The Dynamics of Control

ISBN-13: 9781461271079 / Angielski / Miękka / 2012 / 629 str.

Fritz Colonius; Wolfgang Kliemann; L. Grune

Opis

A book is never the sole accomplishment of the authors. It is built on the foun- dation of established mathematics, and it benefits from current developments within the mathematical community. Many colleagues have contributed ideas, comments, and corrections to this volume. There are, first of all, our students C. Bauer, G. Grammel, 1. Greger, S. Grtinvogel, G. Hackl, and D. Szolnoki in Augs- burg, and E. Joseph, R.-G. Lai, S. Lin, C.-M. Ou, and H. Wang in Ames. We have received comments from, among others, L. Arnold, V. Ayala, K. Grasse, D. Hinrichsen, R. Johnson, Y. Latushkin, J.L. Massera, F.J. de la Rubia, J. San Martin, L.A.B. San Martin, C. Scherer, H. Sussmann, L. Vargas, and W. Du. Special thanks go to a group of engineers who have helped us to identify important problems and have kept us honest in our claim of applicability of the theory: Ariaratnam, S. Namachchivaya, S. Shaw, S. Sinha, B. Spencer, V. Vittal, and W. Wedig. And we appreciate the work of the anonymous referees of our papers who have helped us in so many ways.

Recenzje

From the reviews:

"The scope of the present book is comprehensive and includes a variety of topics related to the theory of systems and control. The main frame is the notion of control flow with its global dynamics and linearization. Time-varying perturbations, global and local dynamics of control systems, as well as relevant numerical methods are treated.... The book is an excellent resource for the foundations and applications of control theory and nonlinear dynamics for mathematicians, physicists, and engineers. The point of view of the authors, who incorporated into this treatise a variety of topics from fields that were often considered rather separately, makes the book especially interesting." -Applications of Mathematics

"The Dynamics of Control provides a non traditional approach to the subjects of Dynamical Systems theory and Control theory. It is probably the first book where such notions as Morse decomposition, chain recurrence from dynamical systems theory are systematically used for control systems. ... self contained appendix is very helpful. ... The book contains many examples which are helpful in mastering the material. ... Also, the systematic use of dynamical systems theory as applied to control systems should be interesting to control theorists." (V. Zharnitsky, Dynamical Systems Magazine, April, 2008)

Spis treści

Preface Introduction Dynamics, Perturbations, and Control Part I. Global Theory Control Sets Control Flows and Limit Behavior Part II. Linearization Theory Linear Flows and Vector Bundles Linearization at a Singular Point Part III. Applications One-Dimensional Control Systems Examples for Global Behavior Examples for the Spectrum Stability Radii and Robust Stability Open and Closed Loop Stabilization Dynamics of Perturbations Part IV. Appendices Geometric Control Theory Dynamical Systems Numerical Computation of Orbits Computation of the Spectrum by Lars Grüne Bibliography Index

Blurb

The Dynamics of Control provides a carefully integrated development of the mathematical connections between nonlinear control, dynamical systems, and time-varying perturbed systems for scientists and engineers. The central theme is the notion of control flow with its global dynamics and linearization presented in detail.

The book's scope is comprehensive and includes global theory of dynamical systems under time-varying perturbations, global and local dynamics of control systems, connections between control systems and dynamical systems and the relevant numerical methods for global dynamics, linearization, and stability. Topics are developed with a diverse and extensive selection of applied problems from control and dynamical systems.

Topics and Features:

* complete coverage of unified theory of control flows

* wide array of motivating problems from control and dynamical systems to appeal to mathematicians, scientists, and engineers

* relevant motivation and a listing of important definitions and results at the beginning of each chapter

* a compilation of essential background information in four appendices: nonlinear geometric control, topological theory of dynamical systems, computations of reachable sets, and numerical solution of Hamilton–Jacobi–Belman equations

* discussion of numerical methods

This new text and self-study reference guide is an excellent resource for the foundations and applications of control theory and nonlinear dynamics. All graduates, practitioners, and professionals in control theory, dynamical systems, perturbation theory, engineering, physics, and nonlinear dynamics will find the book a rich source of ideas, methods, and applications.