Sparse stabilization of mean-field agent dynamics through a three-operator splitting method
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912715160682496 |
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| author | Albi, Giacomo Kalise, Dante Segala, Chiara Zivcovich, Franco |
| author_facet | Albi, Giacomo Kalise, Dante Segala, Chiara Zivcovich, Franco |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13455 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sparse stabilization of mean-field agent dynamics through a three-operator splitting method Albi, Giacomo Kalise, Dante Segala, Chiara Zivcovich, Franco Optimization and Control 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. |
| title | Sparse stabilization of mean-field agent dynamics through a three-operator splitting method |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2511.13455 |