4 citations · 8 across the 21 of their papers we have counts for
24 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…
Global exponential turnpike properties for optimal control of the viscous Burgers equation
Emmanuel Trélat, Xingwu Zeng, Can Zhang
We establish global exponential turnpike properties for quadratic optimal tracking problems governed by the one-dimensional viscous Burgers equation with localized internal control…
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…
Polynomial Turnpike Property for a Class of Infinite-Dimensional Oscillating Systems
Alexander Zuyev, Emmanuel Trélat
We establish a polynomial turnpike estimate for an optimal control problem consisting of a system of infinitely many controlled oscillators, considered as an abstract differential…
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 ,…
Controllability of wave-heat and heat-wave cascades
Hugo Lhachemi, Christophe Prieur, Emmanuel Trélat
We study boundary controllability of one-dimensional coupled hyperbolic-parabolic cascades, focusing on the fine structure of reachable sets. The main model is a wave-heat cascade…
A meaningful optimal control problem in quantum and classical physics
Arnaud Lazarus, Emmanuel Trélat
In this paper we study and solve an optimal control problem motivated by applications in quantum and classical physics. Although apparently simple, this optimal control problem is…
Boundary output feedback stabilization of a cascade of N heat equations
Hugo Lhachemi, Christophe Prieur, Emmanuel Trélat
This paper solves the problem of output feedback stabilization for a cascade of N heat equations that are coupled at the boundary, the input being a scalar boundary control applied…
Boundary control of heat-heat cascades
Hugo Lhachemi, Christophe Prieur, Emmanuel Trélat
This paper addresses the problem of feedback stabilization of a cascade of two heat equations that are coupled in the boundary conditions, the input being a boundary control for th…
Controllability and Stabilization of a Wave-Heat Cascade System
Hugo Lhachemi, Christophe Prieur, Emmanuel Trélat
Considering a wave-reaction-diffusion PDE cascade system with wave Neumann control, we first establish controllability properties in a suitable Hilbert space depending on the coupl…
Solution of the Ovals problem
Yacine Chitour, Jochen Denzler, Frédéric Jean +1
In this paper, we bring a complete solution to the Ovals problem, as formulated in [3] and [24].
Multi-agent systems with multiple-wise interaction: Propagation of chaos and macroscopic limit
Thierry Paul, Stefano Rossi, Emmanuel Trélat
We consider interacting multi-agent systems where the interaction is not only pairwise but involves simultaneous interactions among multiple agents (multiple-wise interaction). By…
Numerical solving of an optimal control problem in large time horizon: the aerial vehicle guidance
Veljko Askovic, Emmanuel Trélat, Hasnaa Zidani
In this paper we consider an optimal control problem in large time horizon and solve it numerically. More precisely, we are interested in an aerial vehicle guidance problem: launch…
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…
Universal approximations of quasilinear PDEs by finite distinguishable particle systems
Thierry Paul, Emmanuel Trélat
In this paper, we prove that sufficiently regular solutions of any quasilinear PDE can be approximated by solutions of systems of N distinguishable particles, to within 1/ ln(N ).…
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…
Spectral asymptotics for sub-Riemannian Laplacians
Yves Colin de Verdìère, Luc Hillairet, Emmanuel Trélat
We study spectral properties of sub-Riemannian Laplacians, which are hypoelliptic operators. The main objective is to obtain quantum ergodicity results, what we have achieved in th…
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…