58 citations · 223 across the 31 of their papers we have counts for
39 papers
Minimal time for heat observability on almost-Riemannian surfaces
Vincent Boulard, Amaury Hayat, Emmanuel Trélat
We determine the minimal observation time for the heat equation on a closed almost-Riemannian surface, for a class of observation sets leaving sufficiently thin collars around simp…
Optimal geometric barriers for weighted observability of heat semigroups on metric measure spaces
Vincent Boulard, Amaury Hayat, Emmanuel Trélat
Weighted integrated observability inequalities for heat equations usually involve a small-time factor of the form . We prove that this scale is not an artefact of Carlema…
Constructive exact control of semilinear 1D wave equations by a least-squares approach
Arnaud Münch, Emmanuel Trélat
It has been proved by Zuazua in the nineties that the internally controlled semilinear 1D wave equation , with Dirichlet boundary condit…
Robustness under control sampling of reachability in fixed time for nonlinear control systems
Loïc Bourdin, Emmanuel Trélat
Under a regularity assumption we prove that reachability in fixed time for nonlinear control systems is robust under control sampling.
Pace and motor control optimization for a runner
Amandine Aftalion, Emmanuel Trélat
Our aim is to present a new model which encompasses pace optimization and motor control effort for a runner on a fixed distance. We see that for long races, the long term behaviour…
Small-time asymptotics of hypoelliptic heat kernels near the diagonal, nilpotentization and related results
Yves Colin de Verdière, Luc Hillairet, Emmanuel Trélat
We establish small-time asymptotic expansions for heat kernels of hypoelliptic Hörmander operators in a neighborhood of the diagonal, generalizing former results obtained in partic…
Shape turnpike for linear parabolic PDE models
Gontran Lance, Emmanuel Trélat, Enrique Zuazua
We introduce and study the turnpike property for time-varying shapes, within the viewpoint of optimal control. We focus here on second-order linear parabolic equations where the sh…
Geometric and spectral characterization of Zoll manifolds, invariant measures and quantum limits
Emmanuel Humbert, Yannick Privat, Emmanuel Trélat
We provide new geometric and spectral characterizations for a Riemannian manifold to be a Zoll manifold, i.e., all geodesics of which are periodic. We analyze relationships with in…
Characterization by observability inequalities of controllability and stabilization properties
Emmanuel Trélat, Gengsheng Wang, Yashan Xu
Given a linear control system in a Hilbert space with a bounded control operator, we establish a characterization of exponential stabilizability in terms of an observability inequa…
Phase portrait control for 1D monostable and bistable reaction-diffusion equations
Camille Pouchol, Emmanuel Trélat, Enrique Zuazua
We consider the problem of controlling parabolic semilinear equations arising in population dynamics, either in finite time or infinite time. These are the monostable and bistable…
Addendum to Pontryagin's maximum principle for dynamic systems on time scales
Loïc Bourdin, Oleksandr Stanzhytskyi, Emmanuel Trélat
This note is an addendum to [1,2], pointing out the differences between these papers and raising open questions.
Optimal Control of Endo-Atmospheric Launch Vehicle Systems: Geometric and Computational Issues
Riccardo Bonalli, Bruno Hérissé, Emmanuel Trélat
In this paper we develop a geometric analysis and a numerical algorithm, based on indirect methods, to solve optimal guidance of endo-atmospheric launch vehicle systems under mixed…
Convergence to consensus of the general finite-dimensional Cucker-Smale model with time-varying delays
Cristina Pignotti, Emmanuel Trélat
We consider the celebrated Cucker-Smale model in finite dimension, modelling interacting collective dynamics and their possible evolution to consensus. The objective of this paper…
Redundancy implies robustness for bang-bang strategies
Antoine Olivier, Thomas Haberkorn, Emmanuel Trélat +2
We develop in this paper a method ensuring robustness properties to bang-bang strategies , for general nonlinear control systems. Our main idea is to add bang arcs in the form of n…
Analytical Initialization of a Continuation-Based Indirect Method for Optimal Control of Endo-Atmospheric Launch Vehicle Systems
Riccardo Bonalli, Bruno Hérissé, Emmanuel Trélat
In this paper, we propose a strategy to solve endo-atmospheric launch vehicle optimal control problems using indirect methods. More specifically, we combine shooting methods with a…
Mean-Field Sparse Jurdjevic--Quinn Control
Marco Caponigro, Benedetto Piccoli, Francesco Rossi +1
We consider nonlinear transport equations with non-local velocity, describing the time-evolution of a measure, which in practice may represent the density of a crowd. Such equation…
Asymptotic analysis and optimal control of an integro-differential system modelling healthy and cancer cells exposed to chemotherapy
Camille Pouchol, Jean Clairambault, Alexander Lorz +1
We consider a system of two coupled integro-differential equations modelling populations of healthy and cancer cells under therapy. Both populations are structured by a phenotypic…
Interaction Network, State Space and Control in Social Dynamics
Aylin Aydogdu, Marco Caponigro, Sean McQuade +4
In the present chapter we study the emergence of global patterns in large groups in first and second-order multi-agent systems, focusing on two ingredients that influence the dynam…
Observability properties of the homogeneous wave equation on a closed manifold
Emmanuel Humbert, Yannick Privat, Emmanuel Trélat
We consider the wave equation on a closed Riemannian manifold. We observe the restriction of the solutions to a measurable subset along a time interval with . It…
Geometric control condition for the wave equation with a time-dependent observation domain
Jérôme Le Rousseau, Gilles Lebeau, Peppino Terpolilli +1
We characterize the observability property (and, by duality, the controllability and the stabilization) of the wave equation on a Riemannian manifold with or without boundary,…
Value function for regional control problems via dynamic programming and Pontryagin maximum principle
Guy Barles, Ariela Briani, Emmanuel Trélat
In this paper we focus on regional deterministic optimal control problems, i.e., problems where the dynamics and the cost functional may be different in several regions of the stat…
Pontryagin maximum principle for optimal sampled-data control problems
Loïc Bourdin, Emmanuel Trélat
In this short communication, we first recall a version of the Pontryagin maximum principle for general finite-dimensional nonlinear optimal sampled-data control problems. This resu…
Finite-dimensional predictor-based feedback stabilization of a 1D linear reaction-diffusion equation with boundary input delay
Delphine Bresch-Pietri, Christophe Prieur, Emmanuel Trélat
We consider a one-dimensional controlled reaction-diffusion equation, where the control acts on the boundary and is subject to a constant delay. Such a model is a paradigm for more…
Coupled attitude and trajectory optimization for a launcher tilting maneuver
Jiamin Zhu, Emmanuel Trélat, Max Cerf
We study the minimum time control problem of the launchers. The optimal trajectories of the problem may contain singular arcs, and thus chattering arcs. The motion of the launcher…