Mathematical Control Theory: Deterministic Finite Dimensional Systems

✍ Scribed by Eduardo D. Sontag (auth.)

• Publisher: Springer-Verlag New York
• Year: 1998
• Tongue: English
• Leaves: 543
• Series: Texts in Applied Mathematics 6
• Edition: 2
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xvi
Introduction....Pages 1-24
Systems....Pages 25-80
Reachability and Controllability....Pages 81-140
Nonlinear Controllability....Pages 141-181
Feedback and Stabilization....Pages 183-260
Outputs....Pages 261-313
Observers and Dynamic Feedback....Pages 315-345
Optimality: Value Function....Pages 347-396
Optimality: Multipliers....Pages 397-421
Optimality: Minimum-Time for Linear Systems....Pages 423-446
Back Matter....Pages 447-531

✦ Subjects

Calculus of Variations and Optimal Control; Optimization; Mathematical Methods in Physics; Numerical and Computational Physics; Computational Intelligence