The Dynamics of Control

The Dynamics of Control by Fritz Colonius, Wolfgang Kliemann.

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 linearizatio...

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Bibliographic Details
Main Authors: Colonius, Fritz (Author), Kliemann, Wolfgang (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2000.
Edition:1st ed. 2000.
Series:Systems & Control: Foundations & Applications,
Springer eBook Collection.
Subjects:
Applied mathematics.
Engineering mathematics.
System theory.
Computational complexity.
Control engineering.
Robotics.
Mechatronics.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 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.

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