分布参数系统能控能观性问题的统一处理及应用

A unified treatment on controllability/observability problems for distributed parameter systems and applications

本文的主要目的是介绍一个统一的处理分布参数系统能控能观性问题的方法,并给出该方法在分布参数控制理论中的应用.为此,本文将从一类"类抛物"偏微分算子(即没有椭圆性条件)的带权恒等式出发,给出所有已知的关于抛物型方程、双曲型方程、Schr¨odinger方程和板方程的基于整体Carleman估计的能控能观性结果.同时,基于该带权的恒等式,本文还给出它在双曲型系统的稳定性问题和在拟线性复Ginzburg-Landau方程能控能观性等问题中的应用.

The purpose of this paper is to present a unifed treatment on controllability/observability problems for distributed parameter systems, and give its applications in distributed parameter control theory. For this purpose, from a basic weighted identity of ＂parabolic-like＂ partial diferential operator（i.e., without elliptic condition）, we will give all the known controllability/observability results for the parabolic, hyperbolic, Schr¨odinger and plate equations that are derived via Carleman estimate. Meanwhile, based on this weighted identity, we also give its applications in the stabilization of hyperbolic equations and the controllability/observability for the complex Ginzburg-Landau equations, etc.