We introduce a time-optimal control theory in the space of positive and finite Borel measures. We prove some natural results, such as a dynamic programming principle, the existence of optimal trajectories, regularity results and an HJB equation for the value function in this infinite-dimensional setting. The main tool used in the superposition principle (by Ambrosio-Gigli-Savaré) which allows to represent the trajectory in the space of measures as weighted superposition of classical characteristic curves in .
Keywords: Time-optimal control, dynamic programming, optimal transport, differential inclusions, multi-agent systems
Cavagnari, Giulia 1 ; Marigonda, Antonio 1 ; Piccoli, Benedetto 1
@article{COCV_2018__24_2_721_0,
author = {Cavagnari, Giulia and Marigonda, Antonio and Piccoli, Benedetto},
title = {Averaged time-optimal control problem in the space of positive {Borel} measures},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {721--740},
year = {2018},
publisher = {EDP Sciences},
volume = {24},
number = {2},
doi = {10.1051/cocv/2017060},
mrnumber = {3816412},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2017060/}
}
TY - JOUR AU - Cavagnari, Giulia AU - Marigonda, Antonio AU - Piccoli, Benedetto TI - Averaged time-optimal control problem in the space of positive Borel measures JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 721 EP - 740 VL - 24 IS - 2 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2017060/ DO - 10.1051/cocv/2017060 LA - en ID - COCV_2018__24_2_721_0 ER -
%0 Journal Article %A Cavagnari, Giulia %A Marigonda, Antonio %A Piccoli, Benedetto %T Averaged time-optimal control problem in the space of positive Borel measures %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 721-740 %V 24 %N 2 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2017060/ %R 10.1051/cocv/2017060 %G en %F COCV_2018__24_2_721_0
Cavagnari, Giulia; Marigonda, Antonio; Piccoli, Benedetto. Averaged time-optimal control problem in the space of positive Borel measures. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 721-740. doi: 10.1051/cocv/2017060
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