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Functional Differential Equations : Application of i-smooth calculus - Arkadii V. Kim

Functional Differential Equations

Application of i-smooth calculus


Published: 31st May 1999
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This monograph presents the basics of i-smooth calculus, a new differential calculus of nonlinear functionals based on the notion of invariant derivative, and its application to some problems of the qualitative theory of functional differential equations. It separates finite and infinite dimensional components in the structures of functional differential equations and functionals, and uses conditional representation of FDEs, which is expedient for the application of methods and constructions of i-smooth calculus. Part I contains a foundation of i-smooth calculus. Part II is an introduction to FDEs based on i-smooth calculus. Part III describes the direct Lyapunov method for systems with delays in terms of i-smooth functionals. Part IV considers an approach to the development of a dynamical programming method for systems with delays in terms of i-smooth Bellman's functionals.

`The book is warmly recommended for students and researchers in mathematics, applied mathematicians, and engineers whose work involves ordinary differential equations, functional analysis, partial equations, optimal control and mathematics system theory.' Acta Scientiarum Mathematicarum

i-Smooth Calculus
Structure of Functionals
Properties of Functionals. Invariant Derivative
Generalized Derivatives of Nonlinear Functionals
Functional Differential Equations
Functional Differential Equations
Neutral Functional Differential Equations
Direct Lyapunov Method for Systems with Delays
The Problem Statement
The Lyapunov Functional Method
The Lyapunov Function Method
Dynamical Programming Method for Systems with Delays
Systems with State Delays
Systems with Control Delays
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780792356899
ISBN-10: 0792356896
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 168
Published: 31st May 1999
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 17.15 x 26.04  x 1.27
Weight (kg): 0.45