35 citations · 69 across the 14 of their papers we have counts for
19 papers
Optimal cost of fast boundary controls for the one-dimensional heat equation
Pierre Lissy
We consider the heat equation on with homogeneous Dirichlet condition at one endpoint and a Dirichlet boundary control at the other. If \(C_{\mathrm H}(T,L)\) denotes the o…
Control and stabilization of cascade coupled systems: application to a 1-d heat and wave coupled system
Lucas Davron, Pierre Lissy, Swann Marx
We study cascade coupled systems, for which our prototypical example is a 1-d heat equation coupled with a 1-d wave equation. The heat component is controlled through one boundary…
Traffic Flow Reconstruction from Limited Collected Data
Nail Baloul, Amaury Hayat, Thibault Liard +1
We propose an efficient method for reconstructing traffic density with low penetration rate of probe vehicles. Specifically, we rely on measuring only the initial and final positio…
Exact output tracking for the one-dimensional heat equation and applications to the interpolation problem in Gevrey classes of order 2
Lucas Davron, Pierre Lissy
This paper provides a complete characterization of the Dirichlet boundary outputs that can be exactly tracked in the one-dimensional heat equation with Neumann boundary control. Th…
Null controllability of the 1D heat equation with interior inverse square potential
Pierre Lissy, Tanguy Lourme
This paper aims to answer an open problem posed by Morancey in 2015 concerning the null controllability of the heat equation on (-1, 1) with an internal inverse square potential lo…
Effective multipliers for weights whose log are Hölder continuous. Application to the cost of fast boundary controls for the 1D Schr{ö}dinger equation
Pierre Lissy
We give a simple proof of the Beurling-Malliavin multiplier theorem (BM1) in the particular case of weights that verify the usual finite logarithmic integral condition and such tha…
Mixing Douglas' and weak majorization and factorization theorems
Pierre Lissy
The Douglas' majorization and factorization theorem characterizes the inclusion of operator ranges in Hilbert spaces. Notably, it reinforces the well-established connections betwee…
Null-controllability of underactuated linear parabolic-transport systems with constant coefficients
Armand Koenig, Pierre Lissy
The goal of the present article is to study controllability properties of mixed systems of linear parabolic-transport equations, with possibly non-diagonalizable diffusion matrix,…
Insensitizing control for linear and semi-linear heat equations with partially unknown domain
Pierre Lissy, Yannick Privat, Yacouba Simporé
We consider a semi-linear heat equation with Dirichlet boundary conditions and globally Lipschitz nonlinearity, posed on a bounded domain of R^N (N N *), assumed to be an unk…
Insensitizing controls for the heat equation with respect to boundary variations
Sylvain Ervedoza, Pierre Lissy, Yannick Privat
This article is dedicated to insensitization issues of a quadratic functional involving the solution of the linear heat equation with respect to domains variations. This work can b…
State-constrained controllability of linear reaction-diffusion systems
Pierre Lissy, Clément Moreau
We study the controllability of a coupled system of linear parabolic equations, with non-negativity constraint on the state. We establish two results of controllability to trajecto…
A Fredholm transformation for the rapid stabilization of a degenerate parabolic equation
Ludovick Gagnon, Pierre Lissy, Swann Marx
This paper deals with the rapid stabilization of a degenerate parabolic equation with a right Dirich-let control. Our strategy consists in applying a backstepping strategy, which s…
Bilinear local controllability to the trajectories of the Fokker-Planck equation with a localized control
Michel Duprez, Pierre Lissy
This work is devoted to the control of the Fokker-Planck equation, posed on a smooth bounded domain of R^d, with a localized drift force. We prove that this equation is locally con…
Necessary conditions for local controllability of a particular class of systems with two scalar controls
Laetitia Giraldi, Pierre Lissy, Clément Moreau +1
We consider affine control systems with two scalar controls, such that one control vector field vanishes at an equilibrium state. We state two necessary conditions of local control…
Indirect controllability of some linear parabolic systems of m equations with m-1 controls involving coupling terms of zero or first order
Michel Duprez, Pierre Lissy
This paper is devoted to the study of the null and approximate controllability for some classes of linear coupled parabolic systems with less controls than equations. More precisel…
Positive and negative results on the internal controllability of parabolic equations coupled by zero and first order terms
Michel Duprez, Pierre Lissy
This paper is devoted to studying the null and approximate controllability of two linear coupled parabolic equations posed on a smooth domain of R^N (N>1) with coupling terms of ze…
Controllability of a bent 3-link magnetic microswimmer
Laetitia Giraldi, Pierre Lissy, Clément Moreau +1
- In this paper, we focus on a variant of a 3-link magnetic microswimmer which consists of three rigid magnetized segments connected by two torsional springs. In particular, we ass…
On the cost of fast controls for some families of dispersive or parabolic equations in one space dimension
Pierre Lissy
In this paper, we consider the cost of null controllability for a large class of linear equations of parabolic or dispersive type in one space dimension in small time. By extending…
Local null controllability of the three-dimensional Navier-Stokes system with a distributed control having two vanishing components
Jean-Michel Coron, Pierre Lissy
In this paper, we prove a local null controllability result for the three-dimensional Navier-Stokes equations on a (smooth) bounded domain of R^3 with null Dirichlet boundary condi…