Two-mode Indirect Adaptive Control Approach for the Synchronization of Uncertain Chaotic Systems by the Use of a Hierarchical Interval Type-2 Fuzzy Neural Network

Two-mode adaptive controllers have two phases of operation: a learning phase and an operation phase. This paper presents a two-mode indirect adaptive control approach for the synchronization of chaotic systems, using a hierarchical interval type-2 fuzzy neural network (HT2FNN). Its contribution to the existing literature is the adaptation laws derived for the parameters of the membership functions, based on Lyapunov stability analysis. Since, in hierarchical case, each T2FNN has only two inputs, the computing of the derivatives is much simpler than the case in classical interval type-2 FNN. Moreover, a novel approach is presented for the compensation of the approximation error. The tuning of the parameters of the membership functions (MF) and the use of an interval type-2 FNN ensures that the estimation error is very small so that it can be negligible. Furthermore, the number of MF required is seen to be less than that needed with type-1 fuzzy sets. The simulation results confirm the efficacy of the proposed scheme in the synchronization of a uncertain nonidentical chaotic systems.