Mathematical theory of control systems design

by V.N. Afanas'ev, V.B. Kolmanovskii, and V.R. Nosov

The many interesting topics covered in Mathematical Theory of Control Systems Design are spread over an Introduction and four parts. Each chapter concludes with a brief review of the main results and formulae, and each part ends with an exercise section. Part One treats the fundamentals of modern stability theory. Part Two is devoted to the optimal control of deterministic systems. Part Three is concerned with problems of the control of systems under random disturbances of their parameters, and Part Four provides an outline of modern numerical methods of control theory. The many examples included illustrate the main assertions, teaching the reader the skills needed to construct models of relevant phenomena, to design nonlinear control systems, to explain the qualitative differences between various classes of control systems, and to apply what they have learned to the investigation of particular systems. Audience: This book will be valuable to both graduate and postgraduate students in such disciplines as applied mathematics, mechanics, engineering, automation and cybernetics.

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  • Preface. Introduction. Part One: Stability of control systems. I. Continuous and discrete deterministic systems. II. Stability of stochastic systems. Part Two: Control of deterministic systems. III. Description of control problems. IV. The classical calculus of variations and optimal control. V. The maximum principle. VI. Linear control systems. VII. Dynamic programming approach. Sufficient conditions for optimal control. VIII. Some additional topics of optimal control theory. Part Three: Optimal control of dynamical systems under random disturbances. IX. Control of stochastic systems. Problem statements and investigation techniques. X. Optimal control on a time level of random duration. XI. Optimal estimation of the state of the system. XII. Optimal control of the observation process. Part Four: Numerical methods in control systems. XIII. Linear time-invariant control systems. XIV. Numerical methods for the investigation of nonlinear control systems. XV. Numerical design of optimal control systems. General references. Subject index.

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書名 Mathematical theory of control systems design
著作者等 Kolmanovskiĭ, Vladimir Borisovich
Nosov, V. R.
Afanasiev V.N.
Kolmanovskii V.
Afanasʹev Valerii Nikolaevich
シリーズ名 Mathematics and its applications
出版元 Kluwer Academic
刊行年月 c1996
ページ数 xxiii, 668 p.
大きさ 25 cm
ISBN 0792337247
NCID BA27163779
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言語 英語
原文言語 ロシア語
出版国 オランダ