2 citations · 4 across the 9 of their papers we have counts for
12 papers
Null-controllable data for cascade heat equations: almost sharp spectral spaces and modal critical times
Hugo Lhachemi, Christophe Prieur, Emmanuel Trélat
We study one-dimensional cascades of heat equations controlled through their last component. For a fixed time , we consider the Hilbert space of all initial da…
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…
Moving localized observations and Ces{à}ro asymptotic observability for conservative PDEs
Maarten V. de Hoop, Antti Kykkänen, Emmanuel Trélat
We develop a deterministic large-time mechanism yielding Ces{à}ro asymptotic observability inequalities from moving localized observations for conservative evolutions. On each obse…
Boundary observability for gas giant metrics
Maarten V. de Hoop, Antti Kykkänen, Emmanuel Trélat
We study the observability of waves on gas giant manifolds which are a class of Riemannian manifolds whose metrics are singular at the boundary. Such manifolds arise naturally in m…
From PDEs on standard domains to self-similar particle systems on fractals
Georgi Medvedev, Emmanuel Trélat
We construct transported PDEs on self-similar fractal domains from reference equations posed on the unit interval, and derive explicit self-similar interacting particle systems tha…
A flatness proof of the exponential turnpike phenomenon for linear-quadratic optimal control problems
Michel Fliess, Claude Lobry, Emmanuel Trélat
We revisit finite-dimensional linear-quadratic optimal control from the viewpoint of differential flatness. If the pair (A, B) is controllable, then the linear control system is fl…
Generalisation of Farkas' lemma beyond closedness: a constructive approach via Fenchel-Rockafellar duality
Camille Pouchol, Emmanuel Trélat, Christophe Zhang
Farkas' lemma is an ubiquitous tool in optimisation, as it provides necessary and sufficient conditions to have , where is a closed convex cone, is a (continuou…
Weyl asymptotics for singular metrics with a variable boundary degeneracy exponent
Yves Colin de Verdière, Charlotte Dietze, Emmanuel Trélat
We consider a compact smooth manifold of dimension with boundary . In a collar neighborhood of , we assume that the metric has the form ,…
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…
An algorithmic guide for finite-dimensional optimal control problems
Jean-Baptiste Caillau, Roberto Ferretti, Emmanuel Trélat +1
We survey the main numerical techniques for finite-dimensional nonlinear optimal control. The chapter is written as a guide to practitioners who wish to get rapidly acquainted with…
Spiraling of sub-Riemannian geodesics around the Reeb flow in the 3D contact case
Yves Colin de Verdière, Luc Hillairet, Emmanuel Trélat
We consider a closed three-dimensional contact sub-Riemannian manifold. The objective of this note is to provide a precise description of the sub-Riemannian geodesics with large in…