基于随机分布理论的递推子空间辨识

Recursive subspace identification based on random distribution theory

在实际生产过程中,采用传统子空间辨识法建立的离线模型并不能有效准确地跟踪系统的动态变化;奇异值分解等线性代数工具虽然增加算法的数值鲁棒性,但也相应增加了子空间辨识的在线递推困难.为解决上述问题,本文针对连续时间系统提出基于随机分布理论的递推子空间辨识方法.首先,通过随机分布理论构建系统的连续随机分布函数,并利用微分计算获得系统等价的输入输出矩阵方程.然后,采用将输入输出数据矩阵“R”规模固定的方法,达到数据压缩的目的.最后,通过最小二乘法和残差分析法递推更新模型的系统矩阵和噪声强度直至达到辨识要求.仿真结果验证了所提方法的有效性和精确性.

In the practical process,the offline model estimated by the traditional subspace identification method cannot track the dynamic of the systems effectively.Although the numerical robustness of the algorithm is improved by the singular value decomposition,it also increases the difficulty of online recursion in subspace identification process.In order to solve the problems above,this paper presents a recursive subspace identification method for continuous-time stochastic systems via random distribution theory.Firstly,the continuous random distribution function is deduced by random distribution theory and the input-output matrix equation of the systems is obtained by the differential calculation.Secondly,we reduce the computational burden and storage cost by keeping the size of input and output data to be constant.Finally,the system matrices and noise intensity are updated recursively by the least square method and residual analysis.Simulation results show the efficiency and accuracy of the proposed method.