We study a multi-agent system for the modeling maritime crime. The model involves three interacting populations of ships: commercial ships, pirate ships, and coast guard ships. Commercial ships follow commercial routes, are subject to traffic congestion, and are repelled by pirate ships. Pirate ships travel stochastically, are attracted by commercial ships and repelled by coast guard ships. Coast guard ships are controlled. We prove well-posedness of the model and existence of optimal controls that minimize dangerous contacts. Then we study, in a two-step procedure, the mean-field limit as the number of commercial ships and pirate ships is large, deriving a mean-field PDE/PDE/ODE model. Via Γ-convergence, we study the limit of the corresponding optimal control problems.

我们研究了用于模拟海上犯罪的多代理系统。该模型涉及三个相互作用的船舶群体：商船、海盗船和海岸警卫队船。商船走的是商业航线，交通拥堵，被海盗船击退。海盗船随机航行，被商船吸引，被海岸警卫队船只击退。海岸警卫队的船只受到控制。我们证明了模型的适定性以及最小化危险接触的最佳控制的存在。然后我们分两步研究商船和海盗船数量大时的平均场极限，推导出平均场 PDE/PDE/ODE 模型。通过Γ收敛，我们研究了相应最优控制问题的极限。