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Article Dans Une Revue Nonlinear Differential Equations and Applications Année : 2013

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

Résumé

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.

Dates et versions

hal-00800199 , version 1 (13-03-2013)

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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, 2013, 20, pp.361-383. ⟨10.1007/s00030-012-0183-0⟩. ⟨hal-00800199⟩
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