Web page of Shengquan XIANG

About me

I am a Tenure Track assistant professor at School of Mathematical Sciences, Peking University. Prior to that I was a Research Scientist (postdoc) at EPFL, in the group of Prof. Joachim Krieger.

Former student at École Normale Supérieure de Paris and Peking University, I obtained my Ph.D. on controllability and stabilization of fluids at Sorbonne Université under the supervision of Prof. Jean-Michel Coron, while in the year 2017 I was invited researcher at ETH Zürich.

You can contact me by shengquan.xiang[AT]pku.edu.cn

Research

Frequency Lyapunov for quantitative stabilization

In [8, 9] I introduced the Frequency Lyapunov method, a constructive method that combines spectral inequalities and Lyapunov functionals, to get quantitative rapid stabilization, null-controllability with optimal costs, and finite time stabilization.

Quantitative controllability and stabilization of dispersive equations

Removing the compactness arguments for dispersive equations by quantitative approaches allows to construct more robust and applicable controls. In [2, 3, 6] we have studied constructive controllabilities for KdV equations describing waves in a canal. We quantitatively stabilise nonlinear waves equations with damping in [7, 15].

Fredholm backstepping transformation

In a series of works [10, 11, 14] we have investigated the Fredholm backstepping for a large class of operators, the compactness/duality method introduced in [14] overcomes the threshold imposed by the classical approach.

Stabilization of systems emphasizing nonlinear effects

In the works [1] and [4] we have benefited from nonlinear structures to stabilize the KdV equations and the viscous Burgers equation for which the linearized systems are not stabilizable.

Control of the semiclassical Schrödinger equations

In [12] we have combined the WKB method, the semiclassical limit and the geometrical nonlinear control techniques to get an approximate controllability of the quantum density and quantum momentum.

Smoothing traffic flows with autonomous vehicles

Traffic jams are generated from the instability of traffic equilibrium states [13], and increase strongly the fuel consumption and the emissions. We construct feedback laws on autonomous vehicles to stabilize these stop-and-go waves.