Sliding Mode Control Approach for Online Learning as Applied to Type-2 Fuzzy Neural Networks and Its Experimental Evaluation

Abstract

Type-2 fuzzy logic systems (FLSs) are proposed in the literature as an alternative to type-1 FLSs because of their ability to more effectively model uncertainties that may exist in the rule base. However, the parameters of the system still need to be optimized. For this purpose, the use of a sliding mode control theory-based learning algorithm is proposed in this paper. In the approach, instead of trying to minimize an error function, the parameters of the network are tuned by the proposed algorithm in such a way that the learning error is enforced to satisfy a stable equation. The update rules to achieve this are derived, and the convergence of the parameters is proved by Lyapunov stability method. The performance of the proposed algorithm is tested by simulations on a Duffing oscillator and also by real-time experiments on a laboratory servo system. The results indicate that the given type-2 fuzzy neural network with the proposed learning algorithm can handle the uncertainties in a better way as compared to its type-1 counterpart. Moreover, it is computationally easier to implement in real-time systems.