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    Minimizing control variation in discrete-time optimal control problems

    Access Status
    Fulltext not available
    Authors
    Zhang, Y.
    Yu, Changjun
    Xu, Y.
    Teo, Kok Lay
    Date
    2016
    Type
    Journal Article
    
    Metadata
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    Citation
    Zhang, Y. and Yu, C. and Xu, Y. and Teo, K.L. 2016. Minimizing control variation in discrete-time optimal control problems. Journal of Computational and Applied Mathematics. 292: pp. 292-306.
    Source Title
    Journal of Computational and Applied Mathematics
    DOI
    10.1016/j.cam.2015.07.010
    ISSN
    0377-0427
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/40776
    Collection
    • Curtin Research Publications
    Abstract

    For a real practical system, a large fluctuation in the control signal is highly undesirable. To address this undesirable situation, we investigate a discrete-time optimal control problem subject to terminal state and all-time-step constraints on the state and control, where the cost function is the sum of terminal cost and the variation of the control signal. The variation of the control signal is expressed in terms of absolute value functions and hence is nonsmooth. By a novel smooth transformation and the constraint transcription technique, this problem is approximated by a constrained discrete-time optimal control with the new cost function involves only smooth functions. A gradient-based computational method is then derived, which is supported by rigorous convergence analysis. Two examples are provided to demonstrate the effectiveness and advantages of the proposed method.

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