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Discretization of semilinear bang-singular-bang control problems

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  • Ursula Felgenhauer

    (Brandenburgische Technische Universität Cottbus – Senftenberg)

Abstract

Bang-singular controls may appear in optimal control problems where the control enters the system linearly. We analyze a discretization of the first-order system of necessary optimality conditions written in terms of a variational inequality (or: inclusion) under appropriate assumptions including second-order optimality conditions. For the so-called semilinear case, it is proved that the discrete control has the same principal bang-singular-bang structure as the reference control and, in $$L_{1}$$ L 1 topology, the convergence is of order one w.r.t. the stepsize.

Suggested Citation

  • Ursula Felgenhauer, 2016. "Discretization of semilinear bang-singular-bang control problems," Computational Optimization and Applications, Springer, vol. 64(1), pages 295-326, May.
    • Handle: RePEc:spr:coopap:v:64:y:2016:i:1:d:10.1007_s10589-015-9800-2
    DOI: 10.1007/s10589-015-9800-2
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    References listed on IDEAS

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    1. 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.
    2. 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.
    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. Stephen M. Robinson, 1980. "Strongly Regular Generalized Equations," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 43-62, February.
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    Cited by:

    1. T. Scarinci & V. M. Veliov, 2018. "Higher-order numerical scheme for linear quadratic problems with bang–bang controls," Computational Optimization and Applications, Springer, vol. 69(2), pages 403-422, March.
    2. Walter Alt & Ursula Felgenhauer & Martin Seydenschwanz, 2018. "Euler discretization for a class of nonlinear optimal control problems with control appearing linearly," Computational Optimization and Applications, Springer, vol. 69(3), pages 825-856, April.

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