Author | Colonius, Fritz. author |
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Title | The Dynamics of Control [electronic resource] / by Fritz Colonius, Wolfgang Kliemann |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2000 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1350-5 |
Descript | XII, 629 p. online resource |
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