Linear Programming Approach to Deterministic Long Run Average Problems of Optimal Control

We establish that deterministic long run average problems of optimal control are "asymptotically equivalent" to infinite-dimensional linear programming problems (LPPs) and we establish that these LPPs can be approximated by finite-dimensional LPPs, the solutions of which can be used for co...

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Bibliographic Details
Published in:SIAM journal on control and optimization Vol. 44; no. 6; pp. 2006 - 2037
Main Authors: Gaitsgory, Vladimir, Rossomakhine, Sergey
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2006
Subjects:
Applied mathematics
Applied sciences
Computer science; control theory; systems
Control theory. Systems
Exact sciences and technology
Linear programming
Optimal control
Optimization
System theory
Averaging method
Differential equation
Singular perturbation
Control system
Average
Linear programming
34C29
34E15
occupational measures
long run average optimal control
Optimal control
93C70
singularly perturbed control systems
Asymptotic approximation
Infinite dimension
Differential inclusion
Deterministic approach
34A60
ISSN:0363-0129, 1095-7138
Online Access:Get full text
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Summary:We establish that deterministic long run average problems of optimal control are "asymptotically equivalent" to infinite-dimensional linear programming problems (LPPs) and we establish that these LPPs can be approximated by finite-dimensional LPPs, the solutions of which can be used for construction of the optimal controls. General results are illustrated with numerical examples.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0363-0129
1095-7138
DOI:10.1137/040616802