论文标题
在预防海上犯罪的多代理互动模型中，平均场景最佳控制
Mean-field optimal control in a multi-agent interaction model for prevention of maritime crime
论文作者
论文摘要
我们研究了用于建模海事犯罪的多代理系统。该模型涉及三艘相互作用的船只：商业船，海盗船和海岸警卫队的船只。商业船遵循商业路线，受到交通拥堵的影响，并被海盗船击退。海盗船随机旅行，被商业船只吸引，并被海岸警卫队击退。海岸警卫队受到控制。我们证明了模型的适应性和最佳控制的存在，从而最大程度地减少了危险的接触。然后，我们以两步的步骤研究，因为商业船只和海盗船的数量很大，均值是平均野外PDE/PDE/ode模型。通过$γ$ -Convergence，我们研究了相应的最佳控制问题的极限。
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.
