Asymptotic Behavior of Dynamical and Control Systems under Pertubation and Discretization

This book provides an approach to the study of perturbation and discretization effects on the long-time behavior of dynamical and control systems. It analyzes the impact of time and space discretizations on asymptotically stable attracting sets, attractors, asumptotically controllable sets and their respective domains of attractions and reachable sets. Combining robust stability concepts from nonlinear control theory, techniques from optimal control and differential games and methods from nonsmooth analysis, both qualitative and quantitative results are obtained and new algorithms are developed, analyzed and illustrated by examples.

List of contents

From the contents:
- Dynamics, Perturbation and Discretization
- Setup and Preliminaries
- Strongly Attracting Sets
- Weakly Attracting Sets
- Relation between Discretization and Perturbation
- Discretizations of Attractive Sets
- Domains of Attraction
- Appendices. Viscosity Solutions. Comparison Functions. Numerical Examples

Summary

This book provides an approach to the study of perturbation and discretization effects on the long-time behavior of dynamical and control systems. It analyzes the impact of time and space discretizations on asymptotically stable attracting sets, attractors, asumptotically controllable sets and their respective domains of attractions and reachable sets. Combining robust stability concepts from nonlinear control theory, techniques from optimal control and differential games and methods from nonsmooth analysis, both qualitative and quantitative results are obtained and new algorithms are developed, analyzed and illustrated by examples.

Product details

• Authors: Lars Grüne
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 25.04.2002
• EAN: 9783540433910
• ISBN: 978-3-540-43391-0
• No. of pages: 238
• Dimensions: 154 mm x 236 mm x 16 mm
• Weight: 370 g
• Illustrations: X, 238 p.
• Series: Lecture Notes in Mathematics; Lecture Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; Optimierung, B, Optimization, Dynamics, Mathematics and Statistics, Systems Theory, Control, Numerical analysis, Dynamical Systems and Ergodic Theory, Ergodic theory, Dynamical systems, Calculus of Variations and Optimization, Calculus of variations, Calculus of Variations and Optimal Control; Optimization, System Theory, Cybernetics & systems theory