1 citations · 3 across the 10 of their papers we have counts for
13 papers
Optimal Actuator Design across Ranks and Control Horizons
Emmanuel Trélat, Enrique Zuazua
We study how actuator rank and control horizon jointly determine worst-case control performance for finite-dimensional linear systems under a fixed total actuator-gain budget. The…
Two-term small-time spectral expansions for controllability Gramians
Emmanuel Trélat, Enrique Zuazua
For a controllable single-input linear system in dimension , the controllability Gramian eigenvalues, ordered decreasingly, are known to have the successive small-time orders $T…
Crossover asymptotics and a sharp confinement rate for the viscous Burgers equation
Maicon Sonego, Enrique Zuazua
We study the one-dimensional viscous Burgers equation on with the conservative boundary conditions . On the half-line, solutions approach a nonlinear self-similar…
Mean-Square Stability of Continuous-Time Stochastic Model Predictive Control
Qi Lü, Bowen Ma, Enrique Zuazua
We propose a stochastic model predictive control (SMPC) framework for a broad class of unconstrained controlled stochastic differential equations (SDEs) and establish its mean-squa…
Boundary and Interior Control in a Diffusive Lotka-Volterra Model
João Carlos Barreira, Maicon Sonego, Enrique Zuazua
We investigate the controllability of a generalized diffusive Lotka-Volterra competition model for two species, incorporating boundary controls and an interior multiplicative contr…
Sensor placement via large deviations in the Eikonal equation
Ilias Ftouhi, Enrique Zuazua
In this work, we address the problem of optimally placing a finite number of sensors within a given region so as to minimize the mean or maximal distance to the points of the domai…
Controllability of diffusive Lotka-Volterra strongly competitive systems under boundary constrained controls
Elisa Affili, Enrique Zuazua
We investigate the controllability of the competition-diffusion Lotka-Volterra system. Our primary focus is on the one-dimensional setting with Dirichlet boundary controls, interpr…
Turnpike in optimal control and beyond: a survey
Emmanuel Trélat, Enrique Zuazua
The turnpike principle is a fundamental concept in optimal control theory, stating that for a wide class of long-horizon optimal control problems, the optimal trajectory spends mos…
Exact Sequence Interpolation with Transformers
Albert Alcalde, Giovanni Fantuzzi, Enrique Zuazua
We prove that transformers can exactly interpolate datasets of finite input sequences in , , with corresponding output sequences of smaller or equal length.…
Optimal -approximation of convex sets by convex subsets
Zakaria Fattah, Ilias Ftouhi, Enrique Zuazua
Given a convex set of , we consider the shape optimization problem of finding a convex subset , of a given measure, minimizing the -distance functi…
Control of a Lotka-Volterra System with Weak Competition
Maicon Sonego, Enrique Zuazua
The Lotka-Volterra model reflects real ecological interactions where species compete for limited resources, potentially leading to coexistence, dominance of one species, or extinct…
Pattern control via Diffussion interaction
Domènec Ruiz-Balet, Enrique Zuazua
We analyse a dynamic control problem for scalar reaction-diffusion equations, focusing on the emulation of pattern formation through the selection of appropriate active controls. W…
Clustering in pure-attention hardmax transformers and its role in sentiment analysis
Albert Alcalde, Giovanni Fantuzzi, Enrique Zuazua
Transformers are extremely successful machine learning models whose mathematical properties remain poorly understood. Here, we rigorously characterize the behavior of transformers…