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The mathematical framework of hybrid system is a recent and general tool to treat control systems involving control action of heterogeneous nature. In this paper, we construct and test a semi-Lagrangian numerical scheme for solving the Dynamic Programming equation of an infinite horizon optimal control problem for hybrid systems. In order to speed up convergence, we also propose and analyze an acceleration technique based on policy iteration. Finally, we validate the approach via some numerical tests in low dimension.
Ferretti, Roberto 1 ; Sassi, Achille 1
@article{COCV_2018__24_3_965_0,
author = {Ferretti, Roberto and Sassi, Achille},
title = {A {semi-Lagrangian} algorithm in policy space for hybrid optimal control problems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {965--983},
publisher = {EDP-Sciences},
volume = {24},
number = {3},
year = {2018},
doi = {10.1051/cocv/2017022},
mrnumber = {3877189},
zbl = {1405.49024},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2017022/}
}
TY - JOUR AU - Ferretti, Roberto AU - Sassi, Achille TI - A semi-Lagrangian algorithm in policy space for hybrid optimal control problems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 965 EP - 983 VL - 24 IS - 3 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2017022/ DO - 10.1051/cocv/2017022 LA - en ID - COCV_2018__24_3_965_0 ER -
%0 Journal Article %A Ferretti, Roberto %A Sassi, Achille %T A semi-Lagrangian algorithm in policy space for hybrid optimal control problems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 965-983 %V 24 %N 3 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2017022/ %R 10.1051/cocv/2017022 %G en %F COCV_2018__24_3_965_0
Ferretti, Roberto; Sassi, Achille. A semi-Lagrangian algorithm in policy space for hybrid optimal control problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 3, pp. 965-983. doi : 10.1051/cocv/2017022. http://geodesic.mathdoc.fr/articles/10.1051/cocv/2017022/
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