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

TL;DR

This paper models maritime crime involving commercial, pirate, and coast guard ships using a multi-agent system, deriving a mean-field PDE model and optimal control strategies to minimize dangerous contacts.

Contribution

It introduces a novel multi-agent model for maritime crime, proves well-posedness, and derives a mean-field limit with optimal control analysis using $ extGamma$-convergence.

Findings

Established well-posedness of the multi-agent model

Derived a mean-field PDE/ODE model for large populations

Analyzed the limit of optimal controls via $ extGamma$-convergence

Abstract

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.