Journal of Convex Analysis 20 (2013), No. 4, 1147--1180
Copyright Heldermann Verlag 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
Institut de Mathématiques, Université P. et M. Curie, Case 247 -- 4 place Jussieu, 75252 Paris, France
frankowska@math.jussieu.fr
Daniela Tonon
Institut de Mathématiques, Université P. et M. Curie, Case 247 -- 4 place Jussieu, 75252 Paris, France
tonondaniela83@gmail.com
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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