On near optimal control of systems with slow observables

Vladimir Gaitsgory, Sergey Rossomakhine

    Research output: Contribution to journalArticleResearchpeer-review

    Abstract

    The paper deals with a problem of control of a system characterized by the fact that the influence of controls on the dynamics of certain functions of state variables (called observables) is relatively weak, and the rates of change of these observables are much slower than the rates of change of the state variables themselves. The contributions of the paper are twofold. First, the averaged system whose solutions approximate the trajectories of the slow observables is introduced, and it is shown that the optimal value of the problem of optimal control with time discounting criterion considered on the solutions of the system with slow observables (this problem is referred to as perturbed) converges to the optimal value of the corresponding problem of optimal control of the averaged system. Second, a method for constructing an asymptotically optimal control of the perturbed problem on the basis of an optimal solution of the averaged problem is indicated, sufficient and necessary optimality conditions for the averaged problem are stated, and a way for constructing numerically a near optimal solution of the latter is outlined (the construction being illustrated with an example).

    LanguageEnglish
    Pages1398-1428
    Number of pages31
    JournalSIAM Journal on Control and Optimization
    Volume55
    Issue number3
    DOIs
    Publication statusPublished - 2017

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    Optimal Control
    Rate of change
    Optimal Solution
    Necessary and Sufficient Optimality Conditions
    Discounting
    Asymptotically Optimal
    Trajectories
    Approximate Solution
    Trajectory
    Converge

    Cite this

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    On near optimal control of systems with slow observables. / Gaitsgory, Vladimir; Rossomakhine, Sergey.

    In: SIAM Journal on Control and Optimization, Vol. 55, No. 3, 2017, p. 1398-1428.

    Research output: Contribution to journalArticleResearchpeer-review

    TY - JOUR

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    AU - Gaitsgory,Vladimir

    AU - Rossomakhine,Sergey

    PY - 2017

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    KW - control of slow observables

    KW - averaged system

    KW - average control generating families

    KW - occupational measures

    KW - numerical solution

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