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Asymptotic Behavior of Dynamical and Control Systems under Pertubation and Discretization
Paperback
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Artikel-Nr:
9783540433910
Veröffentl:
2002
Einband:
Paperback
Erscheinungsdatum:
01.04.2002
Seiten:
244
Autor:
Lars Grüne
Gewicht:
376 g
Format:
235x155x14 mm
Serie:
1783, Lecture Notes in Mathematics
Sprache:
Englisch
Beschreibung:
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.
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.
Includes supplementary material: sn.pub/extras
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
- 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