Asymptotic Behavior of Dynamical and Control Systems under Perturbation and Discretization [electronic resource] / by Lars Grüne.
Material type: TextSeries: Lecture Notes in Mathematics ; 1783Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2002Description: X, 238 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540367840Subject(s): Mathematics | Differentiable dynamical systems | Systems theory | Numerical analysis | Mathematical optimization | Mathematics | Dynamical Systems and Ergodic Theory | Systems Theory, Control | Numerical Analysis | Calculus of Variations and Optimal Control; OptimizationAdditional physical formats: Printed edition:: No titleDDC classification: 515.39 | 515.48 LOC classification: QA313Online resources: Click here to access onlineCurrent library | Home library | Call number | Materials specified | URL | Status | Date due | Barcode |
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IMSc Library | IMSc Library | Link to resource | Available | EBK346 |
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.
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