In this article, we propose a general framework for the study of differential inclusions in the
Wasserstein space of probability measures. Based on earlier geometric insights on the …

In this paper we consider a measure-theoretical formulation of the training of NeurODEs in
the form of a mean-field optimal control with L 2-regularization of the control. We derive first …

In this paper, we prove a Pontryagin Maximum Principle for constrained optimal control
problems in the Wasserstein space of probability measures. The dynamics is described by a …

We derive novel algorithms for optimization problems constrained by partial differential
equations describing multiscale particle dynamics, including non-local integral terms …

Controlling large particle systems in collective dynamics by a few agents is a subject of high
practical importance, eg, in evacuation dynamics. In this paper we study an instantaneous …

The paper addresses an optimal ensemble control problem for nonlocal continuity equations
on the space of probability measures. We admit the general nonlinear cost functional, and …

In this article, we derive conditions for the existence of solutions to state-constrained
continuity inclusions in Wasserstein spaces whose right-hand sides may be discontinuous in …

In this article, we investigate some of the fine properties of the value function associated with
an optimal control problem in the Wasserstein space of probability measures. Building on …

In this article, we consider the problem of controlling the group behavior of a large number of
dynamic systems that are constantly interacting with each other. These systems are …

Motivated by the applications in leader-follower multi-agent dynamics, a class of optimal
control problems is investigated, where the goal is to influence the behavior of a given …