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Parameter Tuning of Multi-Proportional-Integral-Derivative Controllers Based on Optimal Switching Algorithms

Author

Listed:
  • Xiang Wu

    (Southeast University)

  • Kanjian Zhang

    (Southeast University)

  • Changyin Sun

    (Southeast University)

Abstract

Under the framework of switched systems, this paper considers a multi-proportional-integral-derivative controller parameter tuning problem with terminal equality constraints and continuous-time inequality constraints. The switching time and controller parameters are decision variables to be chosen optimally. Firstly, we transform the optimal control problem into an equivalent problem with fixed switching instants by introducing an auxiliary function and a time-scaling transformation. Because of the complexity of constraints, it is difficult to solve the problem by conventional optimization techniques. To overcome this difficulty, a novel exact penalty function is introduced for these constraints. Furthermore, the penalty function is appended to the cost functional to form an augmented cost functional, giving rise to an approximate nonlinear parameter optimization problem that can be solved using any gradient-based method. Convergence results indicate that any local optimal solution of the approximate problem is also a local optimal solution of the original problem as long as the penalty parameter is sufficiently large. Finally, an example is provided to illustrate the effectiveness of the developed algorithm.

Suggested Citation

  • Xiang Wu & Kanjian Zhang & Changyin Sun, 2013. "Parameter Tuning of Multi-Proportional-Integral-Derivative Controllers Based on Optimal Switching Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 159(2), pages 454-472, November.
    • Handle: RePEc:spr:joptap:v:159:y:2013:i:2:d:10.1007_s10957-013-0306-8
    DOI: 10.1007/s10957-013-0306-8
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    References listed on IDEAS

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    1. H. Axelsson & Y. Wardi & M. Egerstedt & E. I. Verriest, 2008. "Gradient Descent Approach to Optimal Mode Scheduling in Hybrid Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 136(2), pages 167-186, February.
    2. C.Y. Kaya & J.L. Noakes, 2003. "Computational Method for Time-Optimal Switching Control," Journal of Optimization Theory and Applications, Springer, vol. 117(1), pages 69-92, April.
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    Cited by:

    1. 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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