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.

  Klappentext

  This new text/reference 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. With its careful use of examples and detailed development, it is suitable for use as a self-study/reference guide for all scientists and engineers.

  Inhalt

  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