中科院数学与系统科学研究院
数学研究所
调和分析及其应用中心
学术报告会
报告人： Dr. Xiang Shengquan(École Normale Supérieure, France)
题目1：Controllability and Stabilization of KdV: power series expansion method
时间：2016年8月3日（星期三）下午3:00-5:00
题目2：Coron's Return Method
时间：2016年8月5日（星期五）下午3:00-5:00
地点：晨兴410室
摘要1：
We will see that sometimes the controllability of linearized control systems and fixed-point methods could imply the controllability of nonlinear control systems (KdV in noncritical cases, hyperbolique system and Schrödinger equations). But when the linearized control system becomes uncontrollable, e.g. KdV equation in critical cases, the power series expansion method introduced by Jean-Michel Coron will gives controllability of nonlinear control system though its linearized system is not controllable. If control problem is an open problem, then stabilization problem should be a closed problem. It is in general more difficult than control problem, so far few advance has been made. I will directly talk about infinite case, KdV, for which I will explain backstepping method and P.S.E method.
摘要2：
Again, we are interested in the systems whose linearized form is not controllable. Coron's return method turns out to be the most useful method for such systems, it has been used for numerous cases: Euler equation, Navier-Stokes equation, Saint-Venant equation and so on. After that, if time allows, I would like to show you several new trends in control theory: Control of the Grushin equation; Stochastique control.
附件：