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    An Efficient Computational Approach to a Class of Minmax Optimal Control Problems with Applications

    153365_29417_LI BIN-ANZIAM.pdf (184.7Kb)
    Access Status
    Open access
    Authors
    Li, Bin
    Teo, Kok Lay
    Zhao, G.
    Duan, G.
    Date
    2009
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Li, B. and Teo, K.L. and Zhao, G.H. and Duan, G.R. 2009. An Efficient Computational Approach to a Class of Minmax Optimal Control Problems with Applications. The ANZIAM Journal. 51: pp. 162-177.
    Source Title
    ANZIAM Journal
    DOI
    10.1017/S1446181110000040
    ISSN
    14461811
    School
    Department of Mathematics and Statistics
    Remarks

    © Cambridge University Press 2009

    URI
    http://hdl.handle.net/20.500.11937/21706
    Collection
    • Curtin Research Publications
    Abstract

    In this paper, an efficient computation method is developed for solving a general class of minmax optimal control problems, where the minimum deviation from the violation of the continuous state inequality constraints is maximized. The constraint transcription method is used to construct a smooth approximate function for each of the continuous state inequality constraints. We then obtain an approximate optimal control problem with the integral of the summation of these smooth approximate functions as its cost function. A necessary condition and a sufficient condition are derived showing the relationship between the original problem and the smooth approximate problem. We then construct a violation function from the solution of the smooth approximate optimal control problem and the original continuous state inequality constraints in such a way that the optimal control of the minmax problem is equivalent to the largest root of the violation function, and hence can be solved by the bisection search method. The control parametrization and a time scaling transform are applied to these optimal control problems. We then consider two practical problems: the obstacle avoidance optimal control problem and the abort landing of an aircraft in a windshear downburst.

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