Continuity properties of the cheap control problem without stability

A.H.W. Geerts

    Research output: Book/ReportReportAcademic

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    Abstract

    An open problem concerning the convergence of the optimal cost for the cheap control problem without stability is solved. It turns out that the definition of a new type of linear-quadratic optimal control problems is necessary. This new problem requires the infimization of the cost functional under the constraint that the state trajectory modulo a certain subspace vanishes as time goes to infinity. The associated optimal cost turns out to be the limit of the optimal cost for the cheap control problem without stability. Moreover, for left invertible systems, the optimal control, state and output for the perturbed problem tend to the optimal control, state and output for the new problem. Also a characterization of the optimal cost for the latter problem is given in terms of the dissipation inequality.
    Original languageEnglish
    Place of PublicationEindhoven
    PublisherTechnische Universiteit Eindhoven
    Number of pages39
    Publication statusPublished - 1987

    Publication series

    NameMemorandum COSOR
    Volume8717
    ISSN (Print)0926-4493

    Fingerprint

    Control Problem
    Costs
    Optimal Control
    Output
    Invertible
    Optimal Control Problem
    Modulo
    Dissipation
    Vanish
    Open Problems
    Subspace
    Infinity
    Tend
    Trajectory
    Necessary

    Cite this

    Geerts, A. H. W. (1987). Continuity properties of the cheap control problem without stability. (Memorandum COSOR; Vol. 8717). Eindhoven: Technische Universiteit Eindhoven.
    Geerts, A.H.W. / Continuity properties of the cheap control problem without stability. Eindhoven : Technische Universiteit Eindhoven, 1987. 39 p. (Memorandum COSOR).
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    Geerts, AHW 1987, Continuity properties of the cheap control problem without stability. Memorandum COSOR, vol. 8717, Technische Universiteit Eindhoven, Eindhoven.

    Continuity properties of the cheap control problem without stability. / Geerts, A.H.W.

    Eindhoven : Technische Universiteit Eindhoven, 1987. 39 p. (Memorandum COSOR; Vol. 8717).

    Research output: Book/ReportReportAcademic

    TY - BOOK

    T1 - Continuity properties of the cheap control problem without stability

    AU - Geerts, A.H.W.

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    N2 - An open problem concerning the convergence of the optimal cost for the cheap control problem without stability is solved. It turns out that the definition of a new type of linear-quadratic optimal control problems is necessary. This new problem requires the infimization of the cost functional under the constraint that the state trajectory modulo a certain subspace vanishes as time goes to infinity. The associated optimal cost turns out to be the limit of the optimal cost for the cheap control problem without stability. Moreover, for left invertible systems, the optimal control, state and output for the perturbed problem tend to the optimal control, state and output for the new problem. Also a characterization of the optimal cost for the latter problem is given in terms of the dissipation inequality.

    AB - An open problem concerning the convergence of the optimal cost for the cheap control problem without stability is solved. It turns out that the definition of a new type of linear-quadratic optimal control problems is necessary. This new problem requires the infimization of the cost functional under the constraint that the state trajectory modulo a certain subspace vanishes as time goes to infinity. The associated optimal cost turns out to be the limit of the optimal cost for the cheap control problem without stability. Moreover, for left invertible systems, the optimal control, state and output for the perturbed problem tend to the optimal control, state and output for the new problem. Also a characterization of the optimal cost for the latter problem is given in terms of the dissipation inequality.

    M3 - Report

    T3 - Memorandum COSOR

    BT - Continuity properties of the cheap control problem without stability

    PB - Technische Universiteit Eindhoven

    CY - Eindhoven

    ER -

    Geerts AHW. Continuity properties of the cheap control problem without stability. Eindhoven: Technische Universiteit Eindhoven, 1987. 39 p. (Memorandum COSOR).