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Switching Time Optimization for Bang-Bang and Singular Controls

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  • G. Vossen

    (RWTH Aachen)

Abstract

Optimal control problems with the control variable appearing linearly are studied. A method for optimization with respect to the switching times of controls containing both bang-bang and singular arcs is presented. This method is based on the transformation of the control problem into a finite-dimensional optimization problem. Therein, first and second-order optimality conditions are thoroughly discussed. Explicit representations of first and second-order variational derivatives of the state trajectory with respect to the switching times are given. These formulas are used to prove that the second-order sufficient conditions can be verified on the basis of only first-order variational derivatives of the state trajectory. The effectiveness of the proposed method is tested with two numerical examples.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:144:y:2010:i:2:d:10.1007_s10957-009-9594-4
    DOI: 10.1007/s10957-009-9594-4
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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.
    3. 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. Poh Ling Tan & Helmut Maurer & Jeevan Kanesan & Joon Huang Chuah, 2022. "Optimal Control of Cancer Chemotherapy with Delays and State Constraints," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 749-770, September.
    2. U. Felgenhauer, 2012. "Structural Stability Investigation of Bang-Singular-Bang Optimal Controls," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 605-631, March.
    3. M. Soledad Aronna & J. Frédéric Bonnans & Pierre Martinon, 2013. "A Shooting Algorithm for Optimal Control Problems with Singular Arcs," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 419-459, August.
    4. Ursula Felgenhauer, 2016. "Discretization of semilinear bang-singular-bang control problems," Computational Optimization and Applications, Springer, vol. 64(1), pages 295-326, May.
    5. 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.
    6. Laura Poggiolini & Gianna Stefani, 2020. "Strong Local Optimality for a Bang–Bang–Singular Extremal: General Constraints," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 24-49, July.

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