Geodesic
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

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We introduce a time-optimal control theory in the space ℳ + ( ℝ d ) 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 ℝ d .

DOI : 10.1051/cocv/2017060
Classification : 34A60, 49J15
Keywords: Time-optimal control, dynamic programming, optimal transport, differential inclusions, multi-agent systems

Cavagnari, Giulia 1 ; Marigonda, Antonio 1 ; Piccoli, Benedetto 1

1 
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     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://geodesic.mathdoc.fr/articles/10.1051/cocv/2017060/}
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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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