基于辅助输出的线性系统状态和未知输入同时估计方法

在未知输入观测器匹配条件不满足的情况下, 针对一类线性时不变系统, 研究了同时估计系统 状态和未知输入的问题. 首先, 基于可测输出对未知输入的相关度的概念, 给出了辅助输出 的构造方法, 使得匹配条件得以满足. 为了处理辅助输出中的未知信息, 提出了一种高增益 观测器设计方法, 它不仅能估计辅助输出, 而且还能估计辅助输出的导数. 然后, 基于辅助 输出的估计值, 提出了一种降维观测器设计方法, 可以在不受未知输入影响的情况下估计系统 的状态; 接下来, 基于状态和辅助输出及其导数的估计值, 给出了未知输入估计. 最后, 对一个五 阶系统进行了数字仿真, 仿真结果表明所提出的方法是有效的.

Simultaneous Estimation of States and Unknown Inputs for Linear Systems Based on Auxiliary Outputs

This paper considers the problem of simultaneously estimating the states and unknown inputs for linear systems when the so-called observer matching condition is not satisfied. Based on the relative degree of the output with respect to the unknown input, a kind of auxiliary output vector which may satisfy the observer matching condition is constructed. To deal with the unknown information contained in the auxiliary output vector, a kind of high-gain observer is developed. The high-gain observer is able to estimate the auxiliary output vector and its derivative. Then, we construct a reduced-order observer which can track the system's states based on the estimation of auxiliary output vector. Moreover, through employing the estimation of auxiliary output vector's derivative, unknown inputs can be estimated. The simulation results of a real model show that the proposed method is effective.