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 …

The connection between Residual Neural Networks (ResNets) and continuous-time control
systems (known as NeurODEs) has led to a mathematical analysis of neural networks, which …

We introduce and study the class of totally dissipative multivalued probability vector fields
(MPVF) $\boldsymbol {\mathrm F} $ on the Wasserstein space $(\mathcal {P} _2 (\mathsf …

This study addresses a stochastic optimal control problem for continuous-time systems
aimed at steering a probability distribution of the terminal state towards a desired probability …

The paper is concerned with the approximation of the deterministic the mean field type
control system by a mean field Markov chain. It turns out that the dynamics of the distribution …

Abstract Optimal Control in Wasserstein spaces addresses control of systems with large
number of agents. It is well known that for optimal control of ODEs, the differential inclisions …