Shengquan Xiang

Shengquan Xiang
Swiss Federal Institute of Technology in Lausanne | EPFL · Mathematics Section

Doctor of Philosophy
Postdoc researcher

About

26
Publications
1,642
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180
Citations

Publications

Publications (26)
Article
The CIRCLES project aims to reduce instabilities in traffic flow, which are naturally occurring phenomena due to human driving behavior. Also called “phantom jams” or “stop-and-go waves,” these instabilities are a significant source of wasted energy. Toward this goal, the CIRCLES project designed a control system, referred to as the MegaController...
Article
This article presents experimental evidence of the ability of a single automated vehicle acting as a controller to effectively dissipate stop-and-go waves in real traffic. The automated vehicle succeeded in stabilizing the speed profile by reducing oscillations in time and speed variations between vehicles during rush hour on I-24 in the Nashville...
Preprint
Continuing the investigations started in the recent work [Krieger-Xiang, 2022] on semi-global controllability and stabilization of the $(1+1)$-dimensional wave maps equation with spatial domain $\mathbb{S}^1$ and target $\mathbb{S}^k$, where {\it semi-global} refers to the $2\pi$-energy bound, we prove global exact controllability of the same syste...
Article
In this paper, we study, in the semiclassical sense, the global approximate controllability in small time of the quantum density and quantum momentum of the 1-D semiclassical cubic Schrödinger equation with two controls between two states with positive quantum densities. We first control the asymptotic expansions of the zeroth and first order of th...
Article
We construct explicit time-varying feedback laws that locally stabilize the two-dimensional internal controlled incompressible Navier–Stokes equations in arbitrarily small time. We also obtain quantitative rapid stabilization via stationary feedback laws, as well as quantitative null-controllability with explicit controls having e^{C/T} costs.
Article
Full-text available
Traffic waves, known also as stop-and-go waves or phantom jams, appear naturally as traffic instabilities, also in confined environments as a ring-road. A multi-population traffic is studied on a ring-road, comprised of drivers with stable and unstable behavior. There exists a critical penetration rate of stable vehicles above which the system is s...
Article
We study the rapid stabilization of the heat equation on the 1-dimensional torus using the backstepping method with a Fredholm transformation. This classical framework allows us to present the backstepping method with Fredholm transformations for the Laplace operator in a sharp functional setting, which is the main objective of this work. We first...
Preprint
We prove the semi-global controllability and stabilization of the $(1+1)$-dimensional wave maps equation with spatial domain $\mathbb{S}^1$ and target $\mathbb{S}^k$. First we show that damping stabilizes the system when the energy is strictly below the threshold $2\pi$, where harmonic maps appear as obstruction for global stabilization. Then, we a...
Article
Full-text available
In this article we study the so-called water tank system. In this system, the behavior of water contained in a one dimensional tank is modelled by Saint-Venant equations, with a scalar distributed control. It is well-known that the linearized systems around uniform steady-states are not controllable, the uncontrollable part being of infinite dimens...
Preprint
Full-text available
Fredholm-type backstepping transformation, introduced by Coron and L\"u, has become a powerful tool for rapid stabilization with fast development over the last decade. Its strength lies in its systematic approach, allowing to deduce rapid stabilization from approximate controllability. But limitations with the current approach exist for operators o...
Preprint
Full-text available
Traffic waves, known also as stop-and-go waves or phantom hams, appear naturally as traffic instabilities, also in confined environments as a ring-road. A multi-population traffic is studied on a ring-road, comprised of drivers with stable and unstable behavior. There exists a critical penetration rate of stable vehicles above which the system is s...
Preprint
Full-text available
In this paper, we study, in the semiclassical sense, the global approximate controllability in small time of the quantum density and quantum momentum of the 1-D semiclassical cubic Schr\"odinger equation with two controls between two states with positive quantum densities. We first control the asymptotic expansions of the zeroth and first order of...
Preprint
Full-text available
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 on the control operator, two scalar controls are necessary and sufficient to get controllability and rapid stabilization. This classical framework allows us to present th...
Preprint
Full-text available
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 distributed control. It is well-known that the linearized systems around uniform steady-states are not controllable, the uncontrollable part being of infinite dimension. Here we...
Article
We construct explicit time-varying feedback laws leading to the global (null) stabilization in small time of the viscous Burgers equation with three scalar controls. Our feedback laws use first the quadratic transport term to achieve the small-time global approximate stabilization and then the linear viscous term to get the small-time local stabili...
Preprint
Full-text available
We provide explicit time-varying feedback laws that locally stabilize the two dimensional internal controlled incompressible Navier-Stokes equations in arbitrarily small time. We also obtain quantitative rapid stabilization via stationary feedback laws, as well as quantitative null controllability with explicit controls having $e^{C/T}$ costs.
Preprint
Full-text available
The null controllability of the heat equation is known for decades [19,23,30]. The finite time stabilizability of the one dimensional heat equation was proved by Coron--Nguy\^en [13], while the same question for high dimensional spaces remained widely open. Inspired by Coron--Tr\'elat [14] we find explicit stationary feedback laws that quantitative...
Article
Full-text available
The controllability of the linearized KdV equation with right Neumann control is studied in the pioneering work of Rosier [25]. However, the proof is by contradiction arguments and the value of the observability constant remains unknown, though rich mathematical theories are built on this totally unknown constant. We introduce a constructive method...
Preprint
Full-text available
We investigate the stability and stabilization of the cubic focusing Klein-Gordon equation around static solutions on the closed ball in $\mathbb{R}^3$. First we show that the system is linearly unstable near the static solution $u\equiv 1$ for any dissipative boundary condition $u_t+ au_{\nu}=0, a\in (0, 1)$. Then by means of boundary controls (bo...
Preprint
Full-text available
The controllability of the linearized KdV equation with right Neumann control is studied in the pioneering work of Rosier [25]. However, the proof is by contradiction arguments and the value of the observability constant remains unknown, though rich mathematical theories are built on this totally unknown constant. We introduce a constructive method...
Thesis
Full-text available
This thesis is devoted to the study of stabilization of partial differential equations by nonlinear feedbacks. We are interested in the cases where classical linearization and stationary feedback law do not work for stabilization problems, for example KdV equations and Burgers equations. More precisely, it includes three important cases : stabiliza...
Article
We prove the null controllability of a linearized Korteweg–de Vries equation with a Dirichlet control on the left boundary. Instead of considering classical methods, i.e., Carleman estimates, the moment method, etc., we use a backstepping approach, which is a method usually used to handle stabilization problems.
Article
This paper focuses on the (local) small-time stabilization of a Korteweg–de Vries equation on bounded interval, thanks to a time-varying Dirichlet feedback law on the left boundary. Recently, backstepping approach has been successfully used to prove the null controllability of the corresponding linearized system, instead of Carleman inequalities. W...
Article
Full-text available
We study the exponential stabilization problem for a nonlinear Korteweg-de Vries equa- tion on bounded interval in cases where the linearized control system is not controllable. The system has Dirichlet boundary conditions at the end-points of the interval, a Neumann nonhomogeneous boundary condition at the right end-point which is the control. We...
Preprint
We study the exponential stabilization problem for a nonlinear Korteweg-de Vries equa- tion on bounded interval in cases where the linearized control system is not controllable. The system has Dirichlet boundary conditions at the end-points of the interval, a Neumann nonhomogeneous boundary condition at the right end-point which is the control. We...

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