基于UD矩阵分解的模糊建模算法及收敛性分析

Fuzzy modeling algorithm via UD matrix decomposition and convergence analysis

实际系统中通过采样得到的数据的噪声、干扰和变量之间耦合等不确定因素,使得描述系统的模糊关系矩阵列间可能存在严重的相关性.为了解决输入空间重构的模糊建模问题,提出利用目标函数确定非线性系统的结构和参数,实现对模糊模型结构简化,删除冗余规则.结构确定过程中采用了UD矩阵分解方法,大大降低了计算量.最后,证明了算法的收敛性,仿真结果表明了方法的有效性.

Due to some uncertainty factors,including noises,interferences and the coupling among variables,the similar linear correlation among columns may exist in fuzzy relation matrix. To reconstruct the input space of the fuzzy model,the algorithm based on the objective function is proposed to confirm the structure and parameters of fuzzy model for nonlinear systems. It makes simplify the structure of model and delete those redundant rules. The UD matrix decomposition is used to greatly reduce the computation cost in the fuzzy modeling. The convergence proof of the presented algorithm is shown. The simulation results demonstrate the effectiveness of the proposed method.