系统辨识(8):耦合辨识概念与方法

耦合辨识是系统辨识的一个重要分支,是新近发展和提炼形成的一种辨识概念,主要用于研究结构复杂的参数耦合线性和非线性多变量系统的辨识问题.辅助模型辨识思想、多新息辨识理论、递阶辨识原理、耦合辨识概念是本文作者提出的一些新的辨识研究思路、理念和方法,分别能够用于研究存在未知过程变量的不可测系统的辨识,能够提高辨识方法的收敛速度和参数估计精度,能够解决结构复杂、大规模多变量系统及参数耦合多变量系统的辨识问题、减小辨识算法的计算量.首先介绍多变量系统耦合辨识概念,在此基础上讨论多变量系统的几种(全)耦合最小二乘辨识方法、(全)耦合随机梯度辨识方法、部分耦合随机梯度辨识方法、部分耦合最小二乘辨识方法等,最后说明耦合辨识方法可推广用于有色噪声干扰多变量系统的辨识,并列出了一些多变量系统模型结构,阐述了耦合辨识概念可以结合辅助模型辨识思想、多新息辨识理论、递阶辨识原理、迭代搜索原理(梯度迭代、最小二乘迭代、牛顿迭代)等来研究线性或非线性多变量系统的辨识问题.

System identification.Part H:Coupled identification concept and methods

Coupled identification is an important branch of system identification and is a new identification concept which is used mainly to study identification problems of linear and nonlinear multivariable systems with complex structures and parameter coupling.The auxiliary model identification idea,the multi-innovation identification theory,the hierarchical identification principle,and the coupled identification concept are new identification research ideas,concepts and methods and can be used to study identification problems of systems with unknown process variables,to improve the convergence rates and accuracies of identification methods,to solve identification problems of large-scale multivariable systems with complex structures and of multivariable systems with parameter coupling,reducing the computational load of the identification algorithms.This paper introduces the coupled identification concept of multivariable systems,discusses the(full) coupled least squares identification methods,the(full) coupled stochastic gradient identification methods,the partially coupled stochastic gradient identification methods,the partially coupled least squares identification methods etc for multivariable systems.Finally,we show that the coupled identification methods can be applied to multivariable systems with colored noises,list some model structures of some multivariable systems,and indicate that the coupled identification concept can combine the auxiliary model identification idea,the multi-innovation identification theory,the hierarchical identification principle,the iterative search principle(the gradient iteration,the least squares iteration,the Newton iteration) to study identification problems of linear and nonlinear multivariable systems with colored noises.