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According to recent results, convergence in a prespecified or prescribed finite time can be achieved under extreme model uncertainty if control is applied continuously over time. This paper shows that this extreme amount of uncertainty…
This work is concerned with the necessary conditions of optimality for a minimal time control problem $(P)$ for the linearized Navier-Stokes periodic flow in a 2D-channel, subject to a boundary input which acts on the transversal component…
Adapted optimal transport (AOT) problems are optimal transport problems for distributions of a time series where couplings are constrained to have a temporal causal structure. In this paper, we develop computational tools for solving AOT…
We study the convexity of the entropy functional along particular interpolating curves defined on the space of finitely supported probability measures on a graph.
Flow matching has recently emerged as a flexible and efficient framework for generative modelling by learning deterministic transport dynamics between probability measures. In this work, we extend flow matching to the space of probability…
The congestion formation on a urban road network is one of the key issue for the development of a sustainable mobility in the future smart cities. In this work we propose a reductionist approach studying the stationary states of a simple…
In this paper, we study the approximate controllability of a system governed by an evolution problem known as the sloshing problem. This problem involves a spatial, nonlocal differential operator inherent in the dynamics of a…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over continuous time. We analyse this problem with respect to the allowable control sets, which are assumed to be the image under a linear…
We consider the optimal distributed controller design problem subject to two structural requirements: locality, i.e. available measurements and sub-controllers' interactions are governed by a graph structure, and relative feedback, i.e.…
Approximate dynamic programming has been investigated and used as a method to approximately solve optimal regulation problems. However, the extension of this technique to optimal tracking problems for continuous time nonlinear systems has…
Stochastic traffic capacity is used in traffic modelling and control for unidirectional sections of road infrastructure, although some of the estimation methods have recently proved flawed. However, even sound estimation methods require…
We address the task of estimating multiple trajectories from unlabeled data. This problem arises in many settings, one could think of the construction of maps of transport networks from passive observation of travellers, or the…
We study the convergence of divergence-regularized optimal transport as the regularization parameter vanishes. Sharp rates for general divergences including relative entropy or $L^{p}$ regularization, general transport costs and…
We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of the approximation. Our approach is based on a general…
In this letter we propose an optimization-based boundary controller for traffic flow dynamics capable of achieving both stability and invariance conditions. The approach is based on the definition of Boundary Control Barrier Functionals,…
This work presents a model reduction approach for problems with coherent structures that propagate over time such as convection-dominated flows and wave-type phenomena. Traditional model reduction methods have difficulties with these…
Replacing positivity constraints by an entropy barrier is popular to approximate solutions of linear programs. In the special case of the optimal transport problem, this technique dates back to the early work of Schr\"odinger. This approach…
In this paper we establish an attainability result for the minimum time function of a control problem in the space of probability measures endowed with Wasserstein distance. The dynamics is provided by a suitable controlled continuity…
Output-based controllers are known to be fragile with respect to model uncertainties. The standard $\mathcal{H}_{\infty}$-control theory provides a general approach to robust controller design based on the solution of the…
The article presents new entropic continuity bounds for conditional expectations and conditional covariance matrices. These bounds are expressed in terms of the relative entropy between different coupling distributions. Our approach…