Mathematical Control Theory: An Introduction

by Jerzy Zabczyk

Overview

Mathematical Control Theory: An Introduction presents, in a mathematically precise manner, a unified introduction to deterministic control theory. With the exception of a few more advanced concepts required for the final part of the book, this presentation requires only a knowledge of basic facts from linear algebra, differential equations, and calculus.

In addition to classical concepts and ideas, the author covers the stabilization of nonlinear systems using topological methods, realization theory for nonlinear systems, impulsive control and positive systems, the control of rigid bodies, the stabilization of infinite dimensional systems, and the solution of minimum energy problems.

The book will be ideal for a beginning graduate course in mathematical control theory, or for self study by professionals needing a complete picture of the mathematical theory that underlies the applications of control theory.

Product Details

ISBN-13:	9780817647322
Publisher:	Birkh�user Boston
Publication date:	10/12/2007
Series:	Modern Birkh�user Classics
Edition description:	1st ed. 1992. 2nd, corr. printing 1995. Reprint 2007
Pages:	260
Product dimensions:	6.10(w) x 9.10(h) x 0.60(d)

About the Author

Jerzy Zabczyk is Professor Emeritus at the Institute of Mathematics at the Polish Academy of Sciences in Warsaw, Poland. His research interests include deterministic and shastic control theory, shastic and deterministic partial differential equations, and mathematical finance. He is the author of more than ninety research papers, and seven mathematical books.

Table of Contents

Elements of classical control theory.- Controllability and observability.- Stability and stabilizability.- Realization theory.- Systems with constraints.- Nonlinear control systems.- Controllability and observability of nonlinear systems.- Stability and stabilizability.- Realization theory.- Optimal control.- Dynamic programming.- Dynamic programming for impulse control.- The maximum principle.- The existence of optimal strategies.- Infinite dimensional linear systems.- Linear control systems.- Controllability.- Stability and stabilizability.- Linear regulators in Hilbert spaces.

Editorial Reviews

A self-contained outline of mathematical control theory. In addition to classical concepts and ideas, the author includes the stabilization of nonlinear systems using topological methods, realization theory for nonlinear systems, impulsive control and positive systems, the control of rigid bodies, the stabilization of infinite dimensional systems and the solution of minimum energy problems. With few exceptions, the presentation requires only a basic knowledge of linear algebra, differential equations, and calculus. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews

It enables the reader to acquire a capability to construct and analyze biological systems. The mathematical exposition is clear and with detailed explanations of important ideas and interesting results. The book takes an expository approach where the continuous prose intersects with several carefully constructed diagrams and figures. … it contains an extensive list of references and can serve as a reference text for researchers in this field.” (Stéphanie Abou and Anita T. Layton, SIAM Review, Vol. 63 (4), December, 2021)

“An appendix summarizes important mathematical background results. The treatment of both finite- and infinite-dimensional systems is a unique feature of the book … . the book remains largely a book on classical methods, though one of highest mathematical standards. The book is decidedly mathematical in style, with complete proofs of all results, stringent mathematical argumentation, and a traditional definition-theorem-proof structure. … this second edition of the classical text remains a highly valuable contribution to the field.” (Lars Grüne, SIAM Review, Vol. 63 (2), September, 2021)

“This new edition should be a useful resource for students and researchers of control theory.” (IEEE Control Systems Magazine, Vol. 41 (2), April, 2021)

From the Publisher