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

/pdf/a-survey-of-recent-results-in-networked-control-systems-2vqnhq8czm.pdf

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

We present a robustness analysis result for a class of neural networks. Specifically, we assume a set of bipolar vectors to be memories for a network, and we establish a sufficient condition under which the given set of vectors are also memories of the original network after perturbations on its parameters. >

http://ieeexplore.ieee.org/iel2/1096/8013/00343271.pdf

Robustness analysis of a class of neural networks

In [9] and in a more recent paper [7] we established results for the uniform stability and the uniform asymptotic stability in the large involving non-monotonic Lyapunov functions for continuous-time dynamical systems. In the present paper we continue this work by addressing finite-dimensional discrete-time dynamical systems. Similarly as in [9] and [7], we prove that in general, the results presented herein are less conservative than the corresponding standard Lyapunov stability results (henceforth called classical Lyapunov stability results) for finite-dimensional discrete-time dynamical systems. We present two specific examples to demonstrate the applicability of our results.

Stability results for finite-dimensional discrete-time dynamical systems involving non-monotonic Lyapunov functions

Stability preserving mappings are used to identify general dynamical systems having equivalent qualitative properties. The authors establish sufficient conditions for a mapping to have stability preserving properties and they use stability preserving mappings to formulate comparison theorems for general dynamical systems. The results developed include most of the corresponding comparison results reported in the literature as special cases. In addition, the present results are applicable to certain classes of general dynamical systems, such as discrete event systems, which cannot be addressed by corresponding previous results. For such systems, the motions which make up a dynamical system are not determined by equations, as is required by the existing results. The applicability of the results developed is demonstrated on a class of discrete event systems. >

Qualitative equivalence of dynamical systems with applications to discrete event systems

A discussion is presented of several techniques for the design of continuous-time and discrete-time neural networks for the purpose of realizing associative memories. The applicability of the methods is demonstrated by means of specific examples, and their strengths and weaknesses are pointed out. To introduce the subject and provide required background material, comments on associative memory, neural models, and stability concepts are presented. >

Design techniques of neural networks for associative memories

In Chapters 2–4 we concerned ourselves primarily with algebraic aspects of certain mathematical systems, while in Chapter 5 we addressed ourselves to topological properties of some mathematical systems. The stage is now set to combine topological and algebraic structures. In doing so, we arrive at linear topological spaces, namely normed linear spaces and inner product spaces, in general, and Banach spaces and Hilbert spaces, in particular. The properties of such spaces are the topic of the present chapter. In the next chapter we will study linear transformations defined on Banach and Hilbert spaces. The material of the present chapter and the next chapter constitutes part of a branch of mathematics called functional analysis.

Anthony N. Michel

Papers

Robustness analysis of a class of neural networks

Stability results for finite-dimensional discrete-time dynamical systems involving non-monotonic Lyapunov functions

Qualitative equivalence of dynamical systems with applications to discrete event systems

Design techniques of neural networks for associative memories

Normed Spaces and Inner Product Spaces