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arXiv · 2403.03580

Stabilization via localized controls in nonlocal models of crowd dynamics

Nikolay Pogodaev·Francesco Rossi
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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 $\varepsilon$ can be reduced to order $\varepsilon^{1+κ}$, where $κ$ is a positive constant.

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Nikolay Pogodaev, Francesco Rossi. 2024-03-06. Stabilization via localized controls in nonlocal models of crowd dynamics. https://arxiv.org/abs/2403.03580

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