一维云模型系统的逼近性研究

On Approximation of One-dimension Cloud Model Systems

针对云模型的基本原理,提出了一类云模型系统的设计方法,并利用Stone-Weierstrass定理对在3σ正态分布随机数条件下的云模型系统任意逼近紧集上的任意连续实函数进行了证明,是对云模型应用于逼近任意连续非线性函数理论的创新,也是今后云模型系统用于系统辨识和控制的理论依据.

A new design method for a class of the cloud model systems is put forward based on the theory of cloud model.Any continuous real function from any approximating compact set under 3-sigma random normal distribution is proved for the cloud model system by using the Stone-Weierstrass theorem.This cloud model system enriches the theory of approximating any continuous non-linear function.The innovative method provides a theoretic basis for the future application in system identification and control.