| Issue |
ESAIM: COCV
Volume 24, Number 2, April–June 2018
|
|
|---|---|---|
| Page(s) | 721 - 740 | |
| DOI | https://doi.org/10.1051/cocv/2017060 | |
| Published online | 26 January 2018 | |
Averaged time-optimal control problem in the space of positive Borel measures★,★★
1
Department of Mathematical Sciences, Rutgers University – Camden,
311 N. 5th Street Camden,
NJ 08102, USA
This email address is being protected from spambots. You need JavaScript enabled to view it.
2
Department of Computer Science, University of Verona,
Strada Le Grazie 15,
37134
Verona, Italy
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a Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
8
February
2017
Revised:
3
August
2017
Accepted:
3
August
2017
Abstract
We introduce a time-optimal control theory in the space ℳ+ (ℝd) 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 is 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 ℝd.
Mathematics Subject Classification: 34A60 / 49J15
Key words: Time-optimal control / dynamic programming / optimal transport / differential inclusions / multi-agent systems
The first two authors have been supported by INdAM - GNAMPA Project 2016: Stochastic Partial Differential Equations and Stochastic Optimal Transport with Applications to Mathematical Finance.
The authors acknowledge the partial support of the NSF Project Kinetic description of emerging challenges in multiscale problems of natural sciences, DMS Grant # 1107444 and the endowment fund of the Joseph and Loretta Lopez Chair.
© EDP Sciences, SMAI 2018
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