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    An Exact Penalty Function Method for Continuous Inequality Constrained Optimal Control Problem

    Access Status
    Fulltext not available
    Authors
    Li, Bin
    Yu, Changjun
    Teo, Kok Lay
    Duan, G.
    Date
    2011
    Type
    Journal Article
    
    Metadata
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    Citation
    Li, Bin and Yu, Chang Jun and Teo, Kok Lay and Duan, Guang Ren. 2011. An Exact Penalty Function Method for Continuous Inequality Constrained Optimal Control Problem. Journal of Optimization Theory and Applications. 151 (2): pp. 260-291.
    Source Title
    Journal of Optimization Theory and Applications
    DOI
    10.1007/s10957-011-9904-5
    ISSN
    0022-3239
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/24732
    Collection
    • Curtin Research Publications
    Abstract

    In this paper, we consider a class of optimal control problems subject to equality terminal state constraints and continuous state and control inequality constraints. By using the control parametrization technique and a time scaling transformation, the constrained optimal control problem is approximated by a sequence of optimal parameter selection problems with equality terminal state constraints and continuous state inequality constraints. Each of these constrained optimal parameter selection problems can be regarded as an optimization problem subject to equality constraints and continuous inequality constraints. On this basis, an exact penalty function method is used to devise a computational method to solve these optimization problems with equality constraints and continuous inequality constraints. The main idea is to augment the exact penalty function constructed from the equality constraints and continuous inequality constraints to the objective function, forming a new one. This gives rise to a sequence of unconstrained optimization problems. It is shown that, for sufficiently large penalty parameter value, any local minimizer of the unconstrained optimization problem is a local minimizer of the optimization problem with equality constraints and continuous inequality constraints. The convergent properties of the optimal parameter selection problems with equality constraints and continuous inequality constraints to the original optimal control problem are also discussed. For illustration, three examples are solved showing the effectiveness and applicability of the approach proposed.

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