Chentsov / Morina Extensions and Relaxations

2002
ISBN: 978-94-017-1527-0
Verlag: Springer Netherland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 542, 408 Seiten, eBook

Reihe: Mathematics and Its Applications

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.

Zielgruppe

Research

Autoren/Hrsg.

Chentsov, A.G.

Morina, S.I.

Inhaltsverzeichnis

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.