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A Hybrid Time-Scaling Transformation for Time-Delay Optimal Control Problems

Author

Listed:
  • Changjun Yu

    (Central South University
    Curtin University)

  • Qun Lin

    (Curtin University)

  • Ryan Loxton

    (Curtin University)

  • Kok Lay Teo

    (Curtin University)

  • Guoqiang Wang

    (Shanghai University of Engineering Science)

Abstract

In this paper, we consider a class of nonlinear time-delay optimal control problems with canonical equality and inequality constraints. We propose a new computational approach, which combines the control parameterization technique with a hybrid time-scaling strategy, for solving this class of optimal control problems. The proposed approach involves approximating the control variables by piecewise constant functions, whose heights and switching times are decision variables to be optimized. Then, the resulting problem with varying switching times is transformed, via a new hybrid time-scaling strategy, into an equivalent problem with fixed switching times, which is much preferred for numerical computation. Our new time-scaling strategy is hybrid in the sense that it is related to two coupled time-delay systems—one defined on the original time scale, in which the switching times are variable, the other defined on the new time scale, in which the switching times are fixed. This is different from the conventional time-scaling transformation widely used in the literature, which is not applicable to systems with time-delays. To demonstrate the effectiveness of the proposed approach, we solve four numerical examples. The results show that the costs obtained by our new approach are lower, when compared with those obtained by existing optimal control methods.

Suggested Citation

  • Changjun Yu & Qun Lin & Ryan Loxton & Kok Lay Teo & Guoqiang Wang, 2016. "A Hybrid Time-Scaling Transformation for Time-Delay Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 876-901, June.
    • Handle: RePEc:spr:joptap:v:169:y:2016:i:3:d:10.1007_s10957-015-0783-z
    DOI: 10.1007/s10957-015-0783-z
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    References listed on IDEAS

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    1. Eunice Blanchard & Ryan Loxton & Volker Rehbock, 2014. "Optimal control of impulsive switched systems with minimum subsystem durations," Journal of Global Optimization, Springer, vol. 60(4), pages 737-750, December.
    2. Changjun Yu & Bin Li & Ryan Loxton & Kok Teo, 2013. "Optimal discrete-valued control computation," Journal of Global Optimization, Springer, vol. 56(2), pages 503-518, June.
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    Cited by:

    1. Mohamed Karim Bouafoura & Naceur Benhadj Braiek, 2019. "Hybrid Functions Direct Approach and State Feedback Optimal Solutions for a Class of Nonlinear Polynomial Time Delay Systems," Complexity, Hindawi, vol. 2019, pages 1-14, April.
    2. Chongyang Liu & Zhaohua Gong & Changjun Yu & Song Wang & Kok Lay Teo, 2021. "Optimal Control Computation for Nonlinear Fractional Time-Delay Systems with State Inequality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 83-117, October.
    3. Marzban, Hamid Reza & Nezami, Atiyeh, 2022. "Analysis of nonlinear fractional optimal control systems described by delay Volterra–Fredholm integral equations via a new spectral collocation method," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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