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 journalArticlepeer-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 languageEnglish
    Pages (from-to)87-131
    Number of pages45
    JournalSet-Valued and Variational Analysis
    Volume23
    Issue number1
    DOIs
    Publication statusPublished - 1 Mar 2015

    Keywords

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

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