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    An optimal control problem involving impulsive integrodifferential systems

    Access Status
    Fulltext not available
    Authors
    Wu, C.
    Teo, Kok Lay
    Zhao, Y.
    Yan, W.
    Date
    2007
    Type
    Journal Article
    
    Metadata
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    Citation
    Wu, C. and Teo, Kok Lay and Zhao, Y. and Yan, W. 2007. An optimal control problem involving impulsive integrodifferential systems. Optimization Methods and Software. 22 (3): pp. 531-549.
    Source Title
    Optimization Methods and Software
    DOI
    10.1080/10556780601135688
    ISSN
    0233-1934
    Faculty
    Department of Mathematics and Statistics
    School of Science
    Faculty of Science and Engineering
    URI
    http://hdl.handle.net/20.500.11937/34875
    Collection
    • Curtin Research Publications
    Abstract

    In this article, we consider a class of optimal control problems involving dynamical systems described by impulsive integrodifferential equations. First, we approximate the integral kernel of the integral equation by a finite expansion of the shifted Chebyshev polynomial. Through this process, the optimal control problem is approximated by a sequence of optimal control problems involving only impulsive ordinary differential equations. Each of them can be viewed as a nonlinear optimization problem. For each of these approximated problems, the gradient formula of the cost functional can be derived and hence can be solved by many efficient optimization techniques. Consequently, the optimal control software, MISER, is applicable for the purpose. Then, we present some convergence results showing the relationship between the sequence of the optimal controls of the approximated problems and that of the original problem. Finally, a numerical example is presented to illustrate the efficiency of the proposed method.

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