Stabilization of solutions of the controlled non-local continuity equation
Dynamical Systems
2025-04-09 v1 Optimization and Control
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.
Keywords
Cite
@article{arxiv.2504.05935,
title = {Stabilization of solutions of the controlled non-local continuity equation},
author = {Aleksei Volkov},
journal= {arXiv preprint arXiv:2504.05935},
year = {2025}
}