We analyze neural ordinary differential equations (NODEs) from a control theoretical
perspective to address some of the main properties and paradigms of deep learning (DL), in …

This study examines the scientific production focused on the Maximum Principle between
1962 and 2021. Results indicate a consistent increase in the absolute number of …

We discuss stabilization around trajectories of the continuity equation with nonlocal vector
fields, where the control is localized, ie, it acts on a fixed subset of the configuration space …

This work is devoted to the control of the Fokker–Planck equation, posed on a smooth
bounded domain of Rd, with a localized drift force. We prove that this equation is locally …

Let $ u $ be the unique viscosity solution of $\alpha (x)|\nabla u|= 1$ in the external domain
${\mathbb R}^{n}\setminus K $ with $ u= 0$ on $ K $. In case $\alpha $ is continuous …

We show the existence of Lipschitz-in-space optimal controls for a class of mean-field
control problems with dynamics given by a non-local continuity equation. The proof relies on …

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 …

We study the problem of transporting one probability measure to another via an autonomous
velocity field. We rely on tools from the theory of optimal transport. In one space-dimension …

This paper explores the controllability and state tracking of ensembles from the perspective
of optimal transport theory. Ensembles, characterized as collections of systems evolving …

The evoluted set is the set of configurations reached from an initial set via a fixed flow for all
times in a fixed interval. We find conditions on the initial set and on the flow ensuring that the …