It is demonstrated that neural networks can be used effectively for the identification and control of nonlinear dynamical systems. The emphasis is on models for both identification and control. Static and dynamic backpropagation methods for the adjustment of parameters are discussed. In the models that are introduced, multilayer and recurrent networks are interconnected in novel configurations, and hence there is a real need to study them in a unified fashion. Simulation results reveal that the identification and adaptive control schemes suggested are practically feasible. Basic concepts and definitions are introduced throughout, and theoretical questions that have to be addressed are also described. >

Identification and control of dynamical systems using neural networks

Networked control systems (NCSs) are spatially distributed systems for which the communication between sensors, actuators, and controllers is supported by a shared communication network. We review several recent results on estimation, analysis, and controller synthesis for NCSs. The results surveyed address channel limitations in terms of packet-rates, sampling, network delay, and packet dropouts. The results are presented in a tutorial fashion, comparing alternative methodologies

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A Survey of Recent Results in Networked Control Systems

By a switched system, we mean a hybrid dynamical system consisting of a family of continuous-time subsystems and a rule that orchestrates the switching between them. The article surveys developments in three basic problems regarding stability and design of switched systems. These problems are: stability for arbitrary switching sequences, stability for certain useful classes of switching sequences, and construction of stabilizing switching sequences. We also provide motivation for studying these problems by discussing how they arise in connection with various questions of interest in control theory and applications.

Basic problems in stability and design of switched systems

关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

During the past several years, there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems. This paper aims to briefly survey recent results in this field. First, the stability analysis for switched systems is reviewed. We focus on the stability analysis for switched linear systems under arbitrary switching, and we highlight necessary and sufficient conditions for asymptotic stability. After a brief review of the stability analysis under restricted switching and the multiple Lyapunov function theory, the switching stabilization problem is studied, and a variety of switching stabilization methods found in the literature are outlined. Then the switching stabilizability problem is investigated, that is under what condition it is possible to stabilize a switched system by properly designing switching control laws. Note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature. A necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here.

Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results

In [1] we established, among other results, a set of sufficient conditions for the uniform asymptotic stability of invariant sets for discontinuous dynamical systems (DDS) defined on metric space, and under some additional minor assumptions, we also established a set of necessary conditions (a converse theorem). This converse theorem involves Lyapunov functions which need not necessarily be continuous. In the present paper, we show that under some additional very mild assumptions, the Lyapunov functions for the converse theorem need actually be continuous. This improvement in the regularity properties of the Lyapunov functions shows that the stability results in [1] (under the additional mild assumptions) are rather robust. To keep our presentation as simple as possible, we confine ourselves to discontinuous dynamical systems determined by ordinary differential equations. However, the methodology em ployed herein can be used to establish converse theorems for DDS involving continuous Lyapunov functions for dynamical systems defined on metric spaces concerning a variety of stability and boundedness types.

Converse stability theorems for discontinuous dynamical systems: Improved results

We develop results for partial stability of discontinuous dynamical systems (DDS) with respect to invariant sets defined on metric space, using stability preserving mappings. Our results are applicable to a much larger class of systems than existing results, including to DDS that cannot be determined by the usual (differential) equations or inequalities. Furthermore, in contrast to existing results which pertain primarily to the analysis of equilibria, the present results apply to invariant sets (including equilibria as special cases). We apply our results in the analysis of a special class of finite dimensional dynamical systems subject to impulse effects, and we show that in this particular case, our results are less conservative than existing ones.

Anthony N. Michel

Papers

Converse stability theorems for discontinuous dynamical systems: Improved results

Partial stability of discontinuous dynamical systems

Nonlinear model-matching design of servomechanisms

A successive substitution approach with embedded phase stability for simultaneous chemical and phase equilibrium calculations

ℒ2 gain analysis of switched symmetric systems with time delays