Constructive algorithm determining knowledge base of NARX local model network

Abstract

The article presents new way of learning, determining suitable Takagi-Sugeno (TS) fuzzy-neural network structure for modeling nonlinear process. The whole structure consists of the NARX models (Nonlinear Auto-Regressive model with eXogenous input) set. Offered algorithm uses for learning in its action cluster method to determine initial divisions of the input space. Then, according to this algorithm the fuzzy-neural network, in which the rules of the knowledge base arise as a combination "peer-to-peer" adequate areas of input is being created. The consequents parameters are determined by means of a well-known Least Squares Method (LSM). Algorithm in the learning process sets an appropriate amount of membership functions, their distribution centers and width. In order to reduce the knowledge base the annihilation method was used like in [1], moreover the fusion operator was proposed. The structure formed in described way is characterized by reduced unnecessary membership functions, lack of nearly activated rules and structure optimized through dividing input space on the worst match areas. In addition, the article presents review of methods using for teaching the TS. Moreover advantages and disadvantages of these methods and main differences in contrast to the presented methods for learning networks were described.