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.

We introduce a time-optimal control theory in the space + ( 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 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},
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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, 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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