In this paper we consider a mean-field optimal control problem with selective action of the control, where the constraint is a continuity equation involving a non-local term and diffusion. First order optimality conditions are formally derived in a general framework, accounting for boundary conditions. Hence, the optimality system is used to construct a reduced gradient method, where we introduce a novel algorithm for the numerical realization of the forward and the backward equations, based on exponential integrators. We illustrate extensive numerical experiments on different control problems for collective motion in the context of opinion formation, pedestrian dynamics, and mass transfer.

Exponential integrators for a mean-field selective optimal control problem

Albi Giacomo;Caliari Marco
;
Calzola Elisa;Cassini Fabio
2024-01-01

Abstract

In this paper we consider a mean-field optimal control problem with selective action of the control, where the constraint is a continuity equation involving a non-local term and diffusion. First order optimality conditions are formally derived in a general framework, accounting for boundary conditions. Hence, the optimality system is used to construct a reduced gradient method, where we introduce a novel algorithm for the numerical realization of the forward and the backward equations, based on exponential integrators. We illustrate extensive numerical experiments on different control problems for collective motion in the context of opinion formation, pedestrian dynamics, and mass transfer.
2024
mean-field control
multi-agent systems
PDE-constrained optimization
exponential integrators
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/1167027
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