Recursive Identification of Takagi-Sugeno Models in the Presence of Piecewise Polynomial Disturbances

Abstract

The paper considers recursive identification of Takagi-Sugeno (TS) models. The TS models consist of finite collection of linear time invariant systems. It is supposed that real systems can be described with the Hammerstein model for which the reasonable approximation is TS model. The disturbance is piecewise polynomial. As identification algorithm the Kaczmarz algorithm is used. Special attention is paid for design of input signal for Hammerstein system and verification signal. Cluster analysis is based on Gustafson-Kessel algorithm. From this analysis it follows determination of membership functions. As a result, the recursive algorithm has structure similar to instrumental variable method. Simulations cover the practical behaviour of algorithm.