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    Switching time and parameter optimization in nonlinear switched systems with multiple time-delays

    212922_212922.pdf (286.1Kb)
    Access Status
    Open access
    Authors
    Liu, C.
    Loxton, Ryan
    Teo, Kok Lay
    Date
    2014
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Liu, C. and Loxton, R. and Teo, K.L. 2014. Switching time and parameter optimization in nonlinear switched systems with multiple time-delays. Journal of Optimization Theory and Applications. 163: pp. 957-988.
    Source Title
    Journal of Optimization Theory and Applications
    DOI
    10.1007/s10957-014-0533-7
    ISSN
    0022-3239
    School
    Department of Mathematics and Statistics
    Remarks

    The final publication is available at Springer via http://doi.org/10.1007/s10957-014-0533-7

    URI
    http://hdl.handle.net/20.500.11937/47016
    Collection
    • Curtin Research Publications
    Abstract

    Abstract In this paper, we consider a dynamic optimization problem involving a general switched system that evolves by switching between several subsystems of nonlinear delay-differential equations. The optimization variables in this system consist of: (1) the times at which the subsystem switches occur; and (2) a set of system parameters that influence the subsystem dynamics. We first establish the existence of the partial derivatives of the system state with respect to both the switching times and the system parameters. Then, on the basis of this result, we show that the gradient of the cost function can be computed by solving the state system forward in timefollowed by a costate system backward in time. This gradient computation procedure can be combined with any gradient-based optimization method to determine the optimal switching times and parameters. We propose an effective optimization algorithm based on this idea. Finally, we consider three numerical examples, one involving the 1,3-propanediol fed-batch production process, to illustrate the effectiveness and applicability of the proposed algorithm.

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