Sliding Mode Algorithm for On-line Learning in Fuzzy Rule-based Neural Networks

A new, variable structure systems theory based, algorithm has been developed for on-line training of fuzzy-neural networks. Such computationally intelligent structures are widely used for modeling, identification and control of nonlinear dynamic systems. The algorithm is applicable to fuzzy rule-based neural nets of Takagi-Sugeno-Kang type with a scalar output. Its convergence is established and the conditions are given. Differently from other similar approaches which are limited to the adaptation of the parameters of the network defuzzification part only, the proposed algorithm tunes also the parameters of the implemented membership functions. The zero level set of the learning error variable is considered as a sliding surface in the space of network learning parameters. The effectiveness of the proposed algorithm is shown when applied to on-line learning of nonlinear functions approximation.