Variable Learning Rate Adaptive Sliding Mode Training Of Type-2 Fuzzy Neural Networks

This paper proposes a novel training method for the parameters of a type-2 fuzzy neural network (T2FNN) using sliding mode control theory with an adaptive learning rate. The implemented control structure consists of a conventional (PD) controller in parallel with a T2FNN. The former is responsible to guarantee global asymptotic stability in compact space and to form a sliding behavior. The output of the conventional controller is used to update the parameters of the T2FNN. The use of sliding mode based training method with adaptive learning rate makes it possible to discard the dependency of the design of the controller to priori knowledge about upper bounds of the states of the system and their derivatives. An appropriate Lyapunov function is proposed to analyze the stability of the adaptation law of the parameters of T2FNN and the adaptive learning rate. Sufficient conditions to guarantee the boundedness of the parameters and the achievement of sliding behavior are derived. Using a two-link rigid robot manipulator as a benchmark, it is shown that the proposed structure improves the performance of the conventional PD controller and guides the states of the system towards sliding manifold. In addition, it is shown that T2FNN outperforms its type-1 counterpart which benefits from the same adaptation laws specially in the presence of high levels of noise.