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Lipschitz solutions of optimal control problems with state constraints of arbitrary order

Joseph Frédéric Bonnans(Frederic.Bonnans***at***inria.fr)

Abstract: In this paper we generalize to an arbitrary order, under minimal hypotheses, some sufficient conditions for Lipschitz continuity of the solution of a state constrained optimal control problems. The proof combines the approach by Hager in 1979 for dealing with first-order state constraints, and the high-order alternative formulation of the optimality conditions.

Keywords: optimal control, state constraints, alternative optimality system

Category 1: Applications -- Science and Engineering (Control Applications )

Category 2: Infinite Dimensional Optimization

Category 3: Nonlinear Optimization (Systems governed by Differential Equations Optimization )

Citation: Published as INRIA Research Report 7229, March 2010. The final version will appear in Mathematics and its Applications / Annals of AOSR 2 (2010).

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Entry Submitted: 03/20/2010
Entry Accepted: 03/20/2010
Entry Last Modified: 03/20/2010

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