About the minimal time crisis problem

Terence Bayen; Alain Rapaport

doi:10.1051/proc/201657001

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About the minimal time crisis problem

Terence Bayen and Alain Rapaport

ESAIM: Proceedings and Surveys, Vol.57, pp.1-11

Emerging Trends in Applied Mathematics and Mechanics, Oana Silvia Serea & Walter Briec Editors

2017

DOI: https://doi.org/10.1051/proc/201657001

Abstract

mathématiques appliquées

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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Title: About the minimal time crisis problem
Creators - without role: Terence Bayen - Université de Montpellier, Institut Montpelliérain Alexander Grothendieck - IMAG
Alain Rapaport - Mathématiques, Informatique et Statistique pour l'Environnement et l'Agronomie
Publication Details: ESAIM: Proceedings and Surveys, Vol.57, pp.1-11
Series: Emerging Trends in Applied Mathematics and Mechanics, Oana Silvia Serea & Walter Briec Editors
Grant note: FMJH Program Gaspard Monge in optimization and operation research
Identifiers: 9979255609311
Academic Unit: Institut Montpelliérain Alexander Grothendieck - IMAG
Language: English
Resource Type: Journal article
Local Fields: hal-01465750