On Average Control Generating Families for Singularly Perturbed Optimal Control Problems with Long Run Average Optimality Criteria

Vladimir Gaitsgory; Ludmila Manic; Sergey Rossomakhine

doi:10.1007/s11228-014-0306-3

On Average Control Generating Families for Singularly Perturbed Optimal Control Problems with Long Run Average Optimality Criteria

Vladimir Gaitsgory^*, Ludmila Manic, Sergey Rossomakhine

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

The paper aims at the development of tools for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems with long run average optimality criteria. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional (ID) linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with a numerical example.

Original language	English
Pages (from-to)	87-131
Number of pages	45
Journal	Set-Valued and Variational Analysis
Volume	23
Issue number	1
DOIs	https://doi.org/10.1007/s11228-014-0306-3
Publication status	Published - 1 Mar 2015

Keywords

Averaging and linear programming
Numerical solution
Occupational measures
Singularly perturbed optimal control problems

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10.1007/s11228-014-0306-3

Cite this

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title = "On Average Control Generating Families for Singularly Perturbed Optimal Control Problems with Long Run Average Optimality Criteria",

abstract = "The paper aims at the development of tools for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems with long run average optimality criteria. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional (ID) linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with a numerical example.",

keywords = "Averaging and linear programming, Numerical solution, Occupational measures, Singularly perturbed optimal control problems",

author = "Vladimir Gaitsgory and Ludmila Manic and Sergey Rossomakhine",

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doi = "10.1007/s11228-014-0306-3",

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T1 - On Average Control Generating Families for Singularly Perturbed Optimal Control Problems with Long Run Average Optimality Criteria

AU - Gaitsgory, Vladimir

AU - Manic, Ludmila

AU - Rossomakhine, Sergey

PY - 2015/3/1

Y1 - 2015/3/1

N2 - The paper aims at the development of tools for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems with long run average optimality criteria. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional (ID) linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with a numerical example.

AB - The paper aims at the development of tools for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems with long run average optimality criteria. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional (ID) linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with a numerical example.

KW - Averaging and linear programming

KW - Numerical solution

KW - Occupational measures

KW - Singularly perturbed optimal control problems

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UR - http://purl.org/au-research/grants/arc/DP130104432

UR - http://purl.org/au-research/grants/arc/DP120100532

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DO - 10.1007/s11228-014-0306-3

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AN - SCOPUS:84958548051

SN - 0927-6947

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EP - 131

JO - Set-Valued and Variational Analysis

JF - Set-Valued and Variational Analysis

IS - 1

ER -

On Average Control Generating Families for Singularly Perturbed Optimal Control Problems with Long Run Average Optimality Criteria

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Keywords

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Construction of Near Optimal Oscillatory Regimes in Singularly Perturbed Control Systems via Solutions of Hamilton-Jacobi-Bellman Inequalities (Vlad Gaitsgory)

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On Average Control Generating Families for Singularly Perturbed Optimal Control Problems with Long Run Average Optimality Criteria

Abstract

Keywords

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Construction of Near Optimal Oscillatory Regimes in Singularly Perturbed Control Systems via Solutions of Hamilton-Jacobi-Bellman Inequalities (Vlad Gaitsgory)

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