We introduce a time-optimal control theory in the space \n {\mathcal{M}}^{+}\left({\mathbb{R}}^{d}\right)\n 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 \n {\mathbb{R}}^{d}\n.

Keywords: Time-optimal control, dynamic programming, optimal transport, differential inclusions, multi-agent systems

^{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}, publisher = {EDP-Sciences}, volume = {24}, number = {2}, year = {2018}, doi = {10.1051/cocv/2017060}, mrnumber = {3816412}, language = {en}, url = {http://archive.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 - http://archive.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 http://archive.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, Volume 24 (2018) no. 2, pp. 721-740. doi : 10.1051/cocv/2017060. http://archive.numdam.org/articles/10.1051/cocv/2017060/

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