Sparse stabilization of mean-field agent dynamics through a three-operator splitting method
Abstract
We study the sparse stabilization of nonlinear multi-agent systems within a mean-field optimal control framework. The goal is to drive large populations of interacting agents toward consensus with minimal control effort. In the mean-field limit, the dynamics are described by a Vlasov-type kinetic equation, and sparsity is enforced through an l1-l2 penalization in the cost functional. The resulting nonsmooth optimization problem is solved via a three-operator splitting (TOS) method that separately handles smooth, nonsmooth, and constraint components through gradient, shrinkage, and projection steps. A particle-based Monte Carlo discretization with random batch interactions enables scalable computation while preserving the mean-field structure. Numerical experiments on the Cucker-Smale model demonstrate effective consensus formation with sparse, localized control actions, confirming the efficiency and robustness of the proposed approach.
Keywords
Cite
@article{arxiv.2511.13455,
title = {Sparse stabilization of mean-field agent dynamics through a three-operator splitting method},
author = {Giacomo Albi and Dante Kalise and Chiara Segala and Franco Zivcovich},
journal= {arXiv preprint arXiv:2511.13455},
year = {2025}
}