Lipschitz Continuity of the Value Function in Optimal Control

Vladimir Veliov ()

Journal of Optimization Theory and Applications, 1997, vol. 94, issue 2, No 3, 335-363

Abstract: 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.

Keywords: Control theory; minimum-time problems; controllability; viability; discretization (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (1)

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DOI: 10.1023/A:1022683628650

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