一类广义模糊控制系统及其特征

A SORT OF EXTENSIVE FUZZY CONTRLER AND PROPROTIES

在具有再生核的希尔伯特空间中(简记为r.k.h,以下同),以一组修正化的再生核作为输入空间的隶属函数,建立了一种广义的模糊控制系统,在一定条件下,该系统事实上包含着是r.k.h中函数的最佳插值逼近,就对未知控制曲线的逼近而言,典型的模糊控制器不可能比这种广义的模糊控制系统做得更好,广义的模糊系统具有以下优点:对样本的学习一次完成,克服了一般模糊控制器学习时所面临的解一个非线性最优化问题的困难;能估计出对待逼近实际控制函数误差的一个确定的上界;从Kosko B所揭示的模糊逼近本质特征,即确定性的角度来看它也是最优的。

In Hibert space with reproducing kernel (r.k.h), we set up a special fuzzy controller with the modified membership function in input space, which is the best approximation operator in the r.k.h. The research shows that the classical controller isn't better than this controller. The new controller has following advantages, it can perform learning once to the sample data and keep over the difficulty that a usual fuzzy controller must come from, and can estimate a super bound. In the nature of fuzzy approximation presented by Kosko B, i.e., the certainly, the new fuzzy system in this paper is also optimal.