Ebook: Extensions and Relaxations
- Tags: Calculus of Variations and Optimal Control, Optimization, Systems Theory Control, Measure and Integration, Functional Analysis, Topology
- Series: Mathematics and Its Applications 542
- Year: 2002
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
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.
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.
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.
Content:
Front Matter....Pages i-xiv
Phase Constraints and Boundary Conditions in Linear Control Problems....Pages 1-14
General Structures....Pages 15-80
Topological Constructions of Extensions and Relaxations....Pages 81-140
Elements of Measure Theory and Extension Constructions....Pages 141-255
Compactifications and Problems of Integration....Pages 257-306
Non-Anticipating Procedures of Control and Iteration Methods for Constructing Them....Pages 307-361
An Extension Construction for Set-Valued Quasi-Strategies....Pages 363-390
Conclusion....Pages 391-392
Back Matter....Pages 393-408
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.
Content:
Front Matter....Pages i-xiv
Phase Constraints and Boundary Conditions in Linear Control Problems....Pages 1-14
General Structures....Pages 15-80
Topological Constructions of Extensions and Relaxations....Pages 81-140
Elements of Measure Theory and Extension Constructions....Pages 141-255
Compactifications and Problems of Integration....Pages 257-306
Non-Anticipating Procedures of Control and Iteration Methods for Constructing Them....Pages 307-361
An Extension Construction for Set-Valued Quasi-Strategies....Pages 363-390
Conclusion....Pages 391-392
Back Matter....Pages 393-408
....