Extensions and Relaxations

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.

List 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.

Summary

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

• Authors: A Chentsov, A G Chentsov, A. G. Chentsov, A.G. Chentsov, Aleksander Chentsov, Aleksander G. Chentsov, S I Morina, S. I. Morina, S.I. Morina
• Publisher: Springer Netherlands
• Languages: English
• Product format: Paperback / Softback
• Released: 07.10.2010
• EAN: 9789048160013
• ISBN: 978-90-481-6001-3
• No. of pages: 408
• Dimensions: 155 mm x 24 mm x 235 mm
• Weight: 1037 g
• Illustrations: XIV, 408 p. 1 illus.
• Series: Mathematics and Its Applications; Mathematics and Its Applications
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Miscellaneous; C, measure theory, Mathematics and Statistics, Topology, Functional Analysis, Systems Theory, Control, Calculus of Variations and Optimization, Calculus of variations, Calculus of Variations and Optimal Control; Optimization, Measure and Integration, System Theory, Cybernetics and systems theory, Functional analysis and transforms, Control theory, Integral calculus and equations