Stabilization of type-2 fuzzy Takagi-Sugeno-Kang identifier using Lyapunov functions

Differing from previous studies, where sliding mode control theory-based rules are proposed for only the consequent part of the network, the developed algorithm in this paper applies fully sliding mode parameter update rules for both the premise and consequent parts of the interval type-2 fuzzy neural networks. The stability of the proposed learning algorithm has been proved by using an appropriate Lyapunov function. Then, the performance of the proposed learning algorithm is tested on the identification of wing flutter data set available online as a benchmark system and the prediction of Mackey-Glass chaotic system. The simulation results indicate that the proposed algorithm is significantly faster than the gradient-based methods as well as providing a slightly better identification performance. The reason for the fast convergence is that the proposed parameter update rules do not have any matrix manipulations which makes them simple to be implemented in real-time systems. In addition, the responsible parameter for sharing the contributions of the lower and upper parts of the type-2 fuzzy membership functions is also tuned. Another prominent feature of the proposed learning algorithm is to have a closed form which makes it easier to implement than the other existing learning methods, e.g. gradient-based methods.