Second-order analysis for the time crisis problem

Térence Bayen (1) , Laurent Pfeiffer (2)

1 LMA - EA2151 Laboratoire de Mathématiques d'Avignon
2 COMMANDS - Controle, Optimisation, modèles, Méthodes et Applications pour les Systèmes Dynamiques non linéaires

In this article, we prove second-order necessary optimality conditions for the so-called time crisis problem that comes up within the context of viability theory. It consists in minimizing the time spent by solutions of a controlled dynamics outside a given subset K of the state space. One essential feature is the discontinuity of the characteristic function involved in the cost functional. Thanks to a change of time and an augmentation of the dynamics, we relate the time crisis problem to an auxiliary Mayer control problem. This allows us to use the classical tools of optimal control for obtaining optimality conditions. Going back to the original problem, we deduce that way second order optimality conditions for the time crisis problem.

Keywords: Optimal control; Pontryagin maximum principle; Second order optimality conditions

Domains: Mathematics [math]

Térence Bayen, Laurent Pfeiffer. Second-order analysis for the time crisis problem. Journal of Convex Analysis, 2020, 27 (1), pp.139-163. ⟨hal-02020146⟩