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Mathematical Theory of Control Systems Design

  • Book
  • © 1996

Overview

Authors:
  1. V. N. Afanas’ev

    1. Moscow University of Electronics and Mathematics, Moscow, Russia

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  2. V. B. Kolmanovskii

    1. Moscow University of Electronics and Mathematics, Moscow, Russia

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  3. V. R. Nosov

    1. Moscow University of Electronics and Mathematics, Moscow, Russia

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Part of the book series: Mathematics and Its Applications (MAIA, volume 341)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xxiii
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  2. Stability of Control Systems

    1. Front Matter

      Pages 1-1
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    2. Continuous and Discrete Deterministic Systems

      • V. N. Afanas’ev, V. B. Kolmanovskii, V. R. Nosov
      Pages 3-71

    3. Stability of Stochastic Systems

      • V. N. Afanas’ev, V. B. Kolmanovskii, V. R. Nosov
      Pages 73-103

  3. Control of Deterministic Systems

    1. Front Matter

      Pages 125-125
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    2. Description of Control Problems

      • V. N. Afanas’ev, V. B. Kolmanovskii, V. R. Nosov
      Pages 127-150

    3. The Classical Calculus of Variations and Optimal Control

      • V. N. Afanas’ev, V. B. Kolmanovskii, V. R. Nosov
      Pages 151-181

    4. The Maximum Principle

      • V. N. Afanas’ev, V. B. Kolmanovskii, V. R. Nosov
      Pages 183-237

    5. Linear Control Systems

      • V. N. Afanas’ev, V. B. Kolmanovskii, V. R. Nosov
      Pages 239-300

    6. Dynamic Programming Approach. Sufficient Conditions for Optimal Control

      • V. N. Afanas’ev, V. B. Kolmanovskii, V. R. Nosov
      Pages 301-341

    7. Some Additional Topics of Optimal Control Theory

      • V. N. Afanas’ev, V. B. Kolmanovskii, V. R. Nosov
      Pages 343-373

  4. Optimal Control of Dynamical Systems under Random Disturbances

    1. Front Matter

      Pages 391-391
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    2. Control of Stochastic Systems. Problem Statements and Investigation Techniques

      • V. N. Afanas’ev, V. B. Kolmanovskii, V. R. Nosov
      Pages 393-434

    3. Optimal Control on a Time Interval of Random Duration

      • V. N. Afanas’ev, V. B. Kolmanovskii, V. R. Nosov
      Pages 435-466

    4. Optimal Estimation of the State of the System

      • V. N. Afanas’ev, V. B. Kolmanovskii, V. R. Nosov
      Pages 467-507

    5. Optimal Control of the Observation Process

      • V. N. Afanas’ev, V. B. Kolmanovskii, V. R. Nosov
      Pages 509-542

  5. Numerical Methods in Control Systems

    1. Front Matter

      Pages 553-553
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    2. Linear Time-Invariant Control Systems

      • V. N. Afanas’ev, V. B. Kolmanovskii, V. R. Nosov
      Pages 555-579

    3. Numerical Methods for the Investigation of Nonlinear Control Systems

      • V. N. Afanas’ev, V. B. Kolmanovskii, V. R. Nosov
      Pages 581-618

    4. Numerical Design of Optimal Control Systems

      • V. N. Afanas’ev, V. B. Kolmanovskii, V. R. Nosov
      Pages 619-639
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Keywords

About this book

Give, and it shall be given unto you. ST. LUKE, VI, 38. The book is based on several courses of lectures on control theory and appli­ cations which were delivered by the authors for a number of years at Moscow Electronics and Mathematics University. The book, originally written in Rus­ sian, was first published by Vysshaya Shkola (Higher School) Publishing House in Moscow in 1989. In preparing a new edition of the book we planned to make only minor changes in the text. However, we soon realized that we like many scholars working in control theory had learned many new things and had had many new insights into control theory and its applications since the book was first published. Therefore, we rewrote the book especially for the English edition. So, this is substantially a new book with many new topics. The book consists of an introduction and four parts. Part One deals with the fundamentals of modern stability theory: general results concerning stability and instability, sufficient conditions for the stability of linear systems, methods for determining the stability or instability of systems of various type, theorems on stability under random disturbances.

Authors and Affiliations

  • Moscow University of Electronics and Mathematics, Moscow, Russia

    V. N. Afanas’ev, V. B. Kolmanovskii, V. R. Nosov

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