About the minimal time crisis problem *

About the minimal time crisis problem *

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 prope...

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Main Authors: Bayen Terence, Rapaport Alain
Format: Article
Language:English
Published: EDP Sciences 2017-01-01
Series:ESAIM: Proceedings and Surveys
Online Access:https://doi.org/10.1051/proc/201657001
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spelling doaj-da0c4352227f417eae5d8355351a2c312021-07-15T14:13:05ZengEDP SciencesESAIM: Proceedings and Surveys2267-30592017-01-015711110.1051/proc/201657001proc_etamm2016_001About the minimal time crisis problem *Bayen TerenceRapaport AlainWe 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.https://doi.org/10.1051/proc/201657001
collection DOAJ
language English
format Article
sources DOAJ
author Bayen Terence
Rapaport Alain
spellingShingle Bayen Terence
Rapaport Alain
About the minimal time crisis problem *
ESAIM: Proceedings and Surveys
author_facet Bayen Terence
Rapaport Alain
author_sort Bayen Terence
title About the minimal time crisis problem *
title_short About the minimal time crisis problem *
title_full About the minimal time crisis problem *
title_fullStr About the minimal time crisis problem *
title_full_unstemmed About the minimal time crisis problem *
title_sort about the minimal time crisis problem *
publisher EDP Sciences
series ESAIM: Proceedings and Surveys
issn 2267-3059
publishDate 2017-01-01
description 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.
url https://doi.org/10.1051/proc/201657001
work_keys_str_mv AT bayenterence abouttheminimaltimecrisisproblem
AT rapaportalain abouttheminimaltimecrisisproblem
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