Exponential integrators for mean-field selective optimal control problems
Optimization and Control
2023-02-02 v1 Numerical Analysis
Numerical Analysis
Abstract
In this paper we consider mean-field optimal control problems 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 and pedestrian dynamics.
Cite
@article{arxiv.2302.00127,
title = {Exponential integrators for mean-field selective optimal control problems},
author = {Giacomo Albi and Marco Caliari and Elisa Calzola and Fabio Cassini},
journal= {arXiv preprint arXiv:2302.00127},
year = {2023}
}