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Switching Time and Parameter Optimization in Nonlinear Switched Systems with Multiple Time-Delays

Author

Listed:
  • Chongyang Liu

    (Shandong Institute of Business and Technology)

  • Ryan Loxton

    (Curtin University
    Zhejiang University)

  • Kok Lay Teo

    (Zhejiang University)

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 time followed 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.

Suggested Citation

  • Chongyang Liu & Ryan Loxton & Kok Lay Teo, 2014. "Switching Time and Parameter Optimization in Nonlinear Switched Systems with Multiple Time-Delays," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 957-988, December.
    • Handle: RePEc:spr:joptap:v:163:y:2014:i:3:d:10.1007_s10957-014-0533-7
    DOI: 10.1007/s10957-014-0533-7
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    Cited by:

    1. Mohammad Ali Abooshahab & Mohsen Ekramian & Mohammad Ataei & Ali Ebrahimpour-Boroojeny, 2019. "Time-Delay Estimation in State and Output Equations of Nonlinear Systems Using Optimal Computational Approach," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 1036-1064, March.
    2. Matheus Henrique Marcolino & Roberto Kawakami Harrop Galvão & Karl Heinz Kienitz & Márcio Santos Vieira, 2017. "Determination of Periodic Trajectories of Dynamic Systems Subject to Switching Input Constraints," Journal of Optimization Theory and Applications, Springer, vol. 175(3), pages 848-864, December.

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