{"ID":2840641,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.13455","arxiv_id":"2511.13455","title":"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.","short_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...","url_abs":"https://arxiv.org/abs/2511.13455","url_pdf":"https://arxiv.org/pdf/2511.13455v1","authors":"[\"Giacomo Albi\",\"Dante Kalise\",\"Chiara Segala\",\"Franco Zivcovich\"]","published":"2025-11-17T14:59:36Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}