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Lipschitz Continuity of the Value Function in Optimal Control

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  • V. M. Veliov

Abstract

For optimal control problems in $$\mathbb{R}^n $$ with given target and free final time, we obtain a necessary and sufficient condition for local Lipschitz continuity of the optimal value as a function of the initial position. The target can be an arbitrary closed set, and the dynamics can depend in a measurable way on the time. As a limit case of this condition, we obtain a characterization of the viability property of the target, in terms of perpendiculars to the target instead of tangent cones. As an application, we analyze the convergence of certain discretization schemes for time-optimal problems.

Suggested Citation

  • V. M. Veliov, 1997. "Lipschitz Continuity of the Value Function in Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 335-363, August.
  • Handle: RePEc:spr:joptap:v:94:y:1997:i:2:d:10.1023_a:1022683628650
    DOI: 10.1023/A:1022683628650
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    Cited by:

    1. Xiaochi Wu, 2021. "Differential Games with Incomplete Information and with Signal Revealing: The Symmetric Case," Dynamic Games and Applications, Springer, vol. 11(4), pages 863-891, December.

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