Calculus of Variations and Geometric Measure Theory

G. Orlando

Mean-field optimal control in a multi-agent interaction model for prevention of maritime crime

created by orlando on 10 Jul 2024


Published Paper

Inserted: 10 jul 2024
Last Updated: 10 jul 2024

Journal: Adv Cont Discr Mod
Volume: 24
Year: 2023

ArXiv: 2212.05341 PDF


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 $\Gamma$-convergence, we study the limit of the corresponding optimal control problems.