Minimum Entropy Control for Time-Varying Systems

ISBN-13: 9780817639723 / Angielski / Twarda / 1997 / 189 str.

Marc A. Peters; Pablo Iglesias

Opis

One of the main goals of optimal control theory is to provide a theoretical basis for choosing an appropriate controller for whatever system is under consideration by the researcher or engineer. Two popular norms that have proved useful are known as H-2 and H - infinity control. The first has been particularly applicable to problems arising in the aerospace industry. However, most industrial problems are badly modeled and the second norm proved to be more appropriate when the actual conditions of the problem did not conform to the stipulated conditions of the theory. This book takes the topic of H-infinity control as a point of departure and pursues an improved controller design which has been suggested in the mainstream of robust control. Its main theme, minimum entropy control, provides a means of trading off some of the features of other control problems. The book is aimed at research workers in networking systems as well as those in operator theory and linear multivariable control. The use of stochastic methods makes the book also of importance to the circuits and systems community. CONTENTS: Preface Introduction Preliminaries Induced Operator Norms Discrete-Time Entropy Connections With Related Optimal Control Problems Minimum Entropy Control Continuous-Time Entropy A. Proof of Theorem B. Proof of Theorem Bibliography Notation Index"

Spis treści

1 Introduction.- 1.1 Optimal control problems.- 1.2 Minimum entropy control.- 1.3 The maximum entropy principle.- 1.4 Extensions to time-varying systems.- 1.5 Organization of the book.- 2 Preliminaries.- 2.1 Discrete-time time-varying systems.- 2.2 State-space realizations.- 2.3 Time-reverse systems.- 3 Induced Operator Norms.- 3.1 Characterizations of the induced norm.- 3.2 Time-varying hybrid systems.- 3.2.1 Sampled continuous-time systems.- 3.2.2 Continuous-time systems with piecewise constant inputs.- 3.2.3 Hybrid feedback systems.- 3.3 Computational issues.- 4 Discrete-Time Entropy.- 4.1 Entropy of a discrete-time time-varying system.- 4.2 Properties.- 4.2.1 Equivalence with the entropy integral.- 4.2.2 Entropy in terms of a state-space realization.- 4.3 Entropy and information theory.- 4.4 Entropy of an anti-causal system.- 4.5 Entropy and the W-transform.- 4.6 Entropy of a non-linear system.- 5 Connections With Related Optimal Control Problems.- 5.1 Relationship with H?control.- 5.2 Relationship with H2 control.- 5.3 Average cost functions.- 5.3.1 Average H2 cost.- 5.3.2 Average entropy.- 5.4 Time-varying risk-sensitive control.- 5.5 Problems defined on a finite horizon.- 6 Minimum Entropy Control.- 6.1 Problem statement.- 6.2 Basic results.- 6.3 Full information.- 6.3.1 Characterizing all closed-loop systems.- 6.3.2 FI minimum entropy controller.- 6.4 Full control.- 6.5 Disturbance feedforward.- 6.5.1 Characterizing all closed-loop systems.- 6.5.2 DF minimum entropy controller.- 6.6 Output estimation.- 6.7 Output feedback.- 6.8 Stability concepts.- 7 Continuous-Time Entropy.- 7.1 Classes of systems considered.- 7.2 Entropy of a continuous-time time-varying system.- 7.3 Properties.- 7.3.1 Equivalence with the entropy integral.- 7.3.2 Entropy in terms of a state-space realization.- 7.3.3 Relationship with discrete-time entropy.- 7.4 Connections with related optimal control problems.- 7.4.1 Relationship with H? control.- 7.4.2 Relationship with H2 control.- 7.4.3 Relationship with risk-sensitive control.- 7.5 Minimum entropy control.- A Proof of Theorem 6.5.- B Proof of Theorem 7.21.- Notation.