Averaged time-optimal control problem in the space of positive Borel measures

Cavagnari, Giulia; Marigonda, Antonio; Piccoli, Benedetto

ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 721-740.

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

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