Integral dynamical models : singularities, signals and control / Denis Sidorov.

Format:

Book

Author/Creator:

Sidorov, Denis, 1974- author.

Series:

World Scientific series on nonlinear science. Monographs and treatises ; Series A, Volume 87.

World Scientific Series on Nonlinear Science. Series A ; Volume 87

Language:

English

Subjects (All):

Nonlinear integral equations.

Volterra equations.

Physical Description:

1 online resource (258 p.)

Place of Publication:

Singapore : World Scientific Publishing Company, 2015.

Language Note:

English

Summary:

This volume provides a broad introduction to nonlinear integral dynamical models and new classes of evolutionary integral equations. It may be used as an advanced textbook by postgraduate students to study integral dynamical models and their applications in machine learning, electrical and electronic engineering, operations research and image analysis. Contents: Introduction and Overview; Volterra Models of Evolving Dynamical Systems: Volterra Equations of the First Kind with Piecewise Continuous Kernels; Volterra Matrix Equation of the First Kind with Piecewise Continuous Kernels; Volterra Op

Contents:

Foreword; Contents; 1. Introduction and Overview; 1.1 Statement of Purpose; 1.2 The Scope of This Book; 1.3 Acknowledgments; Part 1 Volterra Models of Evolving Dynamical Systems; Part Summary; 2. Volterra Equations of the First Kind with Piecewise Continuous Kernels; 2.1 Introduction. The State of the Art; 2.2 The Structure of Solutions; 2.3 Existence Theorem; 2.4 The Method of Asymptotic Approximations Construction; 2.5 Example; 3. Volterra Matrix Equation of the First Kind with Piecewise Continuous Kernels; 3.1 Introduction

3.2 Construction of Asymptotic Approximation of Solutions to Inhomogeneous System3.3 Existence of Continuous Parametric Family of Solutions; 3.4 Sufficient Conditions for Existence of Unique Continuous Solution; 3.4.1 Final Remarks on Volterra Matrix Equations; 4. Volterra Operator Equations of the First Kind with Piecewise Continuous Kernels; 4.1 Introduction. The State of the Art; 4.2 Sufficient Conditions for Existence of the Unique Continuous Solution; 4.3 Construction of the Asymptotic Approximation of Parametric Family of Solutions

4.4 Theorem of Existence of Continuous Parametric Solutions4.5 Final Remarks on Generalized Solutions; 5. Generalized Solutions to the Volterra Equations with Piecewise Continuous Kernels and Sources; 5.1 Problem Statement. The State of the Art; 5.2 Volterra Equations of the First Kind with Discontinuous Sources; Part 2 Nonlinear Models, Singularities and Control; Part Summary; 6. Nonlinear Hammerstein Integral Equations; 6.1 Problem Statement; 6.2 Asymptotics of a Solution and Successive Approximations; 6.3 Solution to the Abstract Operator Equation with Vector Parameter; 6.4 Examples

7. Nonlinear Volterra Operator Equations with Non-invertible Operator7.1 Problem Statement; 7.2 Asymptotics in the Branching Points Neighborhood; 7.3 Perturbation of Linear Equation by Nonlinear Volterra Operator; 8. Nonlinear Differential Equations Near Branching Points; 8.1 Problem Statement; 8.2 The Principal Term of the Solution. Problem Reduction; 8.2.1 Possible Generalizations; 8.3 Magnetic Insulation Model Example; 9. Convex Majorants Method in the Theory of Nonlinear Volterra Equations; 9.1 Problem Statement. The State of the Art; 9.2 Integral Majorants Method

9.3 Algebraic Majorants Method9.4 Application of the Convex Majorants Method; 10. Generalized Solutions to Nonlinear Volterra Equations of the First Kind; 10.1 Problem Statement; 10.2 Singular Component Determination; 10.3 Regular Component Determination; 10.4 Example; 11. On Impulse Control of Nonlinear Dynamical Systems Based on the Volterra Series; 11.1 Introduction. The State of the Art; 11.2 Overview of the Volterra Models Identification Methods; 11.2.1 Kernels Identification via the Special Volterra Equations; 11.3 Impulse Control as Solution of Multiple Integral Equation

11.4 Illustrative Examples

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-68015-855-4

981-4619-19-1