衰减激励条件下递阶最小二乘辨识的均方收敛性  

Mean square convergence of hierarchical least square identification under the attenuating excitation

作　　者：丁锋[1] 丁韬[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：《控制与决策》2002年第1期6-10,共5页Control and Decision

基　　金：国家自然科学基金项目 (6 0 0 740 2 9);国家自然科学基金重点项目 (6 9934 0 10 )

摘　　要：为减少递推辨识的计算量 ,提出了递阶辨识原理 ,它是将系统分解为多个维数较小的虚拟子系统进行辨识 ,从而获得递阶最小二乘辨识方法。在衰减激励条件下 ,针对时不变系统研究了递阶最小二乘法的收敛性 ,得到了参数估计误差均方收敛于零时衰减指数应满足的条件。递阶最小二乘具有良好的性能 ,其计算量比递推最小二乘辨识要小得多 。In order to reduce the computational effort of existing identification algorithms, hierarchical identification principle is presented which is to decompose a system into some imaginary subsystems with smaller dimension and fewer variables. The parameters of each subsystem are estimated respectively, and hierarchical least squares (HLS) algorithm is obtained. For time invariant systems, the convergence of the HLS algorithm is studied under the attenuating excitation condition and the analysis shows that the parameter estimation error given by the HLS algorithm consistently converges to zero. The HLS algorithm has good properties and has less calculation than recursive least square identification and is easy to implement.

关 键 词：参数估计 递阶辨识 衰减激励 均方收敛性 系统辨识 最小二乘算法 

分 类 号：O231.3[理学—运筹学与控制论]