Geodesic
Penalty function method for the minimal time crisis problem
Kenza Boumaza1 ; Térence Bayen2 ; Alain Rapaport1
1MISTEA, Univ. Montpellier, INRAE, Institut Agro (UMR 729), 34060 Montpellier, France
2Avignon Université, Laboratoire de Mathématiques d’Avignon (EA 2151), 84018 Avignon, France
ESAIM. Proceedings, Tome 71 (2021), pp. 21-32
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In this note, we propose a new method to approximate the minimal time crisis problem using an auxiliary control and a penalty function, and show its convergence to a solution to the original problem. The interest of this approach is illustrated on numerical examples for which optimal trajectories can leave and enter the crisis set tangentially.
DOI : 10.1051/proc/202171103

Kenza Boumaza  1   ; Térence Bayen  2   ; Alain Rapaport  1

1 MISTEA, Univ. Montpellier, INRAE, Institut Agro (UMR 729), 34060 Montpellier, France
2 Avignon Université, Laboratoire de Mathématiques d’Avignon (EA 2151), 84018 Avignon, France 
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     author = {Kenza Boumaza and T\'erence Bayen and Alain Rapaport},
     title = {Penalty function method for the minimal time crisis problem},
     journal = {ESAIM. Proceedings},
     pages = {21--32},
     year = {2021},
     volume = {71},
     doi = {10.1051/proc/202171103},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202171103/}
}
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Kenza Boumaza; Térence Bayen; Alain Rapaport. Penalty function method for the minimal time crisis problem. ESAIM. Proceedings, Tome 71 (2021), pp. 21-32. doi: 10.1051/proc/202171103

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