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An integral-type constraint qualification to guarantee nondegeneracy of the maximum principle for optimal control problems with state constraints

Abstract : For optimal control problems involving ordinary differential equations and functional inequality state constraints, the maximum principle may degenerate, producing no useful information about minimizers. This is known as the degeneracy phenomenon. Several non-degenerate forms of the maximum principle, valid under different constraint qualifications, have been proposed in the literature. In this paper we propose a new constraint qualification under which a nondegenerate maximum principle is validated. In contrast with existing results, our constraint qualification is of an integral type. An advantage of the proposed constraint qualification is that it is verified on a larger class of problems with nonsmooth data and convex velocity sets.
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https://hal.inria.fr/hal-00916594
Contributor : Estelle Bouzat <>
Submitted on : Tuesday, December 10, 2013 - 2:39:03 PM
Last modification on : Sunday, November 15, 2020 - 7:40:06 PM

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Sofia Lopes, Fernando Fontes, Maria Do Rosário de Pinho. An integral-type constraint qualification to guarantee nondegeneracy of the maximum principle for optimal control problems with state constraints. Systems and Control Letters, Elsevier, 2013, 62 (8), pp.686-692. ⟨10.1016/j.sysconle.2013.05.005⟩. ⟨hal-00916594⟩

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