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Computational Method for Time-Optimal Switching Control

Author

Listed:
  • C.Y. Kaya

    (University of South Australia)

  • J.L. Noakes

    (University of Western Australia)

Abstract

An efficient algorithm, called the time-optimal switching (TOS) algorithm, is proposed for the time-optimal switching control of nonlinear systems with a single control input. The problem is formulated in the arc times space, arc times being the durations of the arcs. A feasible switching control, or as a special case bang-bang control, is found using the STC method previously developed by the authors to get from an initial point to a target point with a given number of switchings. Then, by means of constrained optimization techniques, the cost being considered as the summation of the arc times, a minimum-time switching control solution is obtained. Example applications of the TOS algorithm involving second-order and third-order systems are presented. Comparisons are made with a well-known general optimal control software package to demonstrate the efficiency of the algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:117:y:2003:i:1:d:10.1023_a:1023600422807
    DOI: 10.1023/A:1023600422807
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    References listed on IDEAS

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    1. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    2. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
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    Cited by:

    1. Michael McAsey & Libin Mou & Weimin Han, 2012. "Convergence of the forward-backward sweep method in optimal control," Computational Optimization and Applications, Springer, vol. 53(1), pages 207-226, September.
    2. Wenhui Luo & Xuewen Tan & Xiufen Zou & Qing Tan, 2023. "Optimal Treatment of Prostate Cancer Based on State Constraint," Mathematics, MDPI, vol. 11(19), pages 1-17, September.
    3. K. H. Wong & H. W. J. Lee & C. K. Chan & C. Myburgh, 2013. "Control Parametrization and Finite Element Method for Controlling Multi-species Reactive Transport in an Underground Channel," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 168-187, April.
    4. Nahid Banihashemi & C. Yalçın Kaya, 2013. "Inexact Restoration for Euler Discretization of Box-Constrained Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 726-760, March.
    5. Yi Jiang & Yi He & Jie Sun, 2011. "Subdifferential properties of the minimal time function of linear control systems," Journal of Global Optimization, Springer, vol. 51(3), pages 395-412, November.
    6. C. Kaya & Helmut Maurer, 2014. "A numerical method for nonconvex multi-objective optimal control problems," Computational Optimization and Applications, Springer, vol. 57(3), pages 685-702, April.
    7. C. Y. Kaya & J. M. Martínez, 2007. "Euler Discretization and Inexact Restoration for Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 134(2), pages 191-206, August.
    8. 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.
    9. G. Vossen, 2010. "Switching Time Optimization for Bang-Bang and Singular Controls," Journal of Optimization Theory and Applications, Springer, vol. 144(2), pages 409-429, February.
    10. Regina S. Burachik & C. Yalçın Kaya & Walaa M. Moursi, 2024. "Infeasible and Critically Feasible Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1219-1245, November.
    11. Kaya, C. Yalcin, 2004. "Time-optimal switching control for the US cocaine epidemic," Socio-Economic Planning Sciences, Elsevier, vol. 38(1), pages 57-72, March.
    12. Elisha R. Pager & Anil V. Rao, 2022. "Method for solving bang-bang and singular optimal control problems using adaptive Radau collocation," Computational Optimization and Applications, Springer, vol. 81(3), pages 857-887, April.

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