传递函数阵递阶随机梯度辨识方法的收敛性分析(英文)  

Convergence of Hierarchical Stochastic Gradient Identification for Transfer Function Matrix Model

作　　者：丁锋[1] 杨家本[1] 徐用懋[1] 

机构地区：[1]清华大学自动化系,北京100084

出　　处：《控制理论与应用》2001年第6期949-953,共5页Control Theory & Applications

基　　金：supportedbytheNationalNaturalScienceFoundationofChina (NSFC) (60 0 740 2 96993 40 10 ) ,andtheFoundationofInformationCollege TsinghuaUniversity ,andCIMSProjectforFujianPetrochemicalCorporationLtd .

摘　　要：阐述了递阶辨识原理 ,提出了传递函数阵模型参数的递阶随机梯度 (HSG)辨识方法 .在递阶辨识中 ,系统参数被分解为参数向量和参数矩阵 .前者是由系统的特征多项式的系数构成的 ,后者是由传递函数矩阵分子多项式的系数构成的 .借助于鞅超收敛定理的收敛性分析表明 ,HSG算法的参数估计误差一致有界 ;当持续激励条件成立时 ,参数估计误差一致收敛于零 .The hierarchical identification principle is stated, and the hierarchical stochastic gradient (HSG) algorithm for the transfer function matrix (TFM) model for multivariable systems is presented. In the hierarchical identification, the system parameters are divided into the parameter vector, which includes the coefficients of the characteristic polynomial of the system, and the parameter matrix, which includes the coefficients of the numerators of the TFM polynomials, respectively. The convergence analysis, using martingale hyperconvergence theorem, shows that the parameter estimation error (PEE) given by the HSG algorithm is consistently bounded, and that PEE consistently converges to zero under the persistent excitation condition. Hierarchical identification has a small amount of calculation and is easy to be realized.

关 键 词：辨识 递阶辨识 多变量系统 参数估计 收敛性 传递函数 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]