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About the minimal time crisis problem

Abstract : We study the minimization of the so-called "time crisis function" that represents the time spent by a solution of a controlled system outside a given set K. One essential feature of this optimal control problem is the discontinuity of the functional at the boundary of K. We provide in this paper properties of the time crisis function together with necessary optimality conditions using the hybrid maximum principle. We also study an approximation of this problem based on the Moreau-Yosida regularization of the indicator function of K.
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Terence Bayen, Alain Rapaport. About the minimal time crisis problem. ESAIM: Proceedings and Surveys, EDP Sciences, 2017, Emerging Trends in Applied Mathematics and Mechanics, Oana Silvia Serea & Walter Briec Editors, 57, pp.1-11. ⟨10.1051/proc/201657001⟩. ⟨hal-01465750⟩

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