20 citations · 21 across the 10 of their papers we have counts for
11 papers
Quantitative Fredholm backstepping and rapid stabilization
Ludovick Gagnon, Amaury Hayat, Swann Marx +2
In this paper, we address the existence of Fredholm backstepping transformations for self-adjoint and skew-adjoint operators . Under suitable assumptions on the operator and…
Constructive reachability for linear control problems under conic constraints
Camille Pouchol, Emmanuel Trélat, Christophe Zhang
Motivated by applications requiring sparse or nonnegative controls, we investigate reachability properties of linear infinite-dimensional control problems under conic constraints.…
Formulas for Hitting Times and Cover Times for Random Walks on Groups
Christopher Zhang
Using the results of Ding, Lee, Peres [3], we develop formulas to compute the hitting times and cover times for random walks on groups. We developed an explicit formula for hitting…
Quasidiagonals in Strata of Translation Surfaces
Christopher Zhang
We classify orbit closures in the product of strata of translation surfaces. Applications exist to joinings of certain Masur-Veech measures.
Approximate control of parabolic equations with on-off shape controls by Fenchel duality
Camille Pouchol, Emmanuel Trélat, Christophe Zhang
We consider the internal control of linear parabolic equations through on-off shape controls, i.e., controls of the form with and with a prescri…
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…
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…
Periodic points on the regular and double -gon surfaces
Paul Apisa, Rafael M. Saavedra, Christopher Zhang
Using the transfer principle, we classify the periodic points on the regular -gon and double -gon translation surfaces and deduce consequences for the finite blocking problem…
Internal rapid stabilization of a 1-D linear transport equation with a scalar feedback
Christophe Zhang
We use the backstepping method to study the stabilization of a 1-D linear transport equation on the interval (0, L), by controlling the scalar amplitude of a piecewise regular func…
Internal control of systems of semilinear coupled 1-D wave equations
Christophe Zhang
We prove the internal controllability of some systems of two coupled wave equations in one space dimension, with one control, under certain conditions on the coupling. To do this w…