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    An exact penalty method for free terminal time optimal control problem with continuous inequality constraints

    Access Status
    Fulltext not available
    Authors
    Jiang, Canghua
    Lin, Qun
    Yu, Changjun
    Teo, Kok Lay
    Duan, Guang-Ren
    Date
    2012
    Type
    Journal Article
    
    Metadata
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    Citation
    Jiang, Canghua and Lin, Qun and Yu, Changjun and Teo, Kok Lay and Duan, Guang-Ren. 2012. An exact penalty method for free terminal time optimal control problem with continuous inequality constraints. Journal of Optimization Theory and Applications. 154 (1): pp. 30-53.
    Source Title
    Journal of Optimization Theory and Applications
    DOI
    10.1007/s10957-012-0006-9
    ISSN
    0022-3239
    URI
    http://hdl.handle.net/20.500.11937/14871
    Collection
    • Curtin Research Publications
    Abstract

    In this paper, we consider a class of optimal control problems with free terminal time and continuous inequality constraints. First, the problem is approximated by representing the control function as a piecewise-constant function. Then the continuous inequality constraints are transformed into terminal equality constraints for an auxiliary differential system. After these two steps, we transform the constrained optimization problem into a penalized problem with only box constraints on the decision variables using a novel exact penalty function. This penalized problem is then solved by a gradient-based optimization technique. Theoretical analysis proves that this penalty function has continuous derivatives, and for a sufficiently large and finite penalty parameter, its local minimizer is feasible in the sense that the continuous inequality constraints are satisfied. Furthermore, this local minimizer is also the local minimizer of the constrained problem. Numerical simulations on the range maximization for a hypersonic vehicle reentering the atmosphere subject to a heating constraint demonstrate the effectiveness of our method.

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