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]


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.

Publications and preprints

19. Global controllability and stabilization of the wave maps equation from a circle to a sphere (with J.-M. Coron)
    arXiv preprint 2024, submitted

18. Traffic Control via Connected and Automated Vehicles: An Open-Road Field Experiment with 100 CAVs (with A. Hayat, A. Bayen, B. Piccoli et. al. )
    arXiv preprint 2024, submitted

17. Traffic smoothing using explicit local controllers (with A. Hayat, A. Bayen, B. Piccoli et. al. )
    arXiv preprint 2023, submitted

16. Global controllability and stabilization of the wave maps equation from a circle to a sphere (with J.-M. Coron and J. Krieger)
    arXiv preprint 2023, submitted

15. Semi-global controllability of a geometric wave equation (with J. Krieger)
    arXiv preprint 2022, submitted

14. Fredholm backstepping for critical operators and application to rapid stabilization for the linearized water waves (with L. Gagnon, A. Hayat and C. Zhang)
    to appear in Annales de l’Institut Fourier, 79p.

13. Stability of multi-population traffic flows (with A. Hayat and B. Piccoli)
    Networks and Heterogeneous Media 18 (2023), Issue 2: 877-905

12. On the global approximate controllability in small time of semiclassical 1-D Schrödinger equations between two states with positive quantum densities (with J.-M. Coron and P. Zhang)
    Journal of Differential Equations 345 (2023), 1-44

11. Fredholm transformation on Laplacian and rapid stabilization for the heat equations (with L. Gagnon, A. Hayat and C. Zhang)
    Journal of Functional Analysis 283 (2022), no.12, 67p.

10. Stabilization of the linearized water tank system (with J.-M. Coron, A. Hayat and C. Zhang)
    Archive for Rational Mechanics and Analysis 244 (2022), 1019–1097

9. Small-time local stabilization of the two dimensional incompressible Navier-Stokes equations
    Annales de l’Institut Henri Poincaré, Analyse Non Linéaire 40 (2023), no. 6, 1487–1511

8. Quantitative rapid and finite time stabilization of the heat equation
    ESAIM: Control, Optimisation and Calculus of Variations

7. Boundary stabilization of focusing NLKG near unstable equilibria: radial case (with J. Krieger)
    Pure and Applied Analysis 5 (2023), no. 4, 833–894

6. Cost for a controlled linear KdV equation (with J. Krieger)
    ESAIM: Control, Optimisation and Calculus of Variations 27 (2021) S21, 41p

5. Stabilisation rapide d'équations de Burgers et de Korteweg-de Vries
    PhD. thesis 2019

4. Small-time global stabilization of the viscous Burgers equation with three scalar controls (with J.-M. Coron)
    Journal de Mathématiques Pures et Appliquées 151 (7), 212-256, 2021

3. Null controllability of a linearized Korteweg-de Vries equation by backstepping approach
    SIAM J. Control Optim. 57 (2019), 1493–1515

2. Small-time local stabilization for a Korteweg-de Vries equation
    Systems & Control Letters 111 (2018), 64–69

1. Local exponential stabilization for a class of Korteweg-de Vries equations by means of time-varying feedback laws (with J.-M. Coron and I. Rivas)
    Analysis & PDE 10 (2017), no. 5, 1089–1122


Spring 2023: I will open a course on PDEs' Control Theory