Dynamic programming in probability spaces via optimal transport
We study discrete-time finite-horizon optimal control problems in probability spaces,
whereby the state of the system is a probability measure. We show that, in many instances …
whereby the state of the system is a probability measure. We show that, in many instances …
From NeurODEs to AutoencODEs: a mean-field control framework for width-varying neural networks
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 …
systems (known as NeurODEs) has led to a mathematical analysis of neural networks, which …
Trajectory stabilization of nonlocal continuity equations by localized controls
N Pogodaev, F Rossi - arXiv preprint arXiv:2403.02837, 2024 - arxiv.org
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 …
fields, where the control is localized, ie, it acts on a fixed subset of the configuration space …
Set-Valued Koopman Theory for Control Systems
B Bonnet-Weill, M Korda - arXiv preprint arXiv:2401.11569, 2024 - arxiv.org
In this paper, we introduce a new definition of the Koopman operator which faithfully
encodes the dynamics of controlled systems, by leveraging the grammar of set-valued …
encodes the dynamics of controlled systems, by leveraging the grammar of set-valued …