Abstract: This paper presents the new learning algorithm for adaptive functional networks loop structures which is designed based on the Banach contraction theorem.This algorithm through levels of thought divides the adaptive functional networks loop structures into multi-storey structure composed of the basic functional networks，then uses algebra algorithm to train all levels of the structure and gets all functional parameters，so as to achieve the overall study.Finally，the simulation results demonstrate that the structure presented has high precision and fast convergence speed.

摘要： 利用Banach压缩映射原理，结合层次系统的思想，提出一种自适应泛函网络循环结构和代数算法，该循环结构是由多层基本泛函网络构成，每层用代数算法训练结构的泛函参数，从而实现对整体网络结构的逼近学习。通过算例分析表明，该算法具有计算精度高、收敛速度快等特点。