The Dynamics of Control

Fritz Colonius, Wolfgang Kliemann (Autoren)

Buch | Hardcover

629 Seiten

2000
Birkhauser Boston Inc (Verlag)
978-0-8176-3683-8 (ISBN)

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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.

1 Introduction.- 2 Dynamics, Perturbations, and Control.- 2.1 Perturbations of Complex behavior.- 2.2 Approximation of Complex Systems.- 2.3 Generic Behavior of Perturbations.- 2.4 Stability Boundaries and Multistability.- 2.5 Reachability in Control Systems.- 2.6 Linear and Nonlinear Stability Radii.- 2.7 Stabilization of Bilinear Systems.- 2.8 The Lyapunov Spectrum of Matrices.- I Global Theory.- 3 Control Sets.- 4 Control Flows and Limit behavior.- II Linearization Theory.- 5 Linear Flows on Vector Bundles.- 6 Bilinear Systems on Vector Bundles.- 7 Linearization at a Singular Point.- III Applications.- 8 One-Dimensional Control Systems.- 9 Examples for Global behavior.- 10 Examples for the Spectrum.- 11 Stability Radii and Robust Stability.- 12 Open and Closed Loop Stabilization.- 13 Dynamics of Perturbations.- IV Appendices.- A Geometric Control Theory.- A.1 Differentiable Manifolds and Vector Fields.- A.2 Basic Definitions for Control Systems.- A.3 The Orbit Theorem.- A.4 Local Accessibility.- A.5 Notes.- B Dynamical Systems.- B.1 Vector Bundles.- B.2 Morse Decompositions, Attractors, Chains.- B.3 Ergodic Theory.- B.4 Notes.- C Numerical Computation of Orbits.- C.1 Orbits and Approximately Invariant Sets.- C.2 Computing Approximately Invariant Sets.- C.3 Computation via Time Optimal Control.- C.4 Notes.- D.1 Problem Formulation and Main Results.- D.2 Discounted and Average Functional.- D.3 Approximation of the Spectrum.- D.4 The Hamilton-Jacobi-Bellman Equation.- D.5 Discounted Optimal Control Problems.- D.6 Notes.

Reihe/Serie	Systems & Control: Foundations & Applications
Mitarbeit	Anhang von: L. Grüne
Zusatzinfo	XII, 629 p.
Verlagsort	Secaucus
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Technik ► Elektrotechnik / Energietechnik
ISBN-10	0-8176-3683-8 / 0817636838
ISBN-13	978-0-8176-3683-8 / 9780817636838
Zustand	Neuware