Stabilization via localized controls in nonlocal models of crowd dynamics

2024/03/06 by Nikolay Pogodaev, Pogodaev, Nikolay, Francesco Rossi +1
Computer Science · Engineering · Medicine · #35Q93 #93C20 #93D20 #Evacuation and Crowd Dynamics #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Dynamics and Pattern Formation #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2403.03580

openalex publication_date 2024/03/06 · openalex created_date 2024/03/08 · openalex updated_date 2026/07/28

Abstract

We consider a control system driven by a nonlocal continuity equation. Admissible controls are Lipschitz vector fields acting inside a fixed open set. We demonstrate that small perturbations of the initial measure, traced along Wasserstein geodesics, may be neutralized by admissible controls. More specifically, initial perturbations of order ε can be reduced to order ε^1+κ, where κ is a positive constant.

Related

• Stabilization of solutions of the controlled non-local continuity equation
• Trajectory stabilization of nonlocal continuity equations by localized controls
• Nonlocal Crowd Dynamics Models for several Populations
• Mean-Field Sparse Jurdjevic--Quinn Control
• Non Local Conservation Laws in Bounded Domains