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Lipschitz Continuity of the Value Function in Optimal Control (1997)

Veliov, V. M.

Springer

Journal of optimization theory and applications 94 (1997), S. 335-363

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ISSN: 1573-2878

Keywords: Control theory ; minimum-time problems ; controllability ; viability ; discretization

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1022683628650

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