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arXiv · 2511.13455

Sparse stabilization of mean-field agent dynamics through a three-operator splitting method

Giacomo Albi·Dante Kalise·Chiara Segala·Franco Zivcovich
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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.

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Giacomo Albi, Dante Kalise, Chiara Segala, Franco Zivcovich. 2025-11-17. Sparse stabilization of mean-field agent dynamics through a three-operator splitting method. https://arxiv.org/abs/2511.13455

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