An IV-QR algorithm for neuro-fuzzy multivariable on-line identification

In this paper an algorithm for neuro-fuzzy identification of multivariable discrete-time nonlinear dynamical systems is proposed based on a decomposed form as a set of coupled multiple input and single output (MISO) Takagi-Sugeno (TS) neuro-fuzzy networks. An on-line scheme is formulated for modeling a nonlinear autoregressive with exogenous input (NARX) neuro-fuzzy structure from samples of a multivariable nonlinear dynamical system in a noisy environment. This approach essentially simplify the original multivariable nonlinear plant to a nonlinear combination of multiple linear MISO subsystems. An adaptive weighted instrumental variable (WIV) algorithm by QR factorization based on the numerically robust orthogonal Householder transformation is developed to modify the consequent parameters of the Takagi-Sugeno multivariable neuro-fuzzy network.