Abstract This paper concerns a class of optimal control problems, where a central planner aims to control a multi-agent system in R^d in order to minimize a certain cost of Bolza type. At every time and for each agent, the set of admissible velocities, describing his/her underlying microscopic dynamics, depends both on his/her position, and on the configuration of all the other agents at the same time. So the problem is naturally stated in the space of probability measures on R^d equipped with the Wasserstein distance. The main result of the paper gives a new characterization of the value function as the unique viscosity solution of a first order partial differential equation. We introduce and discuss several equivalent formulations of the concept of viscosity solutions in the Wasserstein spaces suitable for obtaining a comparison principle of the Hamilton Jacobi Bellman equation associated with the above control problem.

Optimal control of multiagent systems in the Wasserstein space

Marigonda, Antonio
;
2020-01-01

Abstract

Abstract This paper concerns a class of optimal control problems, where a central planner aims to control a multi-agent system in R^d in order to minimize a certain cost of Bolza type. At every time and for each agent, the set of admissible velocities, describing his/her underlying microscopic dynamics, depends both on his/her position, and on the configuration of all the other agents at the same time. So the problem is naturally stated in the space of probability measures on R^d equipped with the Wasserstein distance. The main result of the paper gives a new characterization of the value function as the unique viscosity solution of a first order partial differential equation. We introduce and discuss several equivalent formulations of the concept of viscosity solutions in the Wasserstein spaces suitable for obtaining a comparison principle of the Hamilton Jacobi Bellman equation associated with the above control problem.
2020
Optimal Control, Multiagent Systems, Viscosity Solutions
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/1012644
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