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Mathematical Control Theory

Deterministic Finite Dimensional Systems

  • Textbook
  • © 1998

Overview

Authors:
  1. Eduardo D. Sontag

    1. Department of Mathematics, Rutgers University, New Brunswick, USA

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Part of the book series: Texts in Applied Mathematics (TAM, volume 6)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Introduction

    • Eduardo D. Sontag
    Pages 1-24

  3. Systems

    • Eduardo D. Sontag
    Pages 25-80

  4. Reachability and Controllability

    • Eduardo D. Sontag
    Pages 81-140

  5. Nonlinear Controllability

    • Eduardo D. Sontag
    Pages 141-181

  6. Feedback and Stabilization

    • Eduardo D. Sontag
    Pages 183-260

  7. Outputs

    • Eduardo D. Sontag
    Pages 261-313

  8. Observers and Dynamic Feedback

    • Eduardo D. Sontag
    Pages 315-345

  9. Optimality: Value Function

    • Eduardo D. Sontag
    Pages 347-396

  10. Optimality: Multipliers

    • Eduardo D. Sontag
    Pages 397-421

  11. Optimality: Minimum-Time for Linear Systems

    • Eduardo D. Sontag
    Pages 423-446

  12. Back Matter

    Pages 447-531
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Keywords

About this book

Mathematics is playing an ever more important role in the physical and biologi­ cal sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and rein­ force the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematics Sci­ ences (AMS) series, which will focus on advanced textbooks and research-level monographs. v Preface to the Second Edition The most significant differences between this edition and the first are as follows: • Additional chapters and sections have been written, dealing with: nonlinear controllability via Lie-algebraic methods, variational and numerical approaches to nonlinear control, including a brief introduction to the Calculus of Variations and the Minimum Principle, - time-optimal control of linear systems, feedback linearization (single-input case), nonlinear optimal feedback, controllability of recurrent nets, and controllability of linear systems with bounded controls.

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From the reviews
"This book will be very useful for mathematics and engineering students interested in a modern and rigorous systems course, as well as for the experts in control theory and applications."
MATHEMATICAL REVIEWS

Authors and Affiliations

  • Department of Mathematics, Rutgers University, New Brunswick, USA

    Eduardo D. Sontag

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