Geodesic
On the numerical solution of a free end-time homicidal chauffeur game
Francesca Calà Campana1 ; Alberto De Marchi2 ; Alfio Borzì1 ; Matthias Gerdts2
1 Institut für Mathematik, Universit¨ät Würzburg, Emil-Fischer-Strasse 30, 97074 Würzburg, Germany
2 Institute of Applied Mathematics and Scientific Computing, Department of Aerospace Engineering, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany
ESAIM. Proceedings, Tome 71 (2021), pp. 33-42.

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A functional formulation of the classical homicidal chauffeur Nash game is presented and a numerical framework for its solution is discussed. This methodology combines a Hamiltonian based scheme with proximal penalty to determine the time horizon where the game takes place with a Lagrangian optimal control approach and relaxation to solve the Nash game at a fixed end-time.
DOI : 10.1051/proc/202171104

Francesca Calà Campana 1 ; Alberto De Marchi 2 ; Alfio Borzì 1 ; Matthias Gerdts 2

1 Institut für Mathematik, Universit¨ät Würzburg, Emil-Fischer-Strasse 30, 97074 Würzburg, Germany
2 Institute of Applied Mathematics and Scientific Computing, Department of Aerospace Engineering, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany 
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Francesca Calà Campana; Alberto De Marchi; Alfio Borzì; Matthias Gerdts. On the numerical solution of a free end-time homicidal chauffeur game. ESAIM. Proceedings, Tome 71 (2021), pp. 33-42. doi : 10.1051/proc/202171104. http://geodesic.mathdoc.fr/articles/10.1051/proc/202171104/

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