Overview

This volume is devoted to the investigation of general Borel models of stochastic optimal control, taking into consideration additional performance criteria which must satisfy the constraints-inequalities. It is based on both convex programming theory as well as the Bellman principle, and provides a useful approach for multicriteria control problems. Some new original properties of strategical measure space are established, and among the other subjects that are treated are the existence and the form of optimal control strategy; Markov and homogeneous models; and linear-quadratic systems. The last chapter concentrates on application of these methods to, for example, economics, ecology, insurance and games. This text should be of interest to postgraduate students and researchers whose work involves stochastic control and its applications.

Full Product Details

Author:   A.B. Piunovskiy
Publisher:   Springer
Imprint:   Springer
Edition:   1997 ed.
Volume:   410
Dimensions:   Width: 15.50cm , Height: 2.00cm , Length: 23.50cm
Weight:   0.715kg
ISBN:  

9780792345718

ISBN 10:   0792345711
Pages:   348
Publication Date:   31 May 1997
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Awaiting stock  
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Table of Contents

1 Methods of Stochastic Optimal Control.- 1.1 Statement of the optimal control problem and examples.- 1.2 Markov decision processes.- 2 Optimal Control Problems with Constraints.- 2.1 Statement of the problem.- 2.2 Properties of the strategic measures space.- 2.3 Necessary and sufficient conditions for optimality.- 2.4 Essential and inessential constraints.- 2.5 Algorithm for solving the main convex programming problem.- 2.6 Example.- 3 Solvability of the main constrained problem and some extensions.- 3.1 Existence of solutions in constrained problems.- 3.2 Form of optimal control strategies.- 3.3 Example.- 3.4 Other constrained problems of optimal control.- 4 Linear-quadratic systems.- 4.1 Model with a finite horizon.- 4.2 Homogeneous discounted model.- 4.3 Homogeneous model with average losses.- 5 Some applications.- 5.1 Stochastic macroeconomic model of the Neumann type.- 5.2 Simplest ecological-economic system.- 5.3 Model of insurance.- 5.4 Stochastic stabilization problem.- 5.5 Queueing system.- 5.6 Optimization of publicity expenses.- 5.7 Simplest constrained game.- Conclusion.- A1 Borel spaces and their properties.- A1.1 Main concepts.- A1.2 Probability measures on Borel spaces.- A1.3 Semicontinuous functions and measurable selection.- A2 Elements of convex analysis.- A2.1 Certain definitions.- A2.2 Duality relation and Kuhn-Tucker theorem.- A2.3 Selected properties of convex sets.- A3 Proofs of auxiliary statements.- A4 Linear-quadratic systems: proofs of some statements.- References.- List of symbols.- List of the main statements.

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