On relations of the adjoint state to the value function for optimal control problems with state constraints

Hélène Frankowska 1 Marco Mazzola 1
1 C&O - Equipe combinatoire et optimisation
UPMC - Université Pierre et Marie Curie - Paris 6, CNRS - Centre National de la Recherche Scientifique : FRE3232
Abstract : We consider an optimal control problem under state constraints and show that to every optimal solution corresponds an adjoint state satisfying the first order necessary optimality conditions in the form of a maximum principle and sensitivity relations involving the value function. Such sensitivity relations were recently investigated by P. Bettiol and R.B. Vinter for state constraints with smooth boundary. In the difference with their work, our setting concerns differential inclusions and nonsmooth state constraints. To obtain our result we derive neighboring feasible trajectory estimates using a novel generalization of the so-called inward pointing condition.
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Nonlinear Differential Equations and Applications, Springer Verlag, 2013, 20, pp.361-383. 〈10.1007/s00030-012-0183-0〉
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https://hal.inria.fr/hal-00800199
Contributeur : Estelle Bouzat <>
Soumis le : mercredi 13 mars 2013 - 13:03:25
Dernière modification le : mercredi 21 mars 2018 - 18:57:28

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Hélène Frankowska, Marco Mazzola. On relations of the adjoint state to the value function for optimal control problems with state constraints. Nonlinear Differential Equations and Applications, Springer Verlag, 2013, 20, pp.361-383. 〈10.1007/s00030-012-0183-0〉. 〈hal-00800199〉

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