to determine the type and order of nonlinearity and system parameters. A nonlinear two-degree-of-freedom system is used to illustrate the concepts and characterization of nonlinear normal modes, vibration localization, and nonlinear modal coupling. Numerical simulations show that the proposed method can provide accurate time-frequency characterization of nonlinear normal modes and parametric identification of nonlinear dynamical systems. Moreover, results show that nonlinear modal coupling makes it impossible to decompose a general nonlinear response of a highly nonlinear system into nonlinear normal modes even if nonlinear normal modes exist in the system.
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. PMID:25704057
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. PMID:25415951
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. PMID:26456728
Nonlinear estimation-based dipole source localization for artificial lateral line systems.
Abdulsadda, Ahmad T; Tan, Xiaobo
2013-06-01
As a flow-sensing organ, the lateral line system plays an important role in various behaviors of fish. An engineering equivalent of a biological lateral line is of great interest to the navigation and control of underwater robots and vehicles. A vibrating sphere, also known as a dipole source, can emulate the rhythmic movement of fins and body appendages, and has been widely used as a stimulus in the study of biological lateral lines. Dipole source localization has also become a benchmark problem in the development of artificial lateral lines. In this paper we present two novel iterative schemes, referred to as Gauss-Newton (GN) and Newton-Raphson (NR) algorithms, for simultaneously localizing a dipole source and estimating its vibration amplitude and orientation, based on the analytical model for a dipole-generated flow field. The performance of the GN and NR methods is first confirmed with simulation results and the Cramer-Rao bound (CRB) analysis. Experiments are further conducted on an artificial lateral line prototype, consisting of six millimeter-scale ionic polymer-metal composite sensors with intra-sensor spacing optimized with CRB analysis. Consistent with simulation results, the experimental results show that both GN and NR schemes are able to simultaneously estimate the source location, vibration amplitude and orientation with comparable precision. Specifically, the maximum localization error is less than 5% of the body length (BL) when the source is within the distance of one BL. Experimental results have also shown that the proposed schemes are superior to the beamforming method, one of the most competitive approaches reported in literature, in terms of accuracy and computational efficiency. PMID:23538856
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. PMID:25104646
Zhang, Y; Li, X R
1999-01-01
A fast learning algorithm for training multilayer feedforward neural networks (FNN's) by using a fading memory extended Kalman filter (FMEKF) is presented first, along with a technique using a self-adjusting time-varying forgetting factor. Then a U-D factorization-based FMEKF is proposed to further improve the learning rate and accuracy of the FNN. In comparison with the backpropagation (BP) and existing EKF-based learning algorithms, the proposed U-D factorization-based FMEKF algorithm provides much more accurate learning results, using fewer hidden nodes. It has improved convergence rate and numerical stability (robustness). In addition, it is less sensitive to start-up parameters (e.g., initial weights and covariance matrix) and the randomness in the observed data. It also has good generalization ability and needs less training time to achieve a specified learning accuracy. Simulation results in modeling and identification of nonlinear dynamic systems are given to show the effectiveness and efficiency of the proposed algorithm. PMID:18252590
Modeling of Nonlinear Systems using Genetic Algorithm
NASA Astrophysics Data System (ADS)
Hayashi, Kayoko; Yamamoto, Toru; Kawada, Kazuo
In this paper, a newly modeling system by using Genetic Algorithm (GA) is proposed. The GA is an evolutionary computational method that simulates the mechanisms of heredity or evolution of living things, and it is utilized in optimization and in searching for optimized solutions. Most process systems have nonlinearities, so it is necessary to anticipate exactly such systems. However, it is difficult to make a suitable model for nonlinear systems, because most nonlinear systems have a complex structure. Therefore the newly proposed method of modeling for nonlinear systems uses GA. Then, according to the newly proposed scheme, the optimal structure and parameters of the nonlinear model are automatically generated.
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)
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.
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.
Direct adaptive control for nonlinear uncertain dynamical systems
NASA Astrophysics Data System (ADS)
Hayakawa, Tomohisa
In light of the complex and highly uncertain nature of dynamical systems requiring controls, it is not surprising that reliable system models for many high performance engineering and life science applications are unavailable. In the face of such high levels of system uncertainty, robust controllers may unnecessarily sacrifice system performance whereas adaptive controllers are clearly appropriate since they can tolerate far greater system uncertainty levels to improve system performance. In this dissertation, we develop a Lyapunov-based direct adaptive and neural adaptive control framework that addresses parametric uncertainty, unstructured uncertainty, disturbance rejection, amplitude and rate saturation constraints, and digital implementation issues. Specifically, we consider the following research topics; direct adaptive control for nonlinear uncertain systems with exogenous disturbances; robust adaptive control for nonlinear uncertain systems; adaptive control for nonlinear uncertain systems with actuator amplitude and rate saturation constraints; adaptive reduced-order dynamic compensation for nonlinear uncertain systems; direct adaptive control for nonlinear matrix second-order dynamical systems with state-dependent uncertainty; adaptive control for nonnegative and compartmental dynamical systems with applications to general anesthesia; direct adaptive control of nonnegative and compartmental dynamical systems with time delay; adaptive control for nonlinear nonnegative and compartmental dynamical systems with applications to clinical pharmacology; neural network adaptive control for nonlinear nonnegative dynamical systems; passivity-based neural network adaptive output feedback control for nonlinear nonnegative dynamical systems; neural network adaptive dynamic output feedback control for nonlinear nonnegative systems using tapped delay memory units; Lyapunov-based adaptive control framework for discrete-time nonlinear systems with exogenous disturbances
Experimental nonlinear laser systems: Bigger data for better science?
NASA Astrophysics Data System (ADS)
Kane, D. M.; Toomey, J. P.; McMahon, C.; Noblet, Y.; Argyris, A.; Syvridis, D.
2014-10-01
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.
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. PMID:26838675
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.
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.
Nonlinear Growth of Singular Vector Based Perturbations
NASA Astrophysics Data System (ADS)
Reynolds, C. A.
2002-12-01
The nonlinearity of singular vector-based perturbation growth is examined within the context of a global atmospheric forecast model. The characteristics of these nonlinearities and their impact on the utility of SV-based diagnostics are assessed both qualitatively and quantitatively. Nonlinearities are quantified by examining the symmetry of evolving positive and negative "twin" perturbations. Perturbations initially scaled to be consistent with estimates of analysis uncertainty become significantly nonlinear by 12 hours. However, the relative magnitude of the nonlinearities is a strong function of scale and metric. Small scales become nonlinear very quickly while synoptic scales can remain significantly linear out to three day. Small shifts between positive and negative perturbations can result in significant nonlinearities even when the basic anomaly patterns are quite similar. Thus, singular vectors may be qualitatively useful even when nonlinearities are large. Post-time pseudo-inverse experiments show that despite significant nonlinear perturbation growth, the nonlinear forecast corrections are similar to the expected linear corrections, even at 72 hours. When the nonlinear correction does differ significantly from the expected linear correction, the nonlinear correction is usually better, indicating that in some cases the pseudo-inverse correction effectively suppresses error growth outside the subspace defined by the leading (dry) singular vectors. Because a significant portion of the nonlinear growth occurs outside of the dry singular vector subspace, an a priori nonlinearity index based on the full perturbations is not a good predictor of when pseudo-inverse based corrections will be ineffective. However, one can construct a reasonable predictor of pseudo-inverse ineffectiveness by focusing on nonlinearities in the synoptic scales or in the singular vector subspace only.
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. PMID:24012389
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.
NASA Astrophysics Data System (ADS)
Lin, Tsung-Chih
2010-12-01
In this paper, a novel direct adaptive interval type-2 fuzzy-neural tracking control equipped with sliding mode and Lyapunov synthesis approach is proposed to handle the training data corrupted by noise or rule uncertainties for nonlinear SISO nonlinear systems involving external disturbances. By employing adaptive fuzzy-neural control theory, the update laws will be derived for approximating the uncertain nonlinear dynamical system. In the meantime, the sliding mode control method and the Lyapunov stability criterion are incorporated into the adaptive fuzzy-neural control scheme such that the derived controller is robust with respect to unmodeled dynamics, external disturbance and approximation errors. In comparison with conventional methods, the advocated approach not only guarantees closed-loop stability but also the output tracking error of the overall system will converge to zero asymptotically without prior knowledge on the upper bound of the lumped uncertainty. Furthermore, chattering effect of the control input will be substantially reduced by the proposed technique. To illustrate the performance of the proposed method, finally simulation example will be given.
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.
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.
Describing functions for nonlinear optical systems.
Ghosh, A K
1997-10-10
The concept of describing functions is useful for analyzing and designing nonlinear systems. A proposal for using the idea of describing functions for studying the behavior of a nonlinear optical processing system is given. The describing function can be used in the same way that a coherent transfer function or optical transfer function is used to characterize linear, shift-invariant optical processors. Two coherent optical systems for measuring the magnitude of the describing function of nonlinear optical processors are suggested. PMID:18264243
NASA Astrophysics Data System (ADS)
Chen, Hongxian; Yu, Jianjun; Xiao, Jiangnan; Cao, Zizheng; Li, Fan; Chen, Lin
2013-10-01
The nonlinear effect induced by the Mach-Zehnder modulator (MZM) and optical self-phase modulation (SPM) in the presence of high peak-to-average power ratio (PAPR) is investigated theoretically. We theoretically and experimentally investigate the direct-detection optical orthogonal frequency-division multiplexing (DD-OOFDM) system with an electronic pre-distortion technique of companding transform (CT) to reduce the peak-to-average power ratio (PAPR) of OFDM signals and improve the receiver sensitivity. Experimental results show that the PAPR reduction can reach about 3 dB when the complementary cumulative distribution function is 1 × 10-4, which means the number of random OFDM signals is 1 × 104, and the receiver sensitivity is improved by 0.7, 1.7, and 2.4 dB for the launch power of 2, 6 and 10 dB m, respectively, at the BER of 1 × 10-4 after transmission over 100-km single-mode fiber with the μ of 2. It shows that the PAPR reduction can mitigate not only the nonlinearity of MZM, but also the nonlinear phase noise in the fiber link when the optical power into fiber is high.
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.
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.
Linear pattern dynamics in nonlinear threshold systems
Rundle, John B.; Klein, W.; Tiampo, Kristy; Gross, Susanna
2000-03-01
Complex nonlinear threshold systems frequently show space-time behavior that is difficult to interpret. We describe a technique based upon a Karhunen-Loeve expansion that allows dynamical patterns to be understood as eigenstates of suitably constructed correlation operators. The evolution of space-time patterns can then be viewed in terms of a ''pattern dynamics'' that can be obtained directly from observable data. As an example, we apply our methods to a particular threshold system to forecast the evolution of patterns of observed activity. Finally, we perform statistical tests to measure the quality of the forecasts. (c) 2000 The American Physical Society.
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.
NASA Astrophysics Data System (ADS)
Hua, Changchun; Zhang, Liuliu; Guan, Xinping
2016-04-01
This paper studies the problem of output feedback control for a class of nonlinear time-delay systems with prescribed performance. The system is in the form of triangular structure with unmodelled dynamics. First, we introduce a reduced-order observer to provide the estimate of the unmeasured states. Then, by setting a new condition with the performance function, we design the state transformation with prescribed performance control. By employing backstepping method, we construct the output feedback controller. It is proved that the resulting closed-loop system is asymptotically stable and both transient and steady-state performance of the output are preserved with the changing supply function idea. Finally, a simulation example is conducted to show the effectiveness of the main results.
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.
Berry phase in nonlinear systems
Liu, J.; Fu, L. B.
2010-05-15
The Berry phase acquired by an eigenstate that experienced a nonlinear adiabatic evolution is investigated thoroughly. The circuit integral of the Berry connection of the instantaneous eigenstate cannot account for the adiabatic geometric phase, while the Bogoliubov excitations around the eigenstates are found to be accumulated during the nonlinear adiabatic evolution and contribute a finite phase of geometric nature. A two-mode model is used to illustrate our theory. Our theory is applicable to Bose-Einstein condensate, nonlinear light propagation, and Ginzburg-Landau equations for complex order parameters in condensed-matter physics.
De, Suvranu; Deo, Dhannanjay; Sankaranarayanan, Ganesh; Arikatla, Venkata S.
2012-01-01
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
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
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 normal modes in electrodynamic systems: A nonperturbative approach
NASA Astrophysics Data System (ADS)
Kudrin, A. V.; Kudrina, O. A.; Petrov, E. Yu.
2016-06-01
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.
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
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
Nonlinear control for dual quaternion systems
NASA Astrophysics Data System (ADS)
Price, William D.
The motion of rigid bodies includes three degrees of freedom (DOF) for rotation, generally referred to as roll, pitch and yaw, and 3 DOF for translation, generally described as motion along the x, y and z axis, for a total of 6 DOF. Many complex mechanical systems exhibit this type of motion, with constraints, such as complex humanoid robotic systems, multiple ground vehicles, unmanned aerial vehicles (UAVs), multiple spacecraft vehicles, and even quantum mechanical systems. These motions historically have been analyzed independently, with separate control algorithms being developed for rotation and translation. The goal of this research is to study the full 6 DOF of rigid body motion together, developing control algorithms that will affect both rotation and translation simultaneously. This will prove especially beneficial in complex systems in the aerospace and robotics area where translational motion and rotational motion are highly coupled, such as when spacecraft have body fixed thrusters. A novel mathematical system known as dual quaternions provide an efficient method for mathematically modeling rigid body transformations, expressing both rotation and translation. Dual quaternions can be viewed as a representation of the special Euclidean group SE(3). An eight dimensional representation of screw theory (combining dual numbers with traditional quaternions), dual quaternions allow for the development of control techniques for 6 DOF motion simultaneously. In this work variable structure nonlinear control methods are developed for dual quaternion systems. These techniques include use of sliding mode control. In particular, sliding mode methods are developed for use in dual quaternion systems with unknown control direction. This method, referred to as self-reconfigurable control, is based on the creation of multiple equilibrium surfaces for the system in the extended state space. Also in this work, the control problem for a class of driftless nonlinear systems is
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.
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.
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.
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.
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.
Nanoradar based on nonlinear dimer nanoantenna.
Lapshina, Nadezhda; Noskov, Roman; Kivshar, Yuri
2012-09-15
We introduce the concept of a nanoradar based on the operation of a nonlinear plasmonic nanoantenna. The nanoradar action originates from modulational instability occurring in a dimer nanoantenna consisting of two subwavelength nonlinear nanoparticles. Modulation instability causes a dynamical energy exchange between the nanoantenna eigenmodes resulting in periodic scanning of the nanoantenna scattering pattern. Such nanoradar demonstrates a wide scanning sector, low operation threshold, and ultrafast time response being potentially useful for many applications in nanophotonics circuitry. PMID:23041904
Matter-wave soliton interferometer based on a nonlinear splitter
NASA Astrophysics Data System (ADS)
Sakaguchi, Hidetsugu; Malomed, Boris A.
2016-02-01
We elaborate a model of the interferometer which, unlike previously studied ones, uses a local (δ-functional) nonlinear repulsive potential, embedded into a harmonic-oscillator trapping potential, as the splitter for the incident soliton. An estimate demonstrates that this setting may be implemented by means of the localized Feshbach resonance controlled by a focused laser beam. The same system may be realized as a nonlinear waveguide in optics. Subsequent analysis produces an exact solution for scattering of a plane wave in the linear medium on the δ -functional nonlinear repulsive potential, and an approximate solution for splitting of the incident soliton when the ambient medium is nonlinear. The most essential result, obtained by means of systematic simulations, is that the use of the nonlinear splitter provides the sensitivity of the soliton-based interferometer to the target, inserted into one of its arms, which is much higher than the sensitivity provided by the usual linear splitter.
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.
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.
Markovian master equation for nonlinear systems
NASA Astrophysics Data System (ADS)
de los Santos-Sánchez, O.; Récamier, J.; Jáuregui, R.
2015-06-01
Within the f-deformed oscillator formalism, we derive a Markovian master equation for the description of the damped dynamics of nonlinear systems that interact with their environment. The applicability of this treatment to the particular case of a Morse-like oscillator interacting with a thermal field is illustrated, and the decay of quantum coherence in such a system is analyzed in terms of the evolution on phase space of its nonlinear coherent states via the Wigner function.
Chaotic dynamics of weakly nonlinear systems
Vavriv, D.M.
1996-06-01
A review is given on the recent results in studying chaotic phenomena in weakly nonlinear systems. We are concerned with the class of chaotic states that can arise in physical systems with any degree of nonlinearity however small. The conditions for, and the mechanisms of, the transitions to chaos are discussed. These findings are illustrated by the results of the stability analysis of practical microwave and optical devices. {copyright} {ital 1996 American Institute of Physics.}
Nonlinear transmission line based electron beam driver
NASA Astrophysics Data System (ADS)
French, David M.; Hoff, Brad W.; Tang, Wilkin; Heidger, Susan; Allen-Flowers, Jordan; Shiffler, Don
2012-12-01
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.
Nonlinear transmission line based electron beam driver.
French, David M; Hoff, Brad W; Tang, Wilkin; Heidger, Susan; Allen-Flowers, Jordan; Shiffler, Don
2012-12-01
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. PMID:23277977
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.
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.
Nonlinear Mixing in Optical Multicarrier Systems
NASA Astrophysics Data System (ADS)
Hameed, Mahmood Abdul
Although optical fiber has a vast spectral bandwidth, efficient use of this bandwidth is still important in order to meet the ever increased capacity demand of optical networks. In addition to wavelength division multiplexing, it is possible to partition multiple low-rate subcarriers into each high speed wavelength channel. Multicarrier systems not only ensure efficient use of optical and electrical components, but also tolerate transmission impairments. The purpose of this research is to understand the impact of mixing among subcarriers in Radio-Over-Fiber (RoF) and high speed optical transmission systems, and experimentally demonstrate techniques to minimize this impact. We also analyze impact of clipping and quantization on multicarrier signals and compare bandwidth efficiency of two popular multiplexing techniques, namely, orthogonal frequency division multiplexing (OFDM) and Nyquist modulation. For an OFDM-RoF system, we present a novel technique that minimizes the RF domain signal-signal beat interference (SSBI), relaxes the phase noise limit on the RF carrier, realizes the full potential of optical heterodyne-based RF carrier generation, and increases the performance-to-cost ratio of RoF systems. We demonstrate a RoF network that shares the same RF carrier for both downlink and uplink, avoiding the need of an additional RF oscillator in the customer unit. For multi-carrier optical transmission, we first experimentally compare performance degradations of coherent optical OFDM and single-carrier Nyquist pulse modulated systems in a nonlinear environment. We then experimentally evaluate SSBI compensation techniques in the presence of semiconductor optical amplifier (SOA) induced nonlinearities for a multicarrier optical system with direct detection. We show that SSBI contamination can be significantly reduced from the data signal when the carrier-to-signal power ratio is sufficiently low.
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.
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.
Statistical energy analysis of nonlinear vibrating systems.
Spelman, G M; Langley, R S
2015-09-28
Nonlinearities in practical systems can arise in contacts between components, possibly from friction or impacts. However, it is also known that quadratic and cubic nonlinearity can occur in the stiffness of structural elements undergoing large amplitude vibration, without the need for local contacts. Nonlinearity due purely to large amplitude vibration can then result in significant energy being found in frequency bands other than those being driven by external forces. To analyse this phenomenon, a method is developed here in which the response of the structure in the frequency domain is divided into frequency bands, and the energy flow between the frequency bands is calculated. The frequency bands are assigned an energy variable to describe the mean response and the nonlinear coupling between bands is described in terms of weighted summations of the convolutions of linear modal transfer functions. This represents a nonlinear extension to an established linear theory known as statistical energy analysis (SEA). The nonlinear extension to SEA theory is presented for the case of a plate structure with quadratic and cubic nonlinearity. PMID:26303923
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. PMID:25875591
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
Development of a nonlinear optical measurement-4 coherent imaging system
NASA Astrophysics Data System (ADS)
Chen, Xiaojun; Song, Yinglin; Gu, Jihua; Yang, Junyi; Shui, Min; Hou, Dengke; Zhu, Zongjie
2009-07-01
After the nonlinear optical phenomena were discovered, people began to research the techniques to detect the optical nonlinearities of materials. In this paper, a new optical nonlinear measurement technique-4f coherent imaging system is recommended. The system has many advantages: single shot real-time measurement, simple experimental apparatus, high sensitivity, being able to detect the magnitude and sign of both nonlinear absorption and refraction at the same time, low requirement of beam spatial distribution, and so on. This paper introduces the theory of the 4f system and makes a detailed review and expounds development and application of the 4f coherent image system. The nerve of the experiment is improving the phase diaphragm. The shape of the diaphragm from the double-slits to the small rectangular object, and transition to a circular aperture, finally forming a circular phase diaphragm, which is a circular aperture in the center add a phase object. Following these diaphragm changes, the sensitivity of the system is greatly improved. The latest developments of the system are series-wound double 4f coherent imaging technique and the time-resolved pump-probe system based on NIT-PO. The time-resolved pump-probe system based on NIT-PO can be used to measure the dynamic characteristics of excited states nonlinear absorption and refraction.
Chaotic and hyperchaotic attractors of a complex nonlinear system
NASA Astrophysics Data System (ADS)
Mahmoud, Gamal M.; Al-Kashif, M. A.; Farghaly, A. A.
2008-02-01
In this paper, we introduce a complex nonlinear hyperchaotic system which is a five-dimensional system of nonlinear autonomous differential equations. This system exhibits both chaotic and hyperchaotic behavior and its dynamics is very rich. Based on the Lyapunov exponents, the parameter values at which this system has chaotic, hyperchaotic attractors, periodic and quasi-periodic solutions and solutions that approach fixed points are calculated. The stability analysis of these fixed points is carried out. The fractional Lyapunov dimension of both chaotic and hyperchaotic attractors is calculated. Some figures are presented to show our results. Hyperchaos synchronization is studied analytically as well as numerically, and excellent agreement is found.
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.
Dierks, Travis; Jagannathan, Sarangapani
2012-07-01
In this paper, the Hamilton-Jacobi-Bellman equation is solved forward-in-time for the optimal control of a class of general affine nonlinear discrete-time systems without using value and policy iterations. The proposed approach, referred to as adaptive dynamic programming, uses two neural networks (NNs), to solve the infinite horizon optimal regulation control of affine nonlinear discrete-time systems in the presence of unknown internal dynamics and a known control coefficient matrix. One NN approximates the cost function and is referred to as the critic NN, while the second NN generates the control input and is referred to as the action NN. The cost function and policy are updated once at the sampling instant and thus the proposed approach can be referred to as time-based ADP. Novel update laws for tuning the unknown weights of the NNs online are derived. Lyapunov techniques are used to show that all signals are uniformly ultimately bounded and that the approximated control signal approaches the optimal control input with small bounded error over time. In the absence of disturbances, an optimal control is demonstrated. Simulation results are included to show the effectiveness of the approach. The end result is the systematic design of an optimal controller with guaranteed convergence that is suitable for hardware implementation. PMID:24807137
Chen, Hao; Zhong, Shouming; Li, Min; Liu, Xingwen; Adu-Gyamfi, Fehrs
2016-07-01
In this paper, a novel delay partitioning method is proposed by introducing the theory of geometric progression for the stability analysis of T-S fuzzy systems with interval time-varying delays and nonlinear perturbations. Based on the common ratio α, the delay interval is unequally separated into multiple subintervals. A newly modified Lyapunov-Krasovskii functional (LKF) is established which includes triple-integral terms and augmented factors with respect to the length of every related proportional subintervals. In addition, a recently developed free-matrix-based integral inequality is employed to avoid the overabundance of the enlargement when dealing with the derivative of the LKF. This innovative development can dramatically enhance the efficiency of obtaining the maximum upper bound of the time delay. Finally, much less conservative stability criteria are presented. Numerical examples are conducted to demonstrate the significant improvements of this proposed approach. PMID:27138648
On-line robust nonlinear state estimators for nonlinear bioprocess systems
NASA Astrophysics Data System (ADS)
Iratni, A.; Katebi, R.; Mostefai, M.
2012-04-01
This paper presents the design of a new robust nonlinear estimator for estimation of states of nonlinear systems. Two approaches are considered based on the state-dependent Riccati equation formulation and the technique of H-infinity control design. The proposed method differs from other well-known state estimators, because not only nonlinear dynamics but also the robustness is taken into account. The proposed method is implemented and tested on a biological wastewater system. The simulation study compares the Extended Kalman Estimator ( EKE), the State-Dependent Riccati Estimator ( SDRE), and the Extended H-infinity Estimator ( EHE) with a new proposed State Dependent H-infinity Estimator ( SDHE). The results are compared for different weather conditions, i.e. dry, rain and storm, showing a superior performance of the proposed method.
Energy harvesting in the nonlinear electromagnetic system
NASA Astrophysics Data System (ADS)
Kucab, K.; Górski, G.; Mizia, J.
2015-11-01
We examine the electrical response of electromagnetic device working both in the linear and nonlinear domain. The harvester is consisted of small magnet moving in isolating tube surrounded by the coil attached to the electrical circuit. In the nonlinear case the magnet vibrates in between two fixed magnets attached to the both ends of the tube. Additionally we use two springs which limit the movement of the small magnet. The linear case is when the moving magnet is attached to the repelling springs, and the static magnets have been replaced by the non-magnetic material. The potentials and forces were calculated using both the analytical expressions and the finite elements method. We compare the results for energy harvesting obtained in these two cases. The generated output power in the linear case reaches the peak value 80 mW near the resonance frequency ω0 for maximum base acceleration considered by us, whereas in the non-linear case the corresponding outpot power has the peak value 95 mW and additionally relatively high values in the excitation frequencies range up to ω = 1.2ω0. The numerical results also show that the power efficiency in the nonlinear case exceeds the corresponding efficiency in the linear case at relatively high values of base accelerations greater than 5 g. The results show the increase of harvested energy in the broad band of excitation frequencies in the nonlinear case.
NASA Astrophysics Data System (ADS)
Ayala, Helon Vicente Hultmann; Coelho, Leandro dos Santos
2016-02-01
The present work introduces a procedure for input selection and parameter estimation for system identification based on Radial Basis Functions Neural Networks (RBFNNs) models with an improved objective function based on the residuals and its correlation function coefficients. We show the results when the proposed methodology is applied to model a magnetorheological damper, with real acquired data, and other two well-known benchmarks. The canonical genetic and differential evolution algorithms are used in cascade to decompose the problem of defining the lags taken as the inputs of the model and its related parameters based on the simultaneous minimization of the residuals and higher orders correlation functions. The inner layer of the cascaded approach is composed of a population which represents the lags on the inputs and outputs of the system and an outer layer represents the corresponding parameters of the RBFNN. The approach is able to define both the inputs of the model and its parameters. This is interesting as it frees the designer of manual procedures, which are time consuming and prone to error, usually done to define the model inputs. We compare the proposed methodology with other works found in the literature, showing overall better results for the cascaded approach.
Quadratic boundedness of uncertain nonlinear dynamic systems
NASA Astrophysics Data System (ADS)
Brockman, Mark Lawrence
Physical systems are often perturbed by unknown external disturbances or contain important system parameters which are difficult to model exactly. However, engineers are expected to design systems which perform well even in the presence of uncertainties. For example, an airplane designer can never know the precise direction or magnitude of wind gusts, or the exact mass distribution inside the aircraft, but passengers expect to arrive on time after a smooth ride. This thesis will first present the concept of quadratic boundedness of an uncertain nonlinear dynamic system, and then develop analysis techniques and control design methods for systems containing unknown disturbances and parameters. For a class of nonlinear systems, conditions for quadratic boundedness are given, and the relationship between quadratic boundedness and quadratic stability is explored. An important consequence of quadratic boundedness is the ability to calculate an upper bound on the system gain of an uncertain nonlinear system. For nominally linear systems, necessary and sufficient conditions for quadratic boundedness are given. The innovative use of linear matrix inequalities in an iterative algorithm provides a means to analyze the quadratic boundedness properties of systems containing parameter uncertainties. The analysis results establish a framework for the development of design methods which integrate performance specifications into the control design process for all the types of systems considered. Numerous examples illustrate the major results of the thesis.
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. PMID:26174586
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.
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. PMID:19336317
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.
Squeezing spectra for nonlinear optical systems
NASA Technical Reports Server (NTRS)
Collett, M. J.; Walls, D. F.
1985-01-01
The squeezing spectra for the output fields of several intracavity nonlinear optical systems are obtained. It is shown that at critical points, e.g., the turning points for optical bistability, the threshold for parametric oscillation, and the self-pulsing instability in second-harmonic generation, perfect squeezing in the output field is, in principle, possible.
Nonlinear resonant phenomena in multilevel quantum systems
NASA Astrophysics Data System (ADS)
Hicke, Christian
We study nonlinear resonant phenomena in two-level and multilevel quantum systems. Our results are of importance for applications in the areas of quantum control, quantum computation, and quantum measurement. We present a method to perform fault-tolerant single-qubit gate operations using Landau-Zener tunneling. In a single Landau-Zoner pulse, the qubit transition frequency is varied in time so that it passes through the frequency of a radiation field. We show that a simple three-pulse sequence allows eliminating errors in the gate up to the third order in errors in the qubit energies or the radiation frequency. We study the nonlinear transverse response of a spin S > 1/2 with easy-axis anisotropy. The coherent transverse response displays sharp dips or peaks when the modulation frequency is adiabatically swept through multiphoton resonance. The effect is a consequence of a certain conformal property of the spin dynamics in a magnetic field for the anisotropy energy ∝ S2z . The occurrence of the dips or peaks is determined by the spin state. Their shape strongly depends on the modulation amplitude. Higher-order anisotropy breaks the symmetry, leading to sharp steps in the transverse response as function of frequency. The results bear on the dynamics of molecular magnets in a static magnetic field. We show that a modulated large-spin system has special symmetry. In the presence of dissipation it leads to characteristic nonlinear effects. They include abrupt switching between transverse magnetization branches with varying modulating field without hysteresis and a specific pattern of switching in the presence of multistability and hysteresis. Along with steady forced vibrations the transverse spin components can display transient vibrations at a combination of the Larmor frequency and a slower frequency determined by the anisotropy energy. The analysis is based on a microscopic theory that takes into account relaxation mechanisms important for single
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 dynamics in tunable graphene nanoelectromechanical systems
NASA Astrophysics Data System (ADS)
Guan, Fen; Kumaravadivel, Piranavan; Averin, Dmitri; Du, Xu
2015-03-01
We report the fabrication and characterization of graphene nanoelectromechanical resonators (GNEMR) on flexible substrates. The intrinsic stain in graphene is tuned by bending the substrate, during which a transition from hardening to softening resonance behavior and a minimum resonance frequency are observed. To explain these observations, a resonator model taking into account the intrinsic strain and electrostatic force is developed. Including higher-order nonlinear terms, a minimum frequency is obtained analytically from the model and matches with experimental data. Results from numerical simulation demonstrate also the transition in the nonlinear behavior. Additionally, the model-based fittings determine the intrinsic strain and mass of graphene samples accurately. Our devices allow thorough exploration of the nonlinear dynamics in GNEMR and may help further study of the intrinsic electrical properties of the materials under strain.
Geometric nonlinear formulation for thermal-rigid-flexible coupling system
NASA Astrophysics Data System (ADS)
Fan, Wei; Liu, Jin-Yang
2013-10-01
This paper develops geometric nonlinear hybrid formulation for flexible multibody system with large deformation considering thermal effect. Different from the conventional formulation, the heat flux is the function of the rotational angle and the elastic deformation, therefore, the coupling among the temperature, the large overall motion and the elastic deformation should be taken into account. Firstly, based on nonlinear strain-displacement relationship, variational dynamic equations and heat conduction equations for a flexible beam are derived by using virtual work approach, and then, Lagrange dynamics equations and heat conduction equations of the first kind of the flexible multibody system are obtained by leading into the vectors of Lagrange multiplier associated with kinematic and temperature constraint equations. This formulation is used to simulate the thermal included hub-beam system. Comparison of the response between the coupled system and the uncoupled system has revealed the thermal chattering phenomenon. Then, the key parameters for stability, including the moment of inertia of the central body, the incident angle, the damping ratio and the response time ratio, are analyzed. This formulation is also used to simulate a three-link system applied with heat flux. Comparison of the results obtained by the proposed formulation with those obtained by the approximate nonlinear model and the linear model shows the significance of considering all the nonlinear terms in the strain in case of large deformation. At last, applicability of the approximate nonlinear model and the linear model are clarified in detail.
Geometric nonlinear formulation for thermal-rigid-flexible coupling system
NASA Astrophysics Data System (ADS)
Fan, Wei; Liu, Jin-Yang
2013-09-01
This paper develops geometric nonlinear hybrid formulation for flexible multibody system with large deformation considering thermal effect. Different from the conventional formulation, the heat flux is the function of the rotational angle and the elastic deformation, therefore, the coupling among the temperature, the large overall motion and the elastic deformation should be taken into account. Firstly, based on nonlinear strain-displacement relationship, variational dynamic equations and heat conduction equations for a flexible beam are derived by using virtual work approach, and then, Lagrange dynamics equations and heat conduction equations of the first kind of the flexible multibody system are obtained by leading into the vectors of Lagrange multiplier associated with kinematic and temperature constraint equations. This formulation is used to simulate the thermal included hub-beam system. Comparison of the response between the coupled system and the uncoupled system has revealed the thermal chattering phenomenon. Then, the key parameters for stability, including the moment of inertia of the central body, the incident angle, the damping ratio and the response time ratio, are analyzed. This formulation is also used to simulate a three-link system applied with heat flux. Comparison of the results obtained by the proposed formulation with those obtained by the approximate nonlinear model and the linear model shows the significance of considering all the nonlinear terms in the strain in case of large deformation. At last, applicability of the approximate nonlinear model and the linear model are clarified in detail.
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.
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)
Song, Ningfang; Luo, Xinkai; Li, Huipeng; Li, Jiao
2015-10-01
The non-linearity of the phase shifting mechanism in white light interferometry system can seriously affect the measuring accuracy of the system. In this paper, the correcting method is to combine the displacement feedback control technology with the fuzzy PID control technology. Displacement feedback control mechanism and fuzzy PID controller are designed and then try to figure it out through Matlab simulation and experiment.. The result shows that combining the displacement feedback control technology with the fuzzy PID control technology can fulfill decent overall non-linear correction in the white light interferometry measuring system. Meanwhile, the accuracy of the correction is high and the non-linearity drop from 2% to 0.1%.
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.
NASA Astrophysics Data System (ADS)
Nevolin, V. I.
2003-04-01
We present a method for analyzing the characteristics of nonlinear detectors using the algorithms of first-order nonlinear differential equations. This method is based on numerical solutions of the Fokker-Planck-Kolmogorov (FPK) equations in the form of series of functions over Hermite-Chebyshev polynomials for both nonlinear systems and their linear counterparts. The results of the solutions for the linear case are extended to nonlinear systems in a recurrent way.
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.
Tensor methods for large sparse systems of nonlinear equations
Bouaricha, A.; Schnabel, R.B.
1996-12-31
This paper introduces censor methods for solving, large sparse systems of nonlinear equations. Tensor methods for nonlinear equations were developed in the context of solving small to medium- sized dense problems. They base each iteration on a quadratic model of the nonlinear equations. where the second-order term is selected so that the model requires no more derivative or function information per iteration than standard linear model-based methods, and hardly more storage or arithmetic operations per iteration. Computational experiments on small to medium-sized problems have shown censor methods to be considerably more efficient than standard Newton-based methods, with a particularly large advantage on singular problems. This paper considers the extension of this approach to solve large sparse problems. The key issue that must be considered is how to make efficient use of sparsity in forming and solving the censor model problem at each iteration. Accomplishing this turns out to require an entirely new way of solving the tensor model that successfully exploits the sparsity of the Jacobian, whether the Jacobian is nonsingular or singular. We develop such an approach and, based upon it, an efficient tensor method for solving large sparse systems of nonlinear equations. Test results indicate that this tensor method is significantly more efficient and robust than an efficient sparse Newton-based method. in terms of iterations, function evaluations. and execution time.
Nonlinear Network Dynamics on Earthquake Fault Systems
Rundle, Paul B.; Rundle, John B.; Tiampo, Kristy F.; Sa Martins, Jorge S.; McGinnis, Seth; Klein, W.
2001-10-01
Earthquake faults occur in interacting networks having emergent space-time modes of behavior not displayed by isolated faults. Using simulations of the major faults in southern California, we find that the physics depends on the elastic interactions among the faults defined by network topology, as well as on the nonlinear physics of stress dissipation arising from friction on the faults. Our results have broad applications to other leaky threshold systems such as integrate-and-fire neural networks.
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.
Dissipative control for a class of nonlinear descriptor systems
NASA Astrophysics Data System (ADS)
Zhou, Juan; Zhang, Qingling; Li, Jinghao; Men, Bo; Ren, Junchao
2016-04-01
This paper is concerned with the dissipative control problem for a class of nonlinear descriptor systems. Based on Lyapunov stability theory, sufficient conditions are derived, which guarantee that the underlying systems are strictly dissipative. Then, the design method for a state feedback controller is provided. All the conditions can be expressed via linear matrix inequalities. Finally, a numerical example is presented to demonstrate the validity of the proposed methods.
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…
Nonlinear Tides in Close Binary Systems
NASA Astrophysics Data System (ADS)
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' >~ 10-100 M ⊕ at orbital periods P ≈ 1-10 days. The nearly static "equilibrium" tidal distortion is, however, stable to parametric resonance except for solar binaries with P <~ 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 ≈ 103[P/10 days] for a solar-type star) and drives them as a single coherent unit with growth rates that are a factor of ≈N faster than the
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
NASA Astrophysics Data System (ADS)
Lamarque, C.-H.; Ture Savadkoohi, A.; Naudan, M.
2013-09-01
The concept of energy exchange between coupled oscillators can be endowed for wide variety of applications such as control and energy harvesting. It has been proved that by coupling an essential nonlinear oscillator (cubic nonlinearity) to a main system (mostly linear), the latter system can be controlled in a one way and almost irreversible manner. The phenomenon is called energy pumping and the coupled nonlinear system is named as nonlinear energy sink (NES). The process of energy transfer from the main system to the nonlinear smooth or non-smooth attachment at different scales of time can present several scenarios: It can be attracted to periodic behaviors which present low or high energy levels for the main system and/or to quasi-periodic responses of two oscillators by persistent bifurcations between their stable zones. In this paper we analyze multi-scale dynamics of two attached oscillators: a Bouc-Wen type in general (in particular: a Dahl type and a modified hysteresis system) and a NES (nonsmooth and cubic). The system behavior at fast and first slow times scales by detecting its invariant manifold, its fixed points and singularities will be analyzed. Analytical developments will be accompanied by some numerical examples for systems that present quasi-periodic responses. The endowed Bouc-Wen models correspond to the hysteretic behavior of materials or structures. This paper is clearly connected with the dynamics of systems with hysteresis and nonlinear dynamics based energy harvesting.
Synchronised output regulation of nonlinear multi-agent systems
NASA Astrophysics Data System (ADS)
Xiang, Ji; Li, Yanjun; Wei, Wei
2015-01-01
This paper considers a synchronised output regulation (SOR) problem of nonlinear multi-agent systems with switching graph. The SOR means that all agents have their outputs synchronised but also ultimately evolve on a manifold determined by a predefined exosystem. Each agent constructs its local copy of the predefined exosystem and exchanges the state information of the local exosystem to realise the synchronisation of local exosystem. A controller based on the nonlinear output regulation theory is then presented to force the agent's output track the output of local exosystem. It is shown that the SOR is solvable under the assumptions same as that for nonlinear output regulation of a single agent, if the switching graph satisfies the bounded interconnectivity times condition. Both state feedback and output feedback are addressed. A numerical simulation is made to show the efficacy of the analytic results.
Adaptive RSOV filter using the FELMS algorithm for nonlinear active noise control systems
NASA Astrophysics Data System (ADS)
Zhao, Haiquan; Zeng, Xiangping; He, Zhengyou; Li, Tianrui
2013-01-01
This paper presents a recursive second-order Volterra (RSOV) filter to solve the problems of signal saturation and other nonlinear distortions that occur in nonlinear active noise control systems (NANC) used for actual applications. Since this nonlinear filter based on an infinite impulse response (IIR) filter structure can model higher than second-order and third-order nonlinearities for systems where the nonlinearities are harmonically related, the RSOV filter is more effective in NANC systems with either a linear secondary path (LSP) or a nonlinear secondary path (NSP). Simulation results clearly show that the RSOV adaptive filter using the multichannel structure filtered-error least mean square (FELMS) algorithm can further greatly reduce the computational burdens and is more suitable to eliminate nonlinear distortions in NANC systems than a SOV filter, a bilinear filter and a third-order Volterra (TOV) filter.
Nonlinear Optical Properties of Triphenylalanine-based Peptide Nanostructures
NASA Astrophysics Data System (ADS)
Kudryavtsev, A. V.; Mishina, E. D.; Sigov, A. S.
2016-05-01
Nonlinear optical properties of peptide nanobelts and peptide nanospheres, the two types of self-assembled triphenylalanine-based peptide nanostructures, are studied. Nanobelts nonlinear susceptibility tensor components are evaluated, and nanobelts crystal structure and crystallographic orientation are defined on the basis of nonlinear optical mapping and polarization dependences of the second harmonic signal. The results obtained suggest that it is possible to use these materials as biologically compatible nonlinear optical converters.
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
Observers for discrete-time nonlinear systems
NASA Astrophysics Data System (ADS)
Grossman, Walter D.
Observer synthesis for discrete-time nonlinear systems with special applications to parameter estimation is analyzed. Two new types of observers are developed. The first new observer is an adaptation of the Friedland continuous-time parameter estimator to discrete-time systems. The second observer is an adaptation of the continuous-time Gauthier observer to discrete-time systems. By adapting these observers to discrete-time continuous-time parameter estimation problems which were formerly intractable become tractable. In addition to the two newly developed observers, two observers already described in the literature are analyzed and deficiencies with respect to noise rejection are demonstrated. Improved versions of these observers are proposed and their performance demonstrated. The issues of discrete-time observability, discrete-time system inversion, and optimal probing are also addressed.
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.
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.
Modified kernel-based nonlinear feature extraction.
Ma, J.; Perkins, S. J.; Theiler, J. P.; Ahalt, S.
2002-01-01
Feature Extraction (FE) techniques are widely used in many applications to pre-process data in order to reduce the complexity of subsequent processes. A group of Kernel-based nonlinear FE ( H E ) algorithms has attracted much attention due to their high performance. However, a serious limitation that is inherent in these algorithms -- the maximal number of features extracted by them is limited by the number of classes involved -- dramatically degrades their flexibility. Here we propose a modified version of those KFE algorithms (MKFE), This algorithm is developed from a special form of scatter-matrix, whose rank is not determined by the number of classes involved, and thus breaks the inherent limitation in those KFE algorithms. Experimental results suggest that MKFE algorithm is .especially useful when the training set is small.
Boosted X Waves in Nonlinear Optical Systems
Arevalo, Edward
2010-01-15
X waves are spatiotemporal optical waves with intriguing superluminal and subluminal characteristics. Here we theoretically show that for a given initial carrier frequency of the system localized waves with genuine superluminal or subluminal group velocity can emerge from initial X waves in nonlinear optical systems with normal group velocity dispersion. Moreover, we show that this temporal behavior depends on the wave detuning from the carrier frequency of the system and not on the particular X-wave biconical form. A spatial counterpart of this behavior is also found when initial X waves are boosted in the plane transverse to the direction of propagation, so a fully spatiotemporal motion of localized waves can be observed.
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.
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.
Digital self-triggered robust control of nonlinear systems
NASA Astrophysics Data System (ADS)
Di Benedetto, M. D.; Di Gennaro, S.; D'Innocenzo, A.
2013-09-01
In this paper, we develop novel results on self-triggered control of nonlinear systems, subject to perturbations, and sensing/computation/actuation delays. First, considering an unperturbed nonlinear system with bounded delays, we provide conditions that guarantee the existence of a self-triggered control strategy stabilizing the closed-loop system. Then, considering parameter uncertainties, disturbances and bounded delays, we provide conditions guaranteeing the existence of a self-triggered strategy that keeps the state arbitrarily close to the equilibrium point. In both cases, we provide a methodology for the computation of the next execution time. We show on an example the relevant benefits obtained with this approach in terms of energy consumption with respect to control algorithms based on a constant sampling with a sensible reduction of the average sampling time.
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.
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.
Highly concentrated active nonlinear media based on oxides
Bakin, D.V.; Dorozhkin, L.M.; Krasilov, Yu.I.; Kuznetsov, N.T.; Potemkin, A.V.; Tadzhi-Aglaev, K.S.; Shestakov, A.V.
1987-07-01
Important characteristics of highly concentrated active nonlinear media were studied which were based on oxide compounds of phosphates, niobates, tantalates, and titanates of neodymium with alkaline earth metals. Compounds of the indicated classes were synthesized and their spectral luminescent and nonlinear optical properties were studied. Single crystals were grown from the selected compounds (5-8mm) and preliminary measurements of the laser and nonlinear optical parameters were taken. Formulas are given for materials that demonstrated high nonlinear and luminescent properties simultaneously. Spectroscopic and nonlinear optical properties of some oxygen compounds of rare earth elements are shown.
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.
Nonlinear stability of discrete shocks for systems of conservation laws
NASA Astrophysics Data System (ADS)
Liu, Jian-Guo; Xin, Zhouping
1993-09-01
In this paper we study the asymptotic nonlinear stability of discrete shocks for the Lax-Friedrichs scheme for approximating general m×m systems of nonlinear hyperbolic conservation laws. It is shown that weak single discrete shocks for such a scheme are nonlinearly stable in the L p-norm for all p ≧ 1, provided that the sums of the initial perturbations equal zero. These results should shed light on the convergence of the numerical solution constructed by the Lax-Friedrichs scheme for the single-shock solution of system of hyperbolic conservation laws. If the Riemann solution corresponding to the given far-field states is a superposition of m single shocks from each characteristic family, we show that the corresponding multiple discrete shocks are nonlinearly stable in L p (P ≧ 2). These results are proved by using both a weighted estimate and a characteristic energy method based on the internal structures of the discrete shocks and the essential monotonicity of the Lax-Friedrichs scheme.
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.
Dark state in a nonlinear optomechanical system with quadratic coupling
NASA Astrophysics Data System (ADS)
Huang, Yue-Xin; Zhou, Xiang-Fa; Guo, Guang-Can; Zhang, Yong-Sheng
We consider a hybrid system consisting of a cavity optomechanical device with nonlinear quadratic radiation pressure coupled to an atomic ensemble. By considering the collective excitation, we show that this system supports nontrivial, nonlinear dark states. The coupling strength can be tuned via the lasers that ensure the population transfer adiabatically between the mechanical modes and the collective atomic excitations in a controlled way. In addition, we show how to detect the dark-state resonance by calculating the single-photon spectrum of the output fields and the transmission of the probe beam based on two-phonon optomechanically induced transparency. Possible application and extension of the dark states are also discussed. Supported by the National Fundamental Research Program of China (Grants No. 2011CB921200 and No. 2011CBA00200), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB01030200), and NSFC (Grants No. 61275122 and 11474266).
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.
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)).
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.
On the HAM-based mathematica package BVPh for coupled nonlinear ODEs
NASA Astrophysics Data System (ADS)
Zhao, Yinlong; Liao, Shijun
2012-09-01
The BVPh is a Mathematica package based on the Homotopy analysis method (HAM) for solving nonlinear boundary value problems (BVPs). Its aim is to provide an analytic tool for as many nonlinear BVPs as possible. Its newest version can now deal with many systems of coupled ordinary differential equations (ODEs) defined in finite or semi-infinite intervals.
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.
Liu, Zhi; Lai, Guanyu; Zhang, Yun; Chen, Chun Lung Philip
2015-08-01
This paper addresses the problem of adaptive neural output-feedback control for a class of special nonlinear systems with the hysteretic output mechanism and the unmeasured states. A modified Bouc-Wen model is first employed to capture the output hysteresis phenomenon in the design procedure. For its fusion with the neural networks and the Nussbaum-type function, two key lemmas are established using some extended properties of this model. To avoid the bad system performance caused by the output nonlinearity, a barrier Lyapunov function technique is introduced to guarantee the prescribed constraint of the tracking error. In addition, a robust filtering method is designed to cancel the restriction that all the system states require to be measured. Based on the Lyapunov synthesis, a new neural adaptive controller is constructed to guarantee the prescribed convergence of the tracking error and the semiglobal uniform ultimate boundedness of all the signals in the closed-loop system. Simulations are implemented to evaluate the performance of the proposed neural control algorithm in this paper. PMID:25915964
Applied Nonlinear Dynamics and Stochastic Systems Near The Millenium. Proceedings
Kadtke, J.B.; Bulsara, A.
1997-12-01
These proceedings represent papers presented at the Applied Nonlinear Dynamics and Stochastic Systems conference held in San Diego, California in July 1997. The conference emphasized the applications of nonlinear dynamical systems theory in fields as diverse as neuroscience and biomedical engineering, fluid dynamics, chaos control, nonlinear signal/image processing, stochastic resonance, devices and nonlinear dynamics in socio{minus}economic systems. There were 56 papers presented at the conference and 5 have been abstracted for the Energy Science and Technology database.(AIP)
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 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.
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.
Telescopic systems with dynamic nonlinear optical correction for distortions
Vasil'ev, Michail V; Venediktov, Vladimir Yu; Leshchev, Alexey A
2001-01-31
The review of basic achievements in the field of non-linear adaptive optics is presented. In particular, schematics and properties of adaptive optical telescopes considered in which the image distortions introduced by defects of the primary mirror and other optical elements are compensated by nonlinear optical methods. The conventional methods of laser optics, such as phase conjugation and dynamic holography, make it possible both to solve the problems of classical (imaging) optics related to the building of telescopes for imaging remote objects with high resolution, which are based on large, light-weight or sectional mirrors, and create the systems that produce laser beams with the high-quality wave front. The basic designs of such telescopes are considered and the possibilities of corrections for distortions in them are analysed and confirmed by experiments. (review)
Autonomous navigation system using a fuzzy adaptive nonlinear H∞ filter.
Outamazirt, Fariz; Li, Fu; Yan, Lin; Nemra, Abdelkrim
2014-01-01
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. PMID:25244587
Nonlinearity measure and internal model control based linearization in anti-windup design
Perev, Kamen
2013-12-18
This paper considers the problem of internal model control based linearization in anti-windup design. The nonlinearity measure concept is used for quantifying the control system degree of nonlinearity. The linearizing effect of a modified internal model control structure is presented by comparing the nonlinearity measures of the open-loop and closed-loop systems. It is shown that the linearization properties are improved by increasing the control system local feedback gain. However, it is emphasized that at the same time the stability of the system deteriorates. The conflicting goals of stability and linearization are resolved by solving the design problem in different frequency ranges.
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.
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
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. PMID:26277007
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. PMID:24795034
Neural networks for feedback feedforward nonlinear control systems.
Parisini, T; Zoppoli, R
1994-01-01
This paper deals with the problem of designing feedback feedforward control strategies to drive the state of a dynamic system (in general, nonlinear) so as to track any desired trajectory joining the points of given compact sets, while minimizing a certain cost function (in general, nonquadratic). Due to the generality of the problem, conventional methods are difficult to apply. Thus, an approximate solution is sought by constraining control strategies to take on the structure of multilayer feedforward neural networks. After discussing the approximation properties of neural control strategies, a particular neural architecture is presented, which is based on what has been called the "linear-structure preserving principle". The original functional problem is then reduced to a nonlinear programming one, and backpropagation is applied to derive the optimal values of the synaptic weights. Recursive equations to compute the gradient components are presented, which generalize the classical adjoint system equations of N-stage optimal control theory. Simulation results related to nonlinear nonquadratic problems show the effectiveness of the proposed method. PMID:18267810
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.
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
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
Nonlinear energy transfer in classical and quantum systems.
Manevitch, Leonid; Kovaleva, Agnessa
2013-02-01
In this paper we investigate the effect of slowly-varying parameters on the energy transfer in a weakly coupled system. For definiteness, we consider a system of two nonlinear oscillators, in which the directly excited first oscillator with constant parameter is attached to the oscillator with slowly time-varying frequency. It is proved that the equations of the slow passage through resonance in this system are identical to the equations of nonlinear Landau-Zener (LZ) tunneling. Three types of dynamical behavior are distinguished, namely, quasilinear, moderately nonlinear, and strongly nonlinear ones. Quasilinear systems exhibit a gradual energy transfer from the excited to the attached oscillator, while moderately nonlinear systems are characterized by an abrupt transition from the energy localization on the excited oscillator to the localization on the attached oscillator. In strongly nonlinear systems, the transition from the energy localization to strong energy exchange between the oscillators is revealed. Explicit approximate solutions describing the transient processes in moderately and strongly nonlinear systems are suggested. Correctness of the constructed approximations is confirmed by numerical results. The results presented in this paper, in addition to providing an analytical framework for understanding the transient dynamics, suggest an approximate procedure for solving the nonlinear LZ problem with arbitrary initial conditions over a finite time-interval. PMID:23496588
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.
Simple nonlinear interferometer-based all-optical thresholder and its applications for optical CDMA.
Kravtsov, Konstantin; Prucnal, Paul R; Bubnov, Mikhail M
2007-10-01
We present an experimental demonstration of an ultrafast all-optical thresholder based on a nonlinear Sagnac interferometer. The proposed design is intended for operation at very small nonlinear phase shifts. Therefore, it requires an in-loop nonlinearity lower than for the classical nonlinear loop mirror scheme. Only 15 meters of conventional (non-holey) silica-based fiber is used as a nonlinear element. The proposed thresholder is polarization insensitive and is good for multi-wavelength operation, meeting all the requirements for autocorrelation detection in various optical CDMA communication systems. The observed cubic transfer function is superior to the quadratic transfer function of second harmonic generation-based thresholders. PMID:19550579
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.
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.
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 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.
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.
Nonlinear Optics in Novel Polymer Systems.
NASA Astrophysics Data System (ADS)
Li, Lian
Polymeric nonlinear optical (NLO) materials have recently attracted considerable attention and been the subject of intensive investigations. Polymeric NLO materials possessing large second and third order NLO properties, ultrafast response times, high optical damage threshold, transparency over a broad wavelength range, and capability to be easily processed into good optical quality thin films, offer significant advantages over the traditional inorganic materials for applications in fabricating integrated optical devices, such as waveguide electro-optic (EO) modulators and optical frequency doublers, and optical signal processing devices. This dissertation presents the experimental investigations on novel NLO polymers synthesized in the Laboratory of Electronic and Photonic Materials at University of Massachusetts Lowell. Progress made for the past few years on polymeric NLO materials is reviewed, especially with regard to the second order NLO properties of the polymeric materials. Two novel stable second order NLO polymer systems, an interpenetrating polymer network (IPN) formed via thermal crosslinking and a sol-gel process, and a photocrosslinkable conducting polymer, upon poling and crosslinking, exhibited large and stable second order NLO properties measured for these polymers by using the second harmonic generation (SHG) technique. For the IPN system, the SHG measurements as a function of time at several elevated temperatures indicate the superb stability of the second order NLO properties. For the conducting NLO polymer, the NLO property of the poled and photocrosslinked polymer film is stable at room temperature. The wavelength shifting of a Q-switched Nd:YAG laser by stimulated Raman scattering is also described. Measurements were made on the third order NLO properties of a dye doped photocrosslinkable guest-host polymer system at different dye concentrations with a modified Michelson interferometer. By functionalizing the dye to make it more compatible to
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.
Practical application of equivalent linearization approaches to nonlinear piping systems
Park, Y.J.; Hofmayer, C.H.
1995-05-01
The use of mechanical energy absorbers as an alternative to conventional hydraulic and mechanical snubbers for piping supports has attracted a wide interest among researchers and practitioners in the nuclear industry. The basic design concept of energy absorbers (EA) is to dissipate the vibration energy of piping systems through nonlinear hysteretic actions of EA!s under design seismic loads. Therefore, some type of nonlinear analysis needs to be performed in the seismic design of piping systems with EA supports. The equivalent linearization approach (ELA) can be a practical analysis tool for this purpose, particularly when the response approach (RSA) is also incorporated in the analysis formulations. In this paper, the following ELA/RSA methods are presented and compared to each other regarding their practice and numerical accuracy: Response approach using the square root of sum of squares (SRSS) approximation (denoted RS in this paper). Classical ELA based on modal combinations and linear random vibration theory (denoted CELA in this paper). Stochastic ELA based on direct solution of response covariance matrix (denoted SELA in this paper). New algorithms to convert response spectra to the equivalent power spectral density (PSD) functions are presented for both the above CELA and SELA methods. The numerical accuracy of the three EL are studied through a parametric error analysis. Finally, the practicality of the presented analysis is demonstrated in two application examples for piping systems with EA supports.
Projection methods for solving nonlinear systems of equations
Brown, P.N. ); Saad, Y. . Ames Research Center)
1990-04-01
This paper describes several nonlinear projection methods based on Krylov subspaces and analyzes their convergence. The prototype of these methods is a technique that generalizes the conjugate direction method by minimizing the norm of the function F over some subspace. The emphasis of this paper is on nonlinear least squares problems which can also be handled by this general approach.
Fan, Cairong; Shi, Fenghua; Wu, Hongxing; Chen, Yihang
2015-06-01
Tunable all-optical plasmonic diode is proposed based on the Fano resonance in an asymmetric and nonlinear system, comprising metal-insulator-metal waveguides coupled with nanocavities. The spatial asymmetry of the system gives rise to the nonreciprocity of the field localizations at the nonlinear gap between the coupled cavities and to the nonreciprocal nonlinear response. Nonlinear Fano resonance, originating from the interference between the discrete cavity mode and the continuum traveling mode, is observed and effectively tuned by changing the input power. By combining the unidirectional nonlinear response with the steep dispersion of the Fano asymmetric line shape, a transmission contrast ratio up to 41.46 dB can be achieved between forward and backward transmission. Our all-optical plasmonic diode with compact structure can find important applications in integrated optical nanocircuits. PMID:26030529
On the transmissibilities of nonlinear vibration isolation system
NASA Astrophysics Data System (ADS)
Lu, Zeqi; Brennan, Michael J.; Chen, Li-Qun
2016-08-01
Transmissibility is a key parameter to quantify the effectiveness of a vibration isolation system. Under harmonic excitation, the force transmissibility of a linear vibration isolation system is defined as the ratio between the amplitude of the force transmitted to the host structure and the excitation force amplitude, and the displacement transmissibility is the ratio between the displacement amplitude of the payload and that of the base. For a nonlinear vibration isolation system, the force or the displacement responses usually have more frequency components than the excitation. For a harmonic excitation, the response may be periodic, quasi-periodic or chaotic. Therefore, the amplitude ratio cannot well define the transmissibility. The root-mean-square ratio of the response to the excitation is suggested to define the transmissibility. The significance of the modified transmissibility is highlighted in a nonlinear two-stage vibration isolation system consisting of two linear spring connected linear vibration isolators with two additional horizontal linear springs. Harmonic balance method (HBM) is applied to determine the responses with the fundamental and third harmonic. Numerical simulations reveal that chaos may occur in the responses. In both cases, the modified transmissibility works while the original definition cannot be applied to chaotic response.
Discrete-time neural inverse optimal control for nonlinear systems via passivation.
Ornelas-Tellez, Fernando; Sanchez, Edgar N; Loukianov, Alexander G
2012-08-01
This paper presents a discrete-time inverse optimal neural controller, which is constituted by combination of two techniques: 1) inverse optimal control to avoid solving the Hamilton-Jacobi-Bellman equation associated with nonlinear system optimal control and 2) on-line neural identification, using a recurrent neural network trained with an extended Kalman filter, in order to build a model of the assumed unknown nonlinear system. The inverse optimal controller is based on passivity theory. The applicability of the proposed approach is illustrated via simulations for an unstable nonlinear system and a planar robot. PMID:24807528
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.
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