Geodesic
About the minimal time crisis problem
Terence Bayen1 ; Alain Rapaport2
1Institut de Mathématiques et Modélisation de Montpellier, UMR CNRS 5149, Université Montpellier, CC 051, 34095 Montpellier cedex 5, France.
2UMR INRA-SupAgro 729 ’MISTEA’ 2 place Viala 34060 Montpellier, France.
ESAIM. Proceedings, Tome 57 (2017), pp. 1-11
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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.
DOI : 10.1051/proc/201657001

Terence Bayen  1   ; Alain Rapaport  2

1 Institut de Mathématiques et Modélisation de Montpellier, UMR CNRS 5149, Université Montpellier, CC 051, 34095 Montpellier cedex 5, France.
2 UMR INRA-SupAgro 729 ’MISTEA’ 2 place Viala 34060 Montpellier, France. 
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     author = {Terence Bayen and Alain Rapaport},
     title = {About the minimal time crisis problem},
     journal = {ESAIM. Proceedings},
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     year = {2017},
     volume = {57},
     doi = {10.1051/proc/201657001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201657001/}
}
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Terence Bayen; Alain Rapaport. About the minimal time crisis problem. ESAIM. Proceedings, Tome 57 (2017), pp. 1-11. doi: 10.1051/proc/201657001

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