| Issue |
ESAIM: ProcS
Volume 71, 2021
FGS’2019 - 19th French-German-Swiss conference on Optimization
|
|
|---|---|---|
| Page(s) | 33 - 42 | |
| DOI | https://doi.org/10.1051/proc/202171104 | |
| Published online | 01 September 2021 | |
On the numerical solution of a free end-time homicidal chauffeur game*
1 Institut für Mathematik, Universit¨ät Würzburg, Emil-Fischer-Strasse 30, 97074 Würzburg, Germany
e-mail: francesca.cala-campana@mathematik.uni-wuerzburg.de alfio.borzi@mathematik.uni-wuerzburg.de
2 Institute of Applied Mathematics and Scientific Computing, Department of Aerospace Engineering, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany
e-mail: alberto.demarchi@unibw.de, matthias.gerdts@unibw.de
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.
© The authors. Published by EDP Sciences, SMAI 2021
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