Year: 2024
Type: article
Abstract: . We discuss stabilization around trajectories of the continuity equation with nonlocal vector fields, where the control is localized, i.e., it acts on a fixed subset of the configuration space. We first show that the correct definition of stabilization is the following: given an initial error of order [Formula: see text], measured in Wasserstein distance, one can improve the final error to an order [Formula: see text] with [Formula: see text]. We then prove the main result: assuming that the trajectory crosses the subset of control action, stabilization can be achieved. The key problem lies in regularity issues: the reference trajectory needs to be absolutely continuous, while the initial state to be stabilized needs to be realized by a small Lipschitz perturbation or by being in a very small neighborhood of it.
DOI: 10.1137/24m1644274
Authors: Nikolay Pogodaev, Francesco Rossi
Institutions: University of Padua, Università Iuav di Venezia
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4405377797