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.
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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.
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].
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.
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.
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.
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
15. Semi-global controllability of a semilinear 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)
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)
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)
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)
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)
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
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
8. Quantitative rapid and finite time stabilization of the heat equation
arXiv preprint 2020, submitted
7. Boundary stabilization of focusing NLKG near unstable equilibria: radial case (with J. Krieger)
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)
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
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)
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
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
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)
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
Teaching
Spring 2023: I will open a course on PDEs' Control Theory