Go to content Go to the menu Go to the search

CPDENL: Control of partial differential equations and nonlinearity - Jean-Michel Coron

Quick access, personalized services


Advanced search


Direction de la communication


Marie Pinhas-Diena, in charge of scientific communications l tel: +33 (0)1 44 27 22 89 l email: marie.pinhas@upmc.fr

Control of partial differential equations and nonlinearity, CPDENL, Jean-Michel Coron

A control system is a system in which we can act with a command or control (for example a car where one presses the accelerator and brake pedals and turns the steering wheel). Two major problems arise: controllability and stabilization. The problem of controllability is to know if when starting from a given situation one can achieve a desired situation with the aid of a well-chosen control.


Jean-Michel Coron, Research Director


The problem of stabilizing a system can be easily understood by means of the classic experiment of balancing a broom on one finger. The brush is placed vertically on the finger. If we do not move our finger slowly and then more rapidly, the broom will move away from the vertical position and eventually fall. This is because the equilibrium is unstable. To prevent the broom from falling, we move our finger based on the position and speed of the broom to prevent it from falling down. We are giving the broom "feedback" (a force applied by the finger on the broom which depends on the system status, by the position and speed of the broom) to make this unstable equilibrium in the absence of feedback, stable.


A lock on the Meuse River, currently controlled by the feedback found during the project. © Jean-Michel Coron


The project focuses on the importance of nonlinearities for both problems within systems modeled by partial differential equations. The main results are currently:

- A new method for studying the controllability of coupled systems.

- The first analysis of the controllability in the presence of a boundary layer, that is to say a place near the edge of the area where the system state changes rapidly.

- A detailed analysis of the balance sheet stabilization laws.

This led to the feedback for regulating the level of water in rivers. These feedbacks have been implemented on the River Sambre in Belgium and are being implemented on the river Meuse, also in Belgium. Le projet porte sur l'importance des non-linéarités pour ces deux problèmes dans le cadre de systèmes modélisés par des équations aux dérivées partielles.


The Jacques-Louis Lions Laboratory (LJLL, CNRS/UPMC/Université Paris Diderot/Inria)Nouvelle fenêtre