A general methodology for online TS fuzzy modeling by the extended Kalman filter

•We present an online fuzzy modeling methodology based on the extended Kalman filter.•This methodology can work with noise, is very efficient and completely general.•The model can be obtained in a recursive way only based on input–output data.•There are no restrictions in the type of membership functions used.•Membership functions can even be mixed in the antecedents of the rules.

This paper presents an online TS fuzzy modeling general methodology based on the extended Kalman filter. The model can be obtained in a recursive way only based on input–output data. The methodology can work online with the system, properly in the presence of noise, is very efficient computationally and completely general. It is general in the sense theorically there are no restrictions neither in the number of inputs nor outputs, neither in the type nor distribution of membership functions used (which can even be mixed in the antecedents of the rules). Some examples and comparisons with other online fuzzy identification models from signals are provided to illustrate the skill of the online identification of the proposed methodology.