Stabilization of solutions of the controlled non-local continuity equation

2025/04/08 by Volkov, Aleksei
#35Q70 #35R06 #82C22 (Secondary) #93D15 (Primary) 35F20 #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2504.05935

Abstract

Non-local continuity equation describes an infinite system of identical particles, which interact with each other through the common field. Solution of this equation is a probability measure that stands for spatial distribution of particles. The paper is concerned with stabilization of this solution in the case of controlled dynamic. By generalizing methods used control-Lyapunov function to the case of Wasserstein spaces, we construct a feedback strategy that provides local stabilization, i.e. leads the trajectory to a small neighbourhood of stabilization target. Based on this strategy, we construct a feedback that makes global stabilization, i.e. leads the trajectory infinitely close to stabilization target.

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