4 citations · 8 across the 21 of their papers we have counts for
15 papers · 1 filter
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…
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…
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…
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…
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…
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…
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…