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Structural Stability Investigation of Bang-Singular-Bang Optimal Controls

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  • U. Felgenhauer

    (Brandenburg University of Technology)

Abstract

The paper is devoted to parametric optimal control problems with a scalar, partially singular optimal control function. In contrast to the case of pure bang-bang behavior, the investigation of structural stability properties for partially singular controls so far has been rarely addressed in literature. The central result of the paper deals with the case of one first order singular arc under regular concatenation to bang-arcs. Conditions will be provided which ensure the Lipschitz stability of bang-singular junction times positions with respect to small parameter changes. Three examples illustrate the main theorem.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:152:y:2012:i:3:d:10.1007_s10957-011-9925-0
    DOI: 10.1007/s10957-011-9925-0
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    References listed on IDEAS

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    1. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(4), pages 691-705, August.
    2. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(1), pages 225-228, February.
    3. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(5), pages 879-883, October.
    4. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(6), pages 1195-1198, December.
    5. 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.
    6. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(2), pages 411-413, April.
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    Cited by:

    1. Urszula Ledzewicz & Helmut Maurer & Heinz Schättler, 2019. "Optimal Combined Radio- and Anti-Angiogenic Cancer Therapy," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 321-340, January.
    2. 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.
    3. Ursula Felgenhauer, 2016. "Discretization of semilinear bang-singular-bang control problems," Computational Optimization and Applications, Springer, vol. 64(1), pages 295-326, May.

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