On the viability and invariance of proper sets under continuity inclusions in wasserstein spaces

B Bonnet-Weill, H Frankowska - SIAM Journal on Mathematical Analysis, 2024 - SIAM
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 …

From NeurODEs to AutoencODEs: a mean-field control framework for width-varying neural networks

C Cipriani, M Fornasier, A Scagliotti - European Journal of Applied …, 2024 - cambridge.org
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 …

A Lagrangian approach to totally dissipative evolutions in Wasserstein spaces

G Cavagnari, G Savaré, GE Sodini - arXiv preprint arXiv:2305.05211, 2023 - arxiv.org
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 …

Finite-horizon optimal control of continuous-time stochastic systems with terminal cost of Wasserstein distance

K Hoshino - 2023 62nd IEEE Conference on Decision and …, 2023 - ieeexplore.ieee.org
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 …

Approximation of deterministic mean field type control systems

Y Averboukh - arXiv preprint arXiv:2308.02301, 2023 - arxiv.org
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 …

[PDF][PDF] Differential Inclusions on Wasserstein spaces

H Frankowska - isora2023.imca.edu.pe
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 …