Exponential integrators for a mean-field selective optimal control problem

  • Giacomo Albi University of Verona
  • Marco Caliari University of Verona
  • Elisa Calzola University of Verona
  • Fabio Cassini University of Verona
Keywords: mean-field control, multi-agent systems, PDE-constrained optimization, exponential integrators

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.

Published
2024-09-06
How to Cite
Albi, G., Caliari, M., Calzola, E., & Cassini, F. (2024). Exponential integrators for a mean-field selective optimal control problem. Journal of Approximation Software, 1(2). Retrieved from https://ojs.unito.it/index.php/JAS/article/view/10973
Section
Articles