Inward Pointing Trajectories, Normality of the Maximum Principle and the non Occurrence of the Lavrentieff Phenomenon in Optimal Control under State Constraints - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Convex Analysis Année : 2013

Inward Pointing Trajectories, Normality of the Maximum Principle and the non Occurrence of the Lavrentieff Phenomenon in Optimal Control under State Constraints

Hélène Frankowska
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Daniela Tonon
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Résumé

It is well known that every strong local minimizer of the Bolza problem under state constraints satisfies a constrained maximum principle. In the absence of constraints qualifications the maximum principle may be abnormal, that is, not involving the cost functions. Normality of the maximum principle can be investigated by studying reachable sets of an associated linear system under linearized state constraints. In this paper we provide sufficient conditions for the existence of solutions to such system and apply them to guarantee the non occurrence of the Lavrentieff phenomenon in optimal control under state constraints.
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Dates et versions

hal-00918483 , version 1 (16-12-2013)

Identifiants

  • HAL Id : hal-00918483 , version 1

Citer

Hélène Frankowska, Daniela Tonon. Inward Pointing Trajectories, Normality of the Maximum Principle and the non Occurrence of the Lavrentieff Phenomenon in Optimal Control under State Constraints. Journal of Convex Analysis, 2013, 20 (4). ⟨hal-00918483⟩
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