Asymptotic Behavior Of Dynamical And Control Systems Under Perturbation And Discretization
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Asymptotic Behavior of Dynamical and Control Systems Under Perturbation and Discretization
This text provides an approach to the study of perturbation and discretization effects on the long-time behaviour of dynamical and control systems. It analyzes the impact of time and space discretizations on asymptotically stable attracting sets, attractors and asumptotically controllable sets.
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.
Attractors Under Discretisation
This work focuses on the preservation of attractors and saddle points of ordinary differential equations under discretisation. In the 1980s, key results for autonomous ordinary differential equations were obtained – by Beyn for saddle points and by Kloeden & Lorenz for attractors. One-step numerical schemes with a constant step size were considered, so the resulting discrete time dynamical system was also autonomous. One of the aims of this book is to present new findings on the discretisation of dissipative nonautonomous dynamical systems that have been obtained in recent years, and in particular to examine the properties of nonautonomous omega limit sets and their approximations by numerical schemes – results that are also of importance for autonomous systems approximated by a numerical scheme with variable time steps, thus by a discrete time nonautonomous dynamical system.