Jean-Michel Coron
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Jean-Michel Coron has a total of 78 co-authors. Here are the top co-authors by number of shared publications:
- Amaury Hayat
Institut Polytechnique de Paris, Champs-sur-Marne, France
9 shared publications - Hoai-Minh Nguyen
Sorbonne Université, Universitsé Paris Cité, CNRS, INRIA, Laboratoire Jacques-Louis Lions, LJLL
9 shared publications - Georges Bastin
ICTEAM, UCLouvain
7 shared publications - Shengquan Xiang
School of Mathematical Sciences, Peking University, Beijing, China
7 shared publications - Peipei Shang
Tongji University
6 shared publications - Luis Almeida
LPSM -Sorbonne Université Université Paris-Cité France
5 shared publications
Latest Publications
- Open Access
- 24 April 2026
- Published by EDP Sciences in Mathematical Modelling of Natural Phenomena
- Vol. 21, 18
Feedback stabilization for a spatial-dependent Sterile Insect Technique model with Allee Effect
This work focuses on feedback control strategies for applying the sterile insect technique (SIT) to eliminate pest populations. The presentation is centered on the case of mosquito populations, but most of the results can be extended to other species by adapting the model and selecting appropriate parameter values to describe the reproduction and movement dynamics of the species under consideration. In our study, we address the spatial distribution of the population in a two dimensional bounded domain by extending the temporal SIT model analyzed in [Agbo bidi Math. Biosci. Eng . 21 (2024) 6263–6288], thereby obtaining a reaction-diffusion SIT model. After the analysis of the existence and the uniqueness of the solution of this problem, we construct a feedback law that globally asymptotically stabilizes the extinction equilibrium thus yielding a robust strategy to keep the pest population at very low levels in the long term.
- 24 April 2026
- Published by EDP Sciences in Mathematical Modelling of Natural Phenomena
- Vol. 21, 18
Open AccessFeedback stabilization for a spatial-dependent Sterile Insect Technique model with Allee Effect
This work focuses on feedback control strategies for applying the sterile insect technique (SIT) to eliminate pest populations. The presentation is centered on the case of mosquito populations, but most of the results can be extended to other species by adapting the model and selecting appropriate parameter values to describe the reproduction and movement dynamics of the species under consideration. In our study, we address the spatial distribution of the population in a two dimensional bounded domain by extending the temporal SIT model analyzed in [Agbo bidi Math. Biosci. Eng . 21 (2024) 6263–6288], thereby obtaining a reaction-diffusion SIT model. After the analysis of the existence and the uniqueness of the solution of this problem, we construct a feedback law that globally asymptotically stabilizes the extinction equilibrium thus yielding a robust strategy to keep the pest population at very low levels in the long term.
- Open AccessA necessary and sufficient robustness condition for boundary observer-controllers that stabilize $2\times 2$ hyperbolic systemsWe investigate the robustness of the stabilization of a class of $2 \times 2$ hyperbolic systems with boundary control subject to uncertainties in characteristic velocities. We focus on the single input-single-output setting, examining separately the cases of co-located and anti-located sensing and actuation. In both cases, stabilizing controls are designed via the backstepping technique.For the co-located case, we recall that output feedback stabilization is unconditionally robust with respect to arbitrarily small perturbations in the characteristic velocities. The main contribution addresses the anti-located case. We provide a sharp necessary and sufficient dissipative boundary condition ensuring robustness against small perturbations in the characteristic velocities. The originality of our contribution lies essentially in the proof strategy for robustness in $L^{2}$ -norm. The analysis proceeds in three stages: (i) robustness is first established in $H^{1}$ -norm using a basic quadratic Lyapunov function; (ii) robustness in $H^{1}$ is shown to imply robustness in $L^{2}$ because there is an isomorphism between the respective solution spaces, revealing in addition a new, less intuitive Lyapunov function; and (iii) using degree theory, we prove that the robustness boundary condition is also necessary, by showing that there exist arbitrarily small perturbations for which the associated eigenvalue problem has unstable solutions whenever the condition is not satisfied.Open AccessA necessary and sufficient robustness condition for boundary observer-controllers that stabilize $2\times 2$ hyperbolic systemsWe investigate the robustness of the stabilization of a class of $2 \times 2$ hyperbolic systems with boundary control subject to uncertainties in characteristic velocities. We focus on the single input-single-output setting, examining separately the cases of co-located and anti-located sensing and actuation. In both cases, stabilizing controls are designed via the backstepping technique.For the co-located case, we recall that output feedback stabilization is unconditionally robust with respect to arbitrarily small perturbations in the characteristic velocities. The main contribution addresses the anti-located case. We provide a sharp necessary and sufficient dissipative boundary condition ensuring robustness against small perturbations in the characteristic velocities. The originality of our contribution lies essentially in the proof strategy for robustness in $L^{2}$ -norm. The analysis proceeds in three stages: (i) robustness is first established in $H^{1}$ -norm using a basic quadratic Lyapunov function; (ii) robustness in $H^{1}$ is shown to imply robustness in $L^{2}$ because there is an isomorphism between the respective solution spaces, revealing in addition a new, less intuitive Lyapunov function; and (iii) using degree theory, we prove that the robustness boundary condition is also necessary, by showing that there exist arbitrarily small perturbations for which the associated eigenvalue problem has unstable solutions whenever the condition is not satisfied.
- Open Access
Wave maps from circle to Riemannian manifold: global controllability is equivalent to homotopy
We study wave maps from the circle to a general compact Riemannian manifold. We prove that the global controllability of this geometric equation is characterized precisely by the homotopy class of the data. As a remarkable intermediate result, we establish uniform-time global controllability between steady states, providing a partial answer to an open problem raised by Dehman, Lebeau and Zuazua (2003). Finally, we obtain quantitative exponential stability around closed geodesics with negative sectional curvature. This work highlights the rich interplay between partial differential equations, differential geometry, and control theory.
Open AccessWave maps from circle to Riemannian manifold: global controllability is equivalent to homotopy
We study wave maps from the circle to a general compact Riemannian manifold. We prove that the global controllability of this geometric equation is characterized precisely by the homotopy class of the data. As a remarkable intermediate result, we establish uniform-time global controllability between steady states, providing a partial answer to an open problem raised by Dehman, Lebeau and Zuazua (2003). Finally, we obtain quantitative exponential stability around closed geodesics with negative sectional curvature. This work highlights the rich interplay between partial differential equations, differential geometry, and control theory.
- Open Access
- 29 April 2025
- Published by Elsevier in Systems & Control Letters
- Vol. 202
A novel approach to feedback control with deep reinforcement learning
- 29 April 2025
- Published by Elsevier in Systems & Control Letters
- Vol. 202
Open AccessA novel approach to feedback control with deep reinforcement learning
- Open Access
- 24 March 2025
- Published by Springer Nature in Calculus of Variations and Partial Differential Equations
- Vol. 64 (4) , 1-39
Global controllability and stabilization of the wave maps equation from a circle to a sphere
Continuing the investigations started in the recent work (Krieger and Xiang in Semi-global controllability of a geometric wave equation, 2022. arXiv:2205.00915) 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 semi-global refers to the $$2\pi $$ -energy bound, we prove global exact controllability of the same system for $$k>1$$ and show that the $$2\pi $$ -energy bound is a strict threshold for uniform asymptotic stabilization via continuous time-varying feedback laws indicating that the damping stabilization in Krieger and Xiang (2022) is sharp. Lastly, the global exact controllability for $$\mathbb {S}^1$$ -target within minimum time is discussed.- 24 March 2025
- Published by Springer Nature in Calculus of Variations and Partial Differential Equations
- Vol. 64 (4) , 1-39
Open AccessGlobal controllability and stabilization of the wave maps equation from a circle to a sphere
Continuing the investigations started in the recent work (Krieger and Xiang in Semi-global controllability of a geometric wave equation, 2022. arXiv:2205.00915) 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 semi-global refers to the $$2\pi $$ -energy bound, we prove global exact controllability of the same system for $$k>1$$ and show that the $$2\pi $$ -energy bound is a strict threshold for uniform asymptotic stabilization via continuous time-varying feedback laws indicating that the damping stabilization in Krieger and Xiang (2022) is sharp. Lastly, the global exact controllability for $$\mathbb {S}^1$$ -target within minimum time is discussed. - Open Access
Feedback stabilization for a spatial-dependent Sterile Insect Technique model with Allee Effect
This work focuses on feedback control strategies for applying the sterile insect technique (SIT) to eliminate pest populations. The presentation is centered on the case of mosquito populations, but most of the results can be extended to other species by adapting the model and selecting appropriate parameter values to describe the reproduction and movement dynamics of the species under consideration. In our study, we address the spatial distribution of the population in a two dimensional bounded domain by extending the temporal SIT model analyzed in [2], thereby obtaining a reaction-diffusion SIT model. After the analysis of the existence and the uniqueness of the solution of this problem, we construct a feedback law that globally asymptotically stabilizes the extinction equilibrium thus yielding a robust strategy to keep the pest population at very low levels in the long term.
Open AccessFeedback stabilization for a spatial-dependent Sterile Insect Technique model with Allee Effect
This work focuses on feedback control strategies for applying the sterile insect technique (SIT) to eliminate pest populations. The presentation is centered on the case of mosquito populations, but most of the results can be extended to other species by adapting the model and selecting appropriate parameter values to describe the reproduction and movement dynamics of the species under consideration. In our study, we address the spatial distribution of the population in a two dimensional bounded domain by extending the temporal SIT model analyzed in [2], thereby obtaining a reaction-diffusion SIT model. After the analysis of the existence and the uniqueness of the solution of this problem, we construct a feedback law that globally asymptotically stabilizes the extinction equilibrium thus yielding a robust strategy to keep the pest population at very low levels in the long term.
- 17 January 2025
- Published by Springer Nature in Journal of Optimization Theory and Applications
- Vol. 204 (2) , 1-38
Global Stabilization of a Sterile Insect Technique Model by feedback Laws
- 17 January 2025
- Published by Springer Nature in Journal of Optimization Theory and Applications
- Vol. 204 (2) , 1-38
Global Stabilization of a Sterile Insect Technique Model by feedback Laws
- Open Access
Wave maps from circle to Riemannian manifold: global controllability is equivalent to homotopy
We study wave maps from the circle to a general compact Riemannian manifold. We prove that the global controllability of this geometric equation is characterized precisely by the homotopy class of the data, thereby resolving the conjecture posed in [14, 35]. As a remarkable intermediate result, we establish uniform-time global controllability between steady states, providing a partial answer to an open problem raised in [22]. Finally, we obtain quantitative exponential stability around closed geodesics with negative sectional curvature. This work highlights the rich interplay between partial differential equations, differential geometry, and control theory.
Open AccessWave maps from circle to Riemannian manifold: global controllability is equivalent to homotopy
We study wave maps from the circle to a general compact Riemannian manifold. We prove that the global controllability of this geometric equation is characterized precisely by the homotopy class of the data, thereby resolving the conjecture posed in [14, 35]. As a remarkable intermediate result, we establish uniform-time global controllability between steady states, providing a partial answer to an open problem raised in [22]. Finally, we obtain quantitative exponential stability around closed geodesics with negative sectional curvature. This work highlights the rich interplay between partial differential equations, differential geometry, and control theory.
- Open Access
Global stabilization of a Sterile Insect Technique model by feedback laws
This work concerns feedback global stabilization of the sterile insect technique dynamics. The Sterile Insect Technique (SIT) is presently one of the most ecological methods for controlling insect pests responsible for crop destruction and disease transmission worldwide. This technique consists in releasing sterile males among the insect pest population, the aim being to reduce fertility and, consequently, reduce significantly the wild insect population after a few generations. In this work, we study the global stabilization of a pest population at extinction equilibrium by the SIT method and construct explicit feedback laws that stabilize the model. Numerical simulations show the efficiency of our feedback laws.
Open AccessGlobal stabilization of a Sterile Insect Technique model by feedback laws
This work concerns feedback global stabilization of the sterile insect technique dynamics. The Sterile Insect Technique (SIT) is presently one of the most ecological methods for controlling insect pests responsible for crop destruction and disease transmission worldwide. This technique consists in releasing sterile males among the insect pest population, the aim being to reduce fertility and, consequently, reduce significantly the wild insect population after a few generations. In this work, we study the global stabilization of a pest population at extinction equilibrium by the SIT method and construct explicit feedback laws that stabilize the model. Numerical simulations show the efficiency of our feedback laws.
- Open Access
- 2 May 2024
- Published by European Mathematical Society - EMS - Publishing House GmbH in Annales de l'Institut Henri Poincaré C, Analyse non linéaire
- Vol. 41 (6) , 1327-1365
Lack of local controllability for a water-tank system when the time is not large enough
We consider the small-time local-controllability property of a water tank modeled by one-dimensional Saint-Venant equations, where the control is the acceleration of the tank. It is known from the work of Dubois et al. that the linearized system is not controllable. Moreover, concerning the linearized system, they showed that a traveling time T_{*} is necessary to bring the tank from one position to another for which the water is still at the beginning and at the end. Concerning the nonlinear system, Coron showed that local controllability around equilibrium states holds for a time large enough. In this paper, we show that for local controllability of the nonlinear system around the equilibrium states, the necessary time is at least 2 T_{*} even for the tank being still at the beginning and at the end. The key point of the proof is a coercivity property for the quadratic approximation of the water-tank system.
- 2 May 2024
- Published by European Mathematical Society - EMS - Publishing House GmbH in Annales de l'Institut Henri Poincaré C, Analyse non linéaire
- Vol. 41 (6) , 1327-1365
Open AccessLack of local controllability for a water-tank system when the time is not large enough
We consider the small-time local-controllability property of a water tank modeled by one-dimensional Saint-Venant equations, where the control is the acceleration of the tank. It is known from the work of Dubois et al. that the linearized system is not controllable. Moreover, concerning the linearized system, they showed that a traveling time T_{*} is necessary to bring the tank from one position to another for which the water is still at the beginning and at the end. Concerning the nonlinear system, Coron showed that local controllability around equilibrium states holds for a time large enough. In this paper, we show that for local controllability of the nonlinear system around the equilibrium states, the necessary time is at least 2 T_{*} even for the tank being still at the beginning and at the end. The key point of the proof is a coercivity property for the quadratic approximation of the water-tank system.