有限维线性系统参数辨识问题  

System Identification of Finite-dimensional Linear Systems

作　　者：孙楚仁[1] 

机构地区：[1]上海对外贸易学院国际经贸学院,上海201600

出　　处：《工程数学学报》2006年第6期989-1000,共12页Chinese Journal of Engineering Mathematics

基　　金：上海外贸学院2005年度<数学建模>课程项目(TSKC0504)

摘　　要：本文考虑一维输入输出有限维线性系统参数辨识问题。该问题源于电机系统的参数辨识。首先我们对简单参数形式的线性时不变动态系统,给出了一种精确辨识方法,并给出了这种辨识方法的误差界。这种方法能够保证辨识出的参数是最佳的；而且不用求解对应的非线性最小二乘问题,只需求一元多项式的根,从而大大减少计算量。接着我们考虑了复合参数形式的线性时变系统参数辨识问题,给出了一种近似辨识方法,并导出了该方法的误差界；该方法本质是通过求解非线性最小二乘问题来辨识参数。对于测量存在误差、误差服从区间分布的线性系统,我们给出了其等价的确定性问题,并给出了几个算例。计算结果表明,本文给出的参数辨识方法是有效的。This article discusses the system identification of finite-dimensional linear systems with one-dimensional input and output, which originates from parameter identification of electromotor systems. We first offer an accurate identification approach for linear time-invariance dynamic systems with simple form of parameters, and derive its error bound. This approach can guarantee that the identified parameters are optimal, by solving a one-dimensional polynomial equation instead of a nonlinear least square problem. We then consider system identification of linear time-varied systems with composed form of parameters, derive an approximate identification approach and derive its error bound, which identifies the parameters by solving a nonlinear least square problem. Finally, we derive the deterministic equivalent problems for linear systems with measure errors distributed in known intervals. The given numerical examples show that proposed methods are effective.

关 键 词：连续线性系统 参数辨识 最小二乘问题 不确定性 

分 类 号：TP271.61[自动化与计算机技术—检测技术与自动化装置]