Abstract:
This mini-lecture is composed of two parts. In the first part, I will introduce some basic ideas about this domain. The exact controllability of a linear system can be proved by observability inequalities and the duality between controllability and observability. Some beautiful methods, as Hilbert Uniqueness Method, Carleman estimates, and moment method, could lead to the observability inequality. However, there exists some “critical cases”: nonlinear controllable systems whose linearized systems are not controllable, which means the nonlinear terms lead to the controllability. In particular, we will see the controllability of the Euler equation by using the Return method. Then the lecture is followed by a research talk which is based on a recent joint work with Jean-Michel Coron: Small-time global stabilization of the viscous Burgers equation with three scalar controls.
Biography:
Shengquan Xiang is a Ph.D. student with ENS doctoral fellowship at Sorbonne Université, supervised by Professor Jean-Michel Coron. He works on the controllability and stabilization of fluids, more precisely, small-time stabilization of the systems which are smalltime null controllable. Prior to that, he was normalien at l'école normale supérieure de Paris and was undergraduate student at Peking University. During 2017 he visited ETH Zürich.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai