Asymptotic Behavior of Dynamical and Control Systems under Perturbation and Discretization
Grüne, Lars.
Asymptotic Behavior of Dynamical and Control Systems under Perturbation and Discretization [electronic resource] / by Lars Grüne. - X, 238 p. online resource. - Lecture Notes in Mathematics, 1783 0075-8434 ; . - Lecture Notes in Mathematics, 1783 .
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.
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.
9783540367840
10.1007/b83677 doi
Differentiable dynamical systems.
Systems theory.
Numerical analysis.
Mathematical optimization.
Dynamical Systems and Ergodic Theory.
Systems Theory, Control.
Numerical Analysis.
Calculus of Variations and Optimal Control; Optimization.
QA313
515.39 515.48
Asymptotic Behavior of Dynamical and Control Systems under Perturbation and Discretization [electronic resource] / by Lars Grüne. - X, 238 p. online resource. - Lecture Notes in Mathematics, 1783 0075-8434 ; . - Lecture Notes in Mathematics, 1783 .
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.
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.
9783540367840
10.1007/b83677 doi
Differentiable dynamical systems.
Systems theory.
Numerical analysis.
Mathematical optimization.
Dynamical Systems and Ergodic Theory.
Systems Theory, Control.
Numerical Analysis.
Calculus of Variations and Optimal Control; Optimization.
QA313
515.39 515.48