My PhD research are of two kind. First I want to deeply understand nonlinear dynamical control systems. Using the language of differential geometry my purpose is to classified quadratic nonlinear control systems. During his PhD Witold Respondek classified non linear dynamical system that are equivalent (up to a state diffeomorphism or up to feedback action) to a controllable linear system. We want to extand this results and found conditions for a system to be equivalent to a system with a prodcut of control.
On the other hand, I want to propose an improved version of the continuation method, developped first by Yacine Chitour. This method was developped to compute optimal control. However the method assume that we can avoid the singular set of the system. This is a practical strong assumptions. With Emmanuel Trélat we propose a modified algorithm giving an approximation of the optimal control but dealing with the singular set of the system.
I am really interested in game theory, I myself enjoy playing online chess on Lichess. I’m always up for a game, so if you see me online, drop a challenge! In my free time, I am developping a chess engine iathena mixing alpha-beta search and Monte-Carlo search. Feel free to challenge iathena on Lichess! If you want to get involved in this journey, check the documentation.
Always great games on Lichess TV: