两种新的有效的非线性系统最小二乘辨识算法

TWO NEW EFFECTIVE BIDIAGONALIZATION LEAST SQUARES ALGORITHMS FOR NONLINEAR SYSTEM IDENTIFICATION

提出了两种新的有效的最小二乘算法——改进的双对角化最小二乘算法ＭＢＬＳ－Ⅰ与ＭＢＬＳ－Ⅱ．在存在舍入误差的条件下，证明了算法的收敛性．该算法具有几乎不受舍人误差影响的优点，优于一般常用的最小二乘算法，包括数值性态极佳的ＳＶＤ算法．同时，基于该算法及ＳＶＤ算法，构造出了一种新的ＮＡＲＭＡＸ模型结构与参数辨识的一体化算法．仿真结果证明了此新算法的优越性．

Two new effective least squares algorithms——the modified bidiagonalization least squares algorithms(MBLS Ⅰ and MBLS Ⅱ) are proposed in this paper. Under the condition that round off errors exist, a convergence proof is given. They are superior to the common used least squares algorithms such as the SVD method for round off errors have little influence to their convergence. Furthermore, based on the two algorithms and the SVD method, a new integrated algorithm for the NARMAX model’s structure and parameters’ identification is also proposed here. The simulation results indicate their superiority.