Extensions and Relaxations

by A.G. Chentsov, S.I. Morina

Overview

In this book a general topological construction of extension is proposed for problems of attainability in topological spaces under perturbation of a system of constraints. This construction is realized in a special class of generalized elements defined as finitely additive measures. A version of the method of programmed iterations is constructed. This version realizes multi-valued control quasistrategies, which guarantees the solution of the control problem that consists in guidance to a given set under observation of phase constraints.

Audience: The book will be of interest to researchers, and graduate students in the field of optimal control, mathematical systems theory, measure and integration, functional analysis, and general topology.

Product Details

ISBN-13:	9789048160013
Publisher:	Springer Netherlands
Publication date:	12/07/2010
Series:	Mathematics and Its Applications , #542
Edition description:	Softcover reprint of hardcover 1st ed. 2002
Pages:	408
Product dimensions:	8.27(w) x 10.98(h) x 0.03(d)

Table of Contents

1. Phase Constraints and Boundary Conditions in Linear Control Problems.- 2. General Structures.- 3. Topological Constructions of Extensions and Relaxations.- 4. Elements of Measure Theory and Extension Constructions.- 5. Compactifications and Problems of Integration.- 6. Non-Anticipating Procedures of Control and Iteration Methods for Constructing Them.- 7. An Extension Construction for Set-Valued Quasi-Strategies.- Conclusion.- References.- Notation.