In the 1990s, I applied my expertise in automation to various industrial problems and focused my research on robust control. The aim was to take into account the knowledge of a priori uncertainties on the models during the synthesis of correctors in order to guarantee “minimum performances”. The underlying tools were H_∞ control, convex optimisation, and from the mid-1990s, linear matrix equations (LMI). As an extension of these topics, I have been interested in stability analysis in the presence of uncertainties and in characterising worst-case performance also in the presence of model uncertainties with μ-analysis. I then contributed to create an algebraic approach to the standard formulation of μ-analysis, which allowed to systematise its application to dynamical systems described by complex differential equations.
In the early 2000s, μ-analysis was reaching an advanced level of maturity worldwide. I was pursuing my research on the applications of optimisation in control. I initiated a research that generalized the principle of μ-analysis estimations by upper and lower bounds. The aim was to use jointly convex and non-smooth optimisation on the same problem previously given. The combined results of two bounds allow to quantify the approximation gap, consequence of the reformulation of the problem in convex form. When the gap is zero, this makes it possible to validate a result with respect to an initial specification (generically non-convex).
After joining the Directorate of Studies full time in 2004, I could not keep my research activities. I was successively in charge of the 1st year schooling (2004-2008) and recruitment of the engineering school, then deputy director of studies (2009-2011). Afterwards, I returned to the former structure of the laboratory as head of the Electronic Signals and Systems Department (2009-2015). I was part of a task force for the “CentraleSupélec engineering curriculum project” for the CentraleSupélec management (2015-2017), in parallel I returned to the head of the studies department (deputy director 2016-2020) to accompany the end of the former curricula and help the institution set up its new curriculum. During all these periods, I have managed to maintain a teaching activity in optimisation and applied mathematics without interruption until today.
I have returned to the laboratory at the end of 2020. I am resuming activities in the area of the application of optimisation to modelling and control theory. I am currently working on the generation of intelligent trajectories for vehicle control in a mixed environment (in the presence of both intelligent and human-controlled vehicles).