广义时变系统的最小二乘辨识方法

Least squares identification method of generalized time-varying systems

根据工程背景 ,提出了广义时变参数系统的概念。广义时变系统是指参数随系统可测扰动量变化的一类时变系统 ,即参数是系统可测扰动量函数的时变系统 ,提炼出这类时变系统的数学描述模型。根据最优化技术 ,导出了这类模型的两种辨识方法 ,即最小二乘型算法和随机梯度型算法 ,并应用鞅超收敛定理分析了算法的收敛性。分析表明 :由于该方法同时还利用了系统扰动量所含的信息 ,因而可以给出时变参数的一致估计。数字仿真验证了提出方法用于估计广义时变系统的参数是有效的。

Model was developed for identifying generalized time varying systems (TVS) which widely exist in industrial processes and whose parameters change with some measurable disturbances of the systems. Two identification algorithms (least squares type algorithm and stochastic gradient type algorithm) were derived for this class of TVS. Since these algorithms use additional information concerning the disturbances besides the input and output data, the convergence analysis using the Martingale hyperconvergence theorem indicates that the proposed algorithms can give consistent estimates of the time varying parameters.