From phenomena of synchronization to exact synchronization and approximate synchronization for hyperbolic systems  

作　　者：LI TaTsien 

机构地区：[1]School of Mathematical Sciences, Fudan University [2]Shanghai Key Laboratory for Contemporary Applied Mathematic and Nonlinear Mathematical Modeling and Methods Laboratory, Fudan University

出　　处：《Science China Mathematics》2016年第1期1-18,共18页中国科学：数学（英文版）

基　　金：supported by National Basic Research Program of China(Grant No.2013CB834100);National Natural Science Foundation of China(Grant No.111211101)

摘　　要：In this survey paper, the synchronization will be initially studied for infinite dimensional dynamical systems of partial differential equations instead of finite dimensional systems of ordinary differential equations,and will be connected with the control theory via boundary controls in a finite time interval. More precisely,various kinds of exact boundary synchronization and approximate boundary synchronization will be introduced and realized by means of fewer boundary controls for a coupled system of wave equations with Dirichlet boundary controls. Moreover, as necessary conditions for various kinds of approximate boundary synchronization, criteria of Kalman's type are obtained. Finally, some prospects will be given.In this survey paper, the synchronization will be initially studied for infinite dimensional dynamical systems of partial differential equations instead of finite dimensional systems of ordinary differential equations, and will be connected with the control theory via boundary controls in a finite time interval. More precisely, various kinds of exact boundary synchronization and approximate boundary synchronization will be introduced and realized by means of fewer boundary controls for a coupled system of wave equations with Dirichlet boundary controls. Moreover, as necessary conditions for various kinds of approximate boundary synchronization, criteria of Kalman＇s type are obtained. Finally, some prospects will be given.

关 键 词：SYNCHRONIZATION exact boundary synchronization approximate boundary synchronization cou- pled system of wave equations Dirichlet boundary controls 

分 类 号：O175.2[理学—数学]