多变量系统状态空间模型的递阶辨识

Hierarchical Identification of State Space Models for Multivariable Systems

研究多变量系统状态空间模型的递阶辨识问题,推广了作者提出的标量系统状态和参数联合辨识算法.当状态可量测时,利用最小二乘原理直接辨识状态空间模型的参数矩阵;当状态不可测时,利用递阶辨识原理提出了状态空间模型递阶辨识方法,使用系统输入输出数据来估计系统的未知状态和参数.状态空间模型递阶辨识方法分为两步:首先假设系统状态是已知的(即参数估计算法中的未知系统状态用其估计代替),基于状态估计和系统输入输出数据递归计算系统参数估计;然后基于系统输入输出数据和获得的参数估计,递归计算系统的状态估计.

The combined state and parameter identification algorithm for scalar systems is extended and the hierarchical identification of state space models for mutivariable systems is studied. For systems whose states are measurable, the parameter matrices of state space models are directly identified using the least squares principle. For systems whose states are unmeasurable, according to the hierarchical identification principle, a hierarchical statespace model identification method is presented to estimate unknown parameters and states based on input-output data. The hierarchical state space model identification is divided into two steps： the system states are assumed to be known （that is, unknown states in parameter estimation algorithm are replaced with their estimates）, the parameter estimates are recursively computed based on the state estimates and input-output data; and then the state estimates are recursively computed based on the input-output data and parameter estimates.