Ebook: Asymptotic Behavior of Dynamical and Control Systems under Perturbation and Discretization
Author: Lars Grüne (auth.)
- Genre: Mathematics // Dynamical Systems
- Tags: Dynamical Systems and Ergodic Theory, Systems Theory Control, Numerical Analysis, Calculus of Variations and Optimal Control, Optimization
- Series: Lecture Notes in Mathematics 1783
- Year: 2002
- Publisher: Springer-Verlag Berlin Heidelberg
- City: Berlin; New York
- Edition: 1
- Language: English
- pdf
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.
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