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Veliov, V. M.

Lipschitz continuity of the value function in optimal control. (English) Zbl 0901.49022

J. Optimization Theory Appl. 94, No. 2, 335-363 (1997).
Author’s 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”.
Reviewer: Gianna Stefani (Firenze)

Cited in 19 Documents

MSC:

49K40 Sensitivity, stability, well-posedness
49K24 Optimal control problems with differential inclusions (nec./ suff.) (MSC2000)
34A60 Ordinary differential inclusions
34H05 Control problems involving ordinary differential equations

Keywords:

optimal control theory; minimum-time problems; viability; discretization; value function; Lipschitz continuity
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References:

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