利用点测量的分布参数系统状态重构

分布参数系统的状态在空间上连续分布，但因传感器个数有限，难以获取其全部状态. 对此，该文针对抛物线型分布参数系统，根据有限个传感器点的测量信息，提出一种重构系统全部状态的方法并证明其可行性. 仿真结果表明，该方法在已知系统模型但未知初始状态的情况下可取得很好的状态重构效果，而且与分布参数状态观测器相比，只需要离散的传感器信息就能获得对系统初期状态的更好重构.

Reconstruction of System State with Distributed Parameters Using Measurements from Finite Points

The state space of distributed parameter system (DPS) is infinite dimensional and cannot be measured directly by a finite number of sensors. To solve this problem, we propose a state reconstruction method using a finite number of point measurements. Feasibility of the method is shown theoretically. Numerical simulation indicates that it can achieve good state reconstruction. In contrast to distributed parameter observers,the proposed method only requires measurements taken at discrete time, and it can give better reconstruction of system’s early states.