RECENT PROGRESS ON CONTROLLABILITY/OBSERVABILITY FOR SYSTEMS GOVERNED BY PARTIAL DIFFERENTIAL EQUATI

• 作 者: Hongheng LI Qi L(U) Xu ZHANG
• 机 构: School of Mathematics, Sichuan University, Chengdu 610064, China.;Key Laboratory of Systems and Cont
• 出 处: 系统科学与复杂性学报（英文版）
• 发表日期: 2010年3期
• 关键词: Controllability hyperbolic equations observability parabolic equations

The main purpose of this paper is to overview some recent methods and results on controllability/observability problems for systems goved by partial differential equations. First, the authors review the theory for linear partial differential equations, including the iteration method for the null controllability of the time-invariant heat equation and the Rellich-type multiplier method for the exact controllability of the time-invariant wave equation, and especially a unified controllability/observability theory for parabolic and hyperbolic equations based on a global Carleman estimate. Then, the authors present sharp global controllability results for both semi-linear parabolic and hyperbolic equations, based on linearization approach, sharp observability estimates for the corresponding linearized systems and the fixed point argument. Finally, the authors survey the local null controllability result for a class of quasilinear parabolic equations based on the global Carleman estimate, and the local exact controllability result for general hyperbolic equations based on a new unbounded perturbation technique.