Stable indirect adaptive interval type-2 fuzzy sliding-based control and synchronization of two different chaotic systems

Abstract

An indirect approach to adaptive interval type-2 fuzzy sliding mode control is proposed for the stable synchronization of two different chaotic nonlinear systems with different initial conditions under the presence of uncertainties involving process noises and external disturbances. The indirect model-based approach to adaptation is promoted here as a more suitable strategy for the fast changes that occurs in chaotic systems. In other words, the usual direct adaptive strategies may be too slow to respond to the inherently fast changing dynamics of chaotic systems. Using Lyapunov analysis, the sliding mode approach illustrates the asymptotic convergence of synchronization error to zero as well as good robustness against external disturbances. The interval type-2 structure aims to remedy the undesirable chattering phenomenon that is common in most conventional sliding mode control applications. It also provides a more effective equivalent model in the indirect approach, which leads to improved handling of the chaotic variations and uncertainties. Two numerical pairs of chaotic systems, i.e. the Lorenz and Chen’s systems and the Rössler system and modified Chua’s circuit are considered. In particular, in comparison with its type-1 fuzzy counterpart, the control effort is reduced by an average of 26.25% and 17.4% for the synchronization of the two corresponding systems, respectively. Furthermore, the integral of squared error is also improved by an average of 27.2% and 25.33%. This is while convergence time is reduced to less than 0.5s and 1.5s.