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Birkhäuser - Birkhäuser Mathematics | Mathematical Control Theory - An Introduction

Mathematical Control Theory

An Introduction

Zabczyk, Jerzy

Originally published as a hardcover edition in the series: Systems & Control: Foundations & Applications

1st ed. 1992. 2nd, corr. printing 1995. Reprint 2007, X, 260 p.

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  • Covers a remarkable number of topics in a concise manner
  • Includes material on the realization of both linear and nonlinear systems, impulsive control, and positive linear systems: subjects not usually covered in an introductory-level book
  • Excellent book for introducing a mathematician to control theory
  • Ideal for a novel one-semester course covering both linear and nonlinear systems

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, the 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.

 

"This book is designed as a graduate text on the mathematical theory of deterministic control. It covers a remarkable number of topics...The exposition is excellent, and the book is a joy to read. A novel one-semester course covering both linear and nonlinear systems could be given...The book is an excellent one for introducing a mathematician to control theory."   Bulletin of the AMS

"The book is very well written from a mathematical point of view of control theory. The author deserves much credit for bringing out such a book which is a useful and welcome addition to books on the mathematics of control theory."   — Control Theory and Advance Technology

"At last! We did need an introductory textbook on control which can be read, understood, and enjoyed by anyone."   — Gian-Carlo Rota, The Bulletin of Mathematics Books

Content Level » Research

Keywords » control - control system - control theory - dynamic programming - infinite dimensional linear systems - linear systems - mathematical control theory - nonlinear control - nonlinear system - observability - optimal control - programming - stability - stabilization - sys

Related subjects » Birkhäuser Engineering - Birkhäuser Mathematics

Table of contents 

Preface.- Introduction.- Part I. Elements of classical control theory.- Controllability and observability.- Stability and stabilizability.- Realization theory.- Systems with constraints.- Part II. Nonlinear control systems.- Controllability and observability of nonlinear systems.- Stability and stabilizability.- Realization theory.- Part III. Optimal control.- Dynamic programming.- Dynamic programming for impulse control.- The maximum principle.- The existence of optimal strategies.- Part IV. Infinite dimensional linear systems.- Linear control systems.- Controllability.- Stability and stabilizability.- Linear regulators in Hilbert spaces.- Appendix.- Metric spaces.- Banach spaces.- Hilbert spaces.- Bochner's integral.- Spaces of continuous functions.- Spaces of measurable functions.- References.- Notations.- Index

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