Books.org participates in affiliate programs including Bookshop.org and the Amazon Services LLC Associates Program. We may earn a commission from qualifying purchases made through links on this page, at no additional cost to you.
Overview
In this book we provide a time-domain theory of the entropy criterion. For linear time-invariant systems, this time-domain notion of entropy is equivalent to the usual frequency domain criterion. Moreover, this time-domain notion of entropy enables us to define a suitable entropy for other classes of systems, including the class of linear time-varying systems. Furthermore, by working with this time-domain definition of the entropy we are able to gain new interpretations of the advantages of minimum entropy control. In particular we consider the connections between the time-varying minimum entropy control problem and the time-varying analogues to the H[subscript 2], H[symbol not reproducible] and risk-sensitive control problem. This book is aimed at researchers in mathematical control theory. It will be particularly attractive to those working in both H[symbol not reproducible] control theory as well as linear time-varying systems. While the approach used has its basis in operator theory, it can be followed easily by graduate students with a basis in linear systems theory.Synopsis
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