Class Of Nonlinear Dynamical Systems Research Articles

NONSINGULAR TERMINAL SLIDING MODE CONTROL OF A CLASS OF NONLINEAR DYNAMICAL SYSTEMS

In this paper, a nonsingular terminal sliding mode concept is introduced for the control of a class of nonlinear dynamical systems. This nonsingular terminal sliding mode control not only enables the £nite time convergence of the system equilibrium, but also eliminates the singularity problem associated with conventional terminal sliding mode control. Simulations are presented to show the effectiveness of the design.

Global qualitative description of a class of nonlinear dynamical systems

In this paper we propose a methodology to derive a qualitative description of the behavior of a system from an incompletely known nonlinear dynamical model. The model is written as an algebraic structure with unknown parameters and/or functions. Under some hypotheses, we obtain a graph describing the possible transitions between regions, defined by the trends of the state variables and their relative positions. A qualitative simulation of the model can be compared with on-line data for fault detection purpose. We give the example of a nonlinear biological model (in dimension three) for the growth of cells in a bioreactor.

Intermittency in Turbulent Flows

The conception of this book lies somewhere between a proceedings volume and a monograph. It consists of 16 sections on intermittent hydrodynamic or magnetohydrodynamic flow. Each one is written by a different author or team of authors. Each subsection itself offers a review type of presentation, written for this book. It contains many references to recent original work, emphasizing the authors' expertise and contributions. While there is coherence of the presentation, the notions, the symbols, etc, within the subsections, there is hardly any cross-referencing between them, except for the common headline intermittency. The reader finds a rich variety of topics, of building blocks, on the one hand, but on the other hand will miss the unifying view as well as various features and authors he knows to work on intermittent fluid flow. But altogether he gets quite a representative overview on recent progress in this very active field. Some of the articles particularly nicely demonstrate why there is increasing interest in turbulent fluctuations and excitement of researchers about the phenomenon called intermittency. The book is less devoted to applied fluid flow; it concentrates on the physics of intermittency, even in the broader context. A few items treated in this volume should be mentioned in order to provide the reader with appropriate information. These include how to relate the anomalous scaling exponents of the structure functions - the signature of intermittency in fluid flow - with the near-singular flow structures. Are there relations to the often discussed finite time singularities of the Euler equations? The question of universality of intermittent space-time fluctuations in fluid flow in particular and in large classes of nonlinear dynamical systems is dealt with repeatedly. The cascade picture, fractality, multifractality and beyond, are offered. Clearly the mixture of new ideas, notions and conceptions together with discussions and results of many new experiments, also visualization techniques, stimulate the reader's interest and excitement. Competent authors and new material on very recent approaches are the main reasons to recommend this book for researchers in fluid flow and in nonlinear dynamical systems theory, for students as well as for experts. They can find stimulating information on new ideas, for example on multipoint correlators, on the so-called inverted structure functions, on geometrical statistics, etc, and they find this together with less recent material such as on so-called extended self-similarity, on wavelet use etc, and finally on long-standing items. Intermittency is a very vivid, active field. A unified physical understanding is still missing, but a whole host of models, Ans\"atze and experimental findings contribute to the developing nature of this unique phenomenon intermittency. This volume contributes in compiling many details and providing an overview which might lead, in the future, to a summarizing explanation. The reader already looking for that here will be disappointed. Still, it is worthwhile to read or at least look into this book, to experience the dynamics in this field and, perhaps, become engaged by it. Siegfried Grossmann

Global stabilization of a certain class of nonlinear dynamical systems using state detection

This note is concerned with the stabilization of control systems using an estimated state feedback. The global stabilization problem for a relatively broad class of nonlinear plants is discussed. Moreover, using the “input to state stability” property introduced by Sontag [1–4] and detectability condition, we show that the system can be globally asymptotically stable using a state detection.

On The Approximation Capability of Neural Networks ‐ Dynamic System Modeling and Control

ABSTRACTThis paper discusses issues related to the approximation capability of neural networks in modeling and control. We show that neural networks are universal models and universal controllers for a class of nonlinear dynamic systems. That is, for a given dynamic system, there exists a neural network which can model the system to any degree of accuracy over time. Moreover, if the system to be controlled is stabilized by a continuous controller, then there exists a neural network which can approximate the controller such that the system controlled by the neural network is also stabilized with a given bound of output error.

Stability properties of a general class of nonlinear dynamical systems

We establish sufficient conditions for the boundedness of the trajectories and the stability of the fixed points in a class of general nonlinear systems, the so-called quasi-polynomial vector fields, with the help of a natural embedding of such systems in a family of generalized Lotka-Volterra (LV) equations. A purely algebraic procedure is developed to determine such conditions. We apply our method to obtain new results for LV systems, by a reparametrization in time variable, and to study general nonlinear vector fields, originally far from the LV format.

Global Convergence of a Control System by Means of an Observer

In this paper, we propose some sufficient conditions for the global stabilization of a class of nonlinear dynamic systems by using an estimated state feedback law given by an observer design.

Adaptive radial basis function neural network control with variable variance parameters

The paper presents a direct adaptive control architecture for a class of nonlinear dynamic systems, which are either ill defined or rather complex. The direct adaptive architecture employs radial basis function (RBF) neural network (NN) systems to reconstruct the ideal feedback linearization control. With the modified adaptation algorithm proposed herein, the on-line function approximation capability of the RBF NN a system is enhanced to remove the auxiliary control term and switching element in a conventional RBF-NN-based controller; simultaneously, the tracking performance is upgraded. Global asymptotic stability of the on-line algorithm is established in the Lyapunov sense to guarantee that the tracking error can converge to a small neighbourhood of the origin. Simulation validations for an inverted pendulum system are finally performed to verify the effectiveness of the proposed controller and the theoretical discussion.

Design of Robust Tracking Controllers Using Sliding Mode Technique.

A simple methodology of designing robust tracking controllers using sliding mode technique is proposed in this paper for a class of nonlinear dynamic systems. This control scheme contains a simple perturbation estimation process embedded in the controller, so that the robustness of system’s stability can be maintained without knowing the upper bound information of perturbation itself and the estimation error of it. The perturbation estimator can be implemented by using a simple high pass filter. The tracking accuracy of control can be adjusted through two stages. The first stage is done by refining the perturbation estimation process. The second stage is done by adjusting the parameter of controller. Chattering phenomenon will never occur under this control scheme. The comparison between the proposed control scheme and the traditional sliding mode control in the frequency domain is given. A numerical example and a practical experiment are demonstrated for showing the applicability of the proposed control scheme.

Adaptive fuzzy learning control for a class of nonlinear dynamic systems

Adaptive fuzzy learning control for a class of nonlinear dynamic systems

Design and Stability Analysis of a Fault Accommodation Scheme for a Class of Nonlinear Dynamical Systems

The paper presents a robust fault diagnosis scheme for detecting and accommodating faults occurring in a class of nonlinear multi-input multi-output dynamical systems. Changes in the system dynamics due to a fault are modeled as nonlinear functions of the control input and state variables. The proposed fault accommodation scheme provides a way to augment the nominal controller such that the stability of the closed-loop system is retained in the presence of an unknown fault and of bounded disturbances. The stability of the robust fault accommodation scheme is rigorously established using Lyapunov redesign methods.

Adaptive fuzzy learning control for a class of nonlinear dynamic systems

This paper presents an adaptive iterative learning control scheme that is applicable to a class of nonlinear systems. The control scheme guarantees system stability and bounded-ness by using the feedback controller coupled with the fuzzy compensator and achieves precise tracking by using the iterative learning rules. In the feedback plus fuzzy compensator unit, the feedback control part stabilizes the overall closed-loop system and keeps its error bounded, and the fuzzy compensator estimates and compensates for the nonlinear part of the system, thereby keeping the feedback gains reasonably low in the feedback controller. The fuzzy compensator is designed by applying the fuzzy approximation technique to the uncertain nonlinear term to be compensated. In the iterative learning controller, a simple learning control rule is used to achieve precise tracking of the reference signal and a parameter learning algorithm is used to update the parameters in the fuzzy compensator so as to identify the uncertain nonlinearity as much as possible.

Robust adaptive control of a class of nonlinear systems with unknown backlash-like hysteresis

Deals with adaptive control of a class of nonlinear dynamic systems preceded by unknown backlash-like hysteresis nonlinearities, where the hysteresis is modeled by a differential equation. By exploiting solution properties of the differential equation and combining those properties with adaptive control techniques, a robust adaptive control algorithm is developed without constructing a hysteresis inverse. The new control law ensures global stability of the adaptive system and achieves both stabilization and tracking to within a desired precision. Simulations performed on a nonlinear system illustrate and clarify the approach.

An Approach to Fault Diagnosis for Nonlinear System with Different Operating Points

This paper presents a new approach to fault diagnosis for nonlinear systems with different operating points. The model parameters of a class of nonlinear dynamic systems treated as functions of measured operating point and faults are estimated by radial basis function (RBF) neural networks. The effects caused by occurrence of fault can be differed from the ones caused by variance of operating points precisely with the help of the new concept “reference operating point”. Consequently, the diagnostic result is obtained by means of fuzzy logic. Finally this method is verified in a nonlinear position servo control system.

Pseudolinear neural networks based nonlinear system modeling and control

Pseudo-linear neural networks (PNN) based modeling and control strategy for a class of nonlinear dynamic systems is proposed. The training of the PNN is implemented by using a recursive prediction error (RPE) algorithm. The control strategy is based on one-step-ahead prediction, in which a direct controller design for an affine nonlinear system and the second order based optimization for a general nonlinear system are adopted. The stability of the closed loop control system is investigated, and some sufficient conditions for the local asymptotic stability are derived. The some simulated examples showed the good results of proposed control strategies in this paper.

Implementation of indirect neuro-control for nonlinear dynamic systems

This paper represents identification and control designs using neural networks for a class of nonlinear dynamic systems. The proposed neuro-controller is a combination of a linear controller and a neural network trained by an indirect neuro-control scheme. The proposed neuro-controller is implemented and tested on an IBM PC-based bar system, and is applicable to many dc-motor-driven precision servo mechanisms. The algorithm and experimental results are described. The experimental results are shown to be superior to those of conventional control.

Minimum Time Trajectory Optimization and Learning

This paper presents a numerical algorithm for finding the bang-bang control input associated with the time optimal solution of a class of nonlinear dynamic systems. The proposed algorithm directly searches for the optimal switching instants based on a projected gradient optimization method. It is shown that this algorithm can be made into a learning algorithm by using on-line measurements of the state trajectory. The learning is shown to have the potential for significant robustness to mismatch between the model and the system. It learns a nearly optimal input through repeated trials in which it utilizes the measured terminal state error of the actual system and gradients based on the theoretical state equation of the system but evaluated along the actual state trajectory. The success of the method is demonstrated on an underactuated double pendulum system called the acrobot.

Intelligent learning control for a class of nonlinear dynamic systems

A controller is presented which guarantees system stability by using a feedback controller coupled with an intelligent compensator, and achieves precise tracking by using a set of iterative learning rules. In the feedback plus intelligent controller unit, the feedback control part stabilises the overall closed-loop system and keeps its error bounded, and the intelligent compensator estimates and compensates for the nonlinear part of the system, thereby keeping the feedback gains reasonably low in the feedback controller. In the iterative learning controller, a simple learning control rule is used to achieve precise tracking of the reference signal and a parameter learning rule is used to update the parameters of the intelligent compensator, thereby identifying the uncertain nonlinearity as closely as possible.

Self‐tuning type variable structure control method for a class of nonlinear systems

In this paper we propose a new self-tuning type Variable Structure Control (VSC) method for a class of nonlinear dynamical systems with parametric uncertainties. The controller is designed to satisfy the sliding mode condition; mean-while the on-line parameter identification is incorporated in the control system. Necessary modifications are made for the parameter identification to avoid the control singularity problem. By virtue of the sliding mode, the proposed identification algorithm can be applied to those nonlinear systems which may not be linear in parametric space but are linear while in the sliding mode. A model-based strategy is further introduced to estimate the uncertainty bound. The new approach attains the gain scheduling property by tuning the switching gain in accordance with the estimated system uncertainties, that is, the switching gain decreases asymptotically while the sliding mode condition is still maintained. © 1998 John Wiley & Sons, Ltd.

Self-tuning type variable structure control method for a class of nonlinear systems

In this paper we propose a new self-tuning type variable structure control (VSC) method for a class of nonlinear dynamical systems with parametric uncertainties. The control law is designed to satisfy the sliding mode condition while the online parameter identification is incorporated in the control system. Necessary modifications are made for the parameter identification to avoid the singularity of control input. By virtue of sliding mode, the proposed identification algorithm can be applied to those nonlinear systems which may not be linear in parametric space but are linear while in sliding mode. A model-based strategy is further introduced to estimate the uncertainty bound. The new approach attains the gain scheduling property by tuning the switching gain in accordance with the estimated system uncertainties, that is, the switching gain tends to reduce asymptotically while ensuring that the sliding mode condition is maintained.