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

2022/12/10 by Gianluca Orlando, Orlando, Gianluca
Medicine · Social Sciences · #34F05 #49J15 #49J20 #49J45 #93E20 #Analysis of PDEs (math.AP) #Crime Patterns and Interventions #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Optimization and Control (math.OC) #Terrorism, Counterterrorism, and Political Violence

paper · pdf · doi:10.48550/arxiv.2212.05341

openalex publication_date 2022/12/10 · openalex created_date 2022/12/26 · openalex updated_date 2026/07/28

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 Γ-convergence, we study the limit of the corresponding optimal control problems.

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