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.