基于正交函数逼近变换的分布参数系统可控性与可观性

On the Approximate Controllability and Observability for Distributed Parameter Systems

基于偏微分方程谱分解原理，采用正交函数逼近技术，给出了分布参数系统逼近可控性、可观性的定义，并研究线性分布参数系统逼近可控性与可观性的判定方法。还研究了两种典型分布参数系统在不同形式控制与观测情况下的逼近可控性与可观性判据。

It is especially important for analysis and design of distributed parameter systems (DPS) to study their controllability and observability but is also very difficult because of the distribution characteristics of DPS.In this paper,based on the spectrum de composition principle,the concepts of approximate controllability and observability of DPS have been proposed and their criteria for linear DPS have also been studied by using orthogonal function approximate technique.For two typical cases the approximate controllability and observability criteria of the systems have been given,in which the actuators and the sensors are placed in different positions.The proposed method is simple,and easy for application to analysis and synthesis of DPS.