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Optimal synchronization problem for a multi-agent system

  • * Corresponding author: Giulia Cavagnari

    * Corresponding author: Giulia Cavagnari 
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  • 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.

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


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