基于Laguerre滤波器的核范数子空间辨识

Nuclear norm subspace identification based on Laguerre filters

连续时间随机系统是指各个变量是时间的连续函数并且状态和输出向量受到噪声干扰的动态系统.由于生物学、经济学以及物理学等领域都存在连续随机的现象,连续时间随机系统的辨识受到了各领域专家学者的广泛关注.本文针对连续时间随机系统提出一种基于Laguerre滤波器的核范数子空间辨识方法.首先,采用Laguerre滤波器获得系统的输入输出矩阵方程.然后,通过核范数最小化方法代替主奇异值的截断获得低秩矩阵逼近,并利用交替方向乘子法求解此优化问题.最后,采用最小二乘法和残差分析法分别得到模型的系统矩阵和噪声强度.仿真结果验证了所提方法的有效性、精确性及比较优势.

Continuous-time stochastic systems are dynamic systems in which each variable is a continuous function of time and the state and output vectors are disturbed by noise.Due to the existent phenomenon of continuous stochastic in biology,economics and physics,the identification of continuous-time stochastic systems has attracted much attention by experts and scholars in various fields.This paper presents a nuclear norm subspace identification method for continuoustime stochastic systems via Laguerre filters.Firstly,the input-output matrix equation of the systems is deduced by a bank of Laguerre filters.Then,nuclear norm minimization is adopted,instead of the truncation of dominant singular values,to obtain low-rank matrix approximations.Secondly,the optimization problem is solved by the alternating direction method of multipliers.Finally,the system matrices and noise intensity are obtained by the least square method and residual analysis respectively.Simulation results show the efficiency,accuracy and comparative advantage of the proposed method.