Optimal synchronization problem for a multi-agent system

Giulia Cavagnari; Antonio Marigonda; Benedetto Piccoli

doi:10.3934/nhm.2017012

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2017, Volume 12, Issue 2: 277-295. Doi: 10.3934/nhm.2017012

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Optimal synchronization problem for a multi-agent system

1.
Department of Mathematical Sciences, Rutgers University -Camden, 311 N. 5th Street Camden, NJ 08102, USA
2.
Department of Computer Science, University of Verona, Strada Le Grazie 15, I-37134 Verona, Italy

* Corresponding author: Giulia Cavagnari
* Corresponding author: Giulia Cavagnari

Received: October 2016

Revised: February 2017

Published: October 2017

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Abstract

In this paper we investigate a time-optimal control problem in the space of positive and finite Borel measures on $\mathbb R^d$, motivated by applications in multi-agent systems. We provide a definition of admissible trajectory in the space of Borel measures in a particular non-isolated context, inspired by the so called optimal logistic problem, where the aim is to assign an initial amount of resources to a mass of agents, depending only on their initial position, in such a way that they can reach the given target with this minimum amount of supplies. We provide some approximation results connecting the microscopical description with the macroscopical one in the mass-preserving setting, we construct an optimal trajectory in the non isolated case and finally we are able to provide a Dynamic Programming Principle.

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Mathematics Subject Classification: Primary: 34A60; Secondary: 49J15.

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References

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