
Journal of Convex Analysis 27 (2020), No. 1, 139163 Copyright Heldermann Verlag 2020 SecondOrder Analysis for the Time Crisis Problem Térence Bayen Laboratoire de Mathématiques, Université d'Avignon, 84018 Avignon, France terence.bayen@univavignon.fr Laurent Pfeiffer Institute of Mathematics, University of Graz, 8010 Graz, Austria laurent.pfeiffer@unigraz.at We prove secondorder necessary optimality conditions for the socalled 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 in that way second order optimality conditions for the time crisis problem. Keywords: Optimal control, Pontryagin maximum principle, second order optimality conditions. MSC: 49J15, 49K15, 49J52, 34H05. [ Fulltextpdf (182 KB)] for subscribers only. 