Sliding mode online learning algorithm for type-2 fuzzy CMAC networks

Cerebellar model articulation controller (CMAC) networks have been widely applied to problems involving modeling and control of complex dynamical systems because of their computational simplicity, fast learning and good generalization capability. The integration of fuzzy logic systems and CMAC networks into fuzzy CMAC structures can help to improve their function approximation accuracy in terms of the CMAC weighting coefficients. Type-2 fuzzy logic systems are an area of growing interest over the last years. The ability to model uncertainties and to perform under noisy conditions in a better way than type-1 fuzzy systems increases their applicability. A new stable incremental learning algorithm for interval type-2 fuzzy CMAC (T2FCMAC) networks is proposed in this paper. The algorithm is based on the variable structure systems theory principles. It can tune online the parameters of the membership functions and the weights in the fourth and fifth layer of the T2FCMAC network. Simulation results from the identification of two nonlinear systems demonstrate the better performance of the T2FCMAC structure with the newly proposed algorithm in comparison to the on-line learning type-1 and type-2 Takagi-Sugeno-Kang (TSK) fuzzy neural networks.