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    Control parameterization for optimal control problems with continuous inequality constraints: New convergence results

    186815_186815.pdf (262.5Kb)
    Access Status
    Open access
    Authors
    Loxton, Ryan
    Lin, Qun
    Rehbock, Volker
    Teo, Kok Lay
    Date
    2012
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Loxton, Ryan and Lin, Qun and Rehbock, Volker and Teo, Kok Lay. 2012. Control parameterization for optimal control problems with continuous inequality constraints: New convergence results. Numerical Algebra, Control and Optimization. 2 (3): pp. 571-599.
    Source Title
    Numerical Algebra, Control and Optimization
    DOI
    10.3934/naco.2012.2.571
    ISSN
    21553289
    Remarks

    This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Numerical Algebra, Control and Optimization following peer review. The definitive publisher-authenticated version, Loxton, Ryan and Lin, Qun and Rehbock, Volker and Teo, Kok Lay. 2012. Control parameterization for optimal control problems with continuous inequality constraints: New convergence results. Numerical Algebra, Control and Optimization. 2 (3): pp. 571-599, is available online at: http://dx.doi.org/10.3934/naco.2012.2.571

    URI
    http://hdl.handle.net/20.500.11937/23872
    Collection
    • Curtin Research Publications
    Abstract

    Control parameterization is a powerful numerical technique for solving optimal control problems with general nonlinear constraints. The main idea of control parameterization is to discretize the control space by approximating the control by a piecewise-constant or piecewise-linear function, thereby yielding an approximate nonlinear programming problem. This approximate problem can then be solved using standard gradient-based optimization techniques. In this paper, we consider the control parameterization method for a class of optimal control problems in which the admissible controls are functions of bounded variation and the state and control are subject to continuous inequality constraints. We show that control parameterization generates a sequence of suboptimal controls whose costs converge to the true optimal cost. This result has previously only been proved for the case when the admissible controls are restricted to piecewise continuous functions.

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