基于信息压缩矩阵特征值映射的时变系统UD分解辨识算法

UD Decomposition Algorithm for Time-Varying System Identification Based on Information Matrix Eigenvalue Mapping

在系统辨识领域遗忘因子UD分解算法(一种通过对系统数据矩阵进行UD分解的在线辨识算法)具有对时变系统阶次和参数同步估计的优异性能,但传统的遗忘策略不能从根本上解决信息压缩矩阵数据过饱和问题,为了拓展现有UD分解算法在时变系统的适用范围,同时针对数据空间分布不均匀性,提出一种基于信息压缩矩阵特征值映射的UD分解辨识算法.从理论上分析辨识算法跟踪能力与参数估计矩阵有界性的对应关系,从而构造出一种基于信息压缩矩阵特征值映射的有界函数,特征值映射函数能够根据系统数据传递过程中信息量的大小动态调整遗忘因子,解决了参数辨识过程中数据过饱和及数据分布不均匀问题.仿真结果表明,相比于常规时变遗忘因子策略,带有特征值映射的UD分解算法能够更加准确跟踪系统参数的变化,且能够保证系统不是2N阶持续激励信号的情况下,也能对时变系统参数进行跟踪.

In the field of system identification,the forgetting factor UD decomposition algorithm(an identification algorithm based on system data matrix UD decomposition)has excellent ability of order and parameter estimation for time-varying system.The traditional forgetting strategy cannot fundamentally solve the super-saturation problem of information compression matrix data,in order to expand the usage of existing UD decomposition algorithm,and to solve the non-uniformity distribution of system data,a UD decomposition identification algorithm based on information compression matrix eigenvalue was proposed.The correspondence between the tracking ability of the identification algorithm and the boundedness of the parameter estimation matrix was analyzed theoretically,thus a mapping bounded function of eigenvalue based on information compression matrix was constructed which could dynamically adjust the forgetting factor according to the amount of information during the system data transferring process,which could solve the problem of data super-saturation and the uneven distribution of system data.The simulation results show that compared with the traditional time-varying forgetting factor,the UD decomposition algorithm with eigenvalue mapping could track the changes of system parameters more accurately,and be able to ensure the tracking ability for time-varying system with a non 2N-order continuous excitation input signal.