Construction of Global Lyapunov Functions Using Radial Basis Functions

Peter Giesl

ISBN 10: 3540699074 / ISBN 13: 9783540699071

Published by Springer Berlin Heidelberg, Springer Berlin Heidelberg Apr 2007, 2007

About this Item

Neuware -This book combines two mathematical branches: dynamical systems and radialbasisfunctions.Itismainlywrittenformathematicianswithexperience in at least one of these two areas. For dynamical systems we provide a method to construct a Lyapunov function and to determine the basin of attraction of an equilibrium. For radial basis functions we give an important application for the approximation of solutions of linear partial di erential equations. The book includes a summary of the basic facts of dynamical systems and radial basis functions which are needed in this book. It is, however, no introduction textbook of either area; the reader is encouraged to follow the references for a deeper study of the area. The study of di erential equations is motivated from numerous appli- tions in physics, chemistry, economics, biology, etc. We focus on autonomous n di erential equations x = f(x), x R which de ne a dynamical system. The simplest solutions x(t) of such an equation are equilibria, i.e. solutions x(t)= x which remain constant. An important and non-trivial task is the 0 determination of their basin of attraction. The determination of the basin of attraction is achieved through sublevel sets of a Lyapunov function, i.e. a function with negative orbital derivative. TheorbitalderivativeV (x)ofafunctionV(x)isthederivativealongsolutions of the di erential equation. In this book we present a method to construct Lyapunov functions for an equilibrium. We start from a theorem which ensures the existence of aSpringer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 184 pp. Englisch.

Seller Inventory # 9783540699071

Bibliographic Details

• Title: Construction of Global Lyapunov Functions Using Radial Basis Functions
• Publisher: Springer Berlin Heidelberg, Springer Berlin Heidelberg Apr 2007
• Publication Date: 2007
• Language: English
• ISBN 10: 3540699074
• ISBN 13: 9783540699071
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 11D millimeters 235 millimeters width by 155 millimeters height by 11 millimeters depth
• Weight: 289 grams

About this title

Synopsis

This book combines two mathematical branches: dynamical systems and radialbasisfunctions.Itismainlywrittenformathematicianswithexperience in at least one of these two areas. For dynamical systems we provide a method to construct a Lyapunov function and to determine the basin of attraction of an equilibrium. For radial basis functions we give an important application for the approximation of solutions of linear partial di?erential equations. The book includes a summary of the basic facts of dynamical systems and radial basis functions which are needed in this book. It is, however, no introduction textbook of either area; the reader is encouraged to follow the references for a deeper study of the area. The study of di?erential equations is motivated from numerous appli- tions in physics, chemistry, economics, biology, etc. We focus on autonomous n di?erential equations x ? = f(x), x? R which de?ne a dynamical system. The simplest solutions x(t) of such an equation are equilibria, i.e. solutions x(t)= x which remain constant. An important and non-trivial task is the 0 determination of their basin of attraction. The determination of the basin of attraction is achieved through sublevel sets of a Lyapunov function, i.e. a function with negative orbital derivative. TheorbitalderivativeV (x)ofafunctionV(x)isthederivativealongsolutions of the di?erential equation. In this book we present a method to construct Lyapunov functions for an equilibrium. We start from a theorem which ensures the existence of a

From the Back Cover

The basin of attraction of an equilibrium of an ordinary differential equation can be determined using a Lyapunov function. A new method to construct such a Lyapunov function using radial basis functions is presented in this volume intended for researchers and advanced students from both dynamical systems and radial basis functions. Besides an introduction to both areas and a detailed description of the method, it contains error estimates and many examples.