I am currently in secondment at Inria Paris, as a researcher in the CAGE team. I work on control, stabilization and optimal control problems in infinite dimension (PDEs and evolution equation), with a particular focus on constrained control.
I have also dabbled in data-driven modelling and control, in particular methods involving the Koopman operator.
More recently, I have taken an interest in reachability analysis. I co-supervised the PhD thesis of Ivan Hasenohr with Camille Pouchol and Yannick Privat, during which we developed computer-assisted proofs of reachability and non-reachability.
PhD in applied mathematics
2016-10-01
2019-10-25
Laboratoire Jacques-Louis Lions
Master 2 in applied mathematics
2015-09-01
2016-07-31
Université Pierre et Marie Curie (now Sorbonne University)
Engineering degree
2012-09-01
2015-07-31
Ecole polytechnique
My research lies on the theoretical side of applied mathematics: I mainly work with abstract models to study their properties in terms of control theory. Are they controllable? Stabilizable? Why? What if we add constraints? What if we are looking for optimal controls?
My background makes me a thoroughly theoretical researcher, and I try to let that shape how I look at practical problems. Conversely, I try to let practical considerations shape my theoretical problem solving. In that spirit, I have been looking into constructive methods for some time now: in control theory, there are situations and methods that allow us to complement classical existence results with some information on the solutions. These can lead to strong characterisations and/or numerical approximations.
In stabilisation, my co-authors and I have contributed several key insights to expand the constructive method that is backstepping, to general control systems in infinite dimension. This method consists in solving an more complex problem than stabilisation, which requires more work but rewards us with more information on the feedback law, in the best cases an explicit expression.
In controllability and reachability analysis, our use of duality theory leads to constructive characterizations of admissible controls or certificates of non-reachability. This allows for their numerical approximation, and sometimes even their numerical certification in the case of non-reachability.
Farkas' lemma is an ubiquitous tool in optimisation, as it provides necessary and sufficient conditions to have $b \in A(P)$, where $P$ is a closed convex cone, $A$ is a …
In this article, we explore connections between two stabilization methods: Gramian stabilization and backstepping (and more generally F-equivalence). These methods are related to …
Analysing reachability associated to a control system is a subtle issue, especially for infinitedimensional dynamics, and when controls are subject to bounded constraints. We …
We consider the internal control of linear parabolic equations through on-off shape controls, with a prescribed maximal measure. We establish small-time approximate controllability …
