A new proof of optimality conditions for the time of crisis via regularization

Térence Bayen (1) , Kenza Boumaza (2) , Alain Rapaport (2)

1 LMA - EA2151 Laboratoire de Mathématiques d'Avignon
2 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie

Our aim in this paper is to derive optimality conditions for the time of crisis problem under a weaker hypothesis than the usual one encountered in the hybrid setting, and which asserts that any optimal solution should cross the boundary of the constraint set transversally. Doing so, we apply the Pontryagin Maximum Principle to a sequence of regular optimal control problems whose integral cost approximates the time of crisis. Optimality conditions are derived by passing to the limit in the Hamiltonian system. This convergence result essentially relies on the boundedness of the sequence of adjoint vectors in L∞. Our main contribution is to relate this property to the boundedness in L1 of a suitable sequence which allows to bypass the use of the transverse hypothesis on optimal paths.

Domaines: Optimisation et contrôle [math.OC]

Térence Bayen, Kenza Boumaza, Alain Rapaport. A new proof of optimality conditions for the time of crisis via regularization. 2021. ⟨hal-03153881v1⟩