20 citations · 40 across the 12 of their papers we have counts for
12 papers
Boundary stabilization of one-dimensional cross-diffusion systems in a moving domain: linearized system
Jean Cauvin-Vila, Virginie Ehrlacher, Amaury Hayat
We study the boundary stabilization of one-dimensional cross-diffusion systems in a moving domain. We show first exponential stabilization and then finite-time stabilization in arb…
Diffusion and robustness of boundary feedback stabilization of hyperbolic systems
Georges Bastin, Jean-Michel Coron, Amaury Hayat
We consider the problem of boundary feedback control of single-input-single-output (SISO) one-dimensional linear hyperbolic systems when sensing and actuation are anti-located. The…
Fredholm backstepping for critical operators and application to rapid stabilization for the linearized water waves
Ludovick Gagnon, Amaury Hayat, Shengquan Xiang +1
Fredholm-type backstepping transformation, introduced by Coron and Lü, has become a powerful tool for rapid stabilization with fast development over the last decade. Its strength l…
Fredholm transformation on Laplacian and rapid stabilization for the heat equation
Ludovick Gagnon, Amaury Hayat, Shengquan Xiang +1
We study the rapid stabilization of the heat equation on the 1-dimensional torus using the backstepping method with a Fredholm transformation. We prove that, under some assumption…
PI controllers for the general Saint-Venant equations
Amaury Hayat
We study the exponential stability in the norm of the nonlinear Saint-Venant (or shallow water) equations with arbitrary friction and slope using a single Proportional-Inte…
Stabilization of the linearized water tank system
Jean-Michel Coron, Amaury Hayat, Shengquan Xiang +1
In this article we study the so-called water tank system. In this system, the behavior of water contained in a 1-D tank is modelled by Saint-Venant equations, with a scalar distrib…
Global exponential stability and Input-to-State Stability of semilinear hyperbolic systems for the norm
Amaury Hayat
In this paper we study the global exponential stability in the norm of semilinear - hyperbolic systems on a bounded domain, when the source term and the nonlinear bou…
Learning advanced mathematical computations from examples
François Charton, Amaury Hayat, Guillaume Lample
Using transformers over large generated datasets, we train models to learn mathematical properties of differential systems, such as local stability, behavior at infinity and contro…
Feedforward boundary control of nonlinear hyperbolic systems with application to Saint-Venant equations
Georges Bastin, Jean-Michel Coron, Amaury Hayat
Because they represent physical systems with propagation delays, hyperbolic systems are well suited for feedforward control. This is especially true when the delay between a distur…
Input-to-State Stability in sup norms for hyperbolic systems with boundary disturbances
Georges Bastin, Jean-Michel Coron, Amaury Hayat
We give sufficient conditions for Input-to-State Stability in norm of general quasilinear hyperbolic systems with boundary input disturbances. In particular the derivation…
Exponential stability of general 1-D quasilinear systems with source terms for the norm under boundary conditions
Amaury Hayat
We address the question of the exponential stability for the norm of general 1-D quasilinear systems with source terms under boundary conditions. To reach this aim, we intr…
Lateral Chirality-sorting Optical Spin Forces in Evanescent Fields
Amaury Hayat, J. P. Balthasar Müller, Federico Capasso
The transverse component of the spin angular momentum of evanescent waves gives rise to lateral optical forces on chiral particles, which have the unusual property of acting in a d…