Intuitionistic Fuzzy Sliding Controller for Uncertain Hyperchaotic Synchronization

Abstract

In this study, the design of an intuitionistic fuzzy controller for synchronization of two non-identical hyperchaotic systems is proposed. Since hyperchaotic systems has high sensitivity to the initial condition, disturbance and parameter variability. Synchronization of hyperchaotic systems is used to test the controller performance. On the other hand, using of fuzzy logic-based controller has an increasing tendency. As known, fuzzy logic control (FLC), only membership functions are used to obtain a realistic model of the systems. But the intuitionistic fuzzy logic control (IFLC) allows us to obtain a more realistic model than FLC because it also takes into account the degree of non-membership and the degree of uncertainty beside of degree of membership to model examined system. Fuzzy logic-based controllers are hybridized with robust control methods such as sliding mode controller to improve the performance of controller. To take advantages of SMC with fuzzy logic-based IFLC, the IFSMC controller obtained by hybridizing these two methods was designed for hyperchaotic systems. To demonstrate the performance of IFSMC, the results obtained from the synchronization of hyperchaotic systems with FSMC (fuzzy sliding mode controller) and IFSMC were compared. The stability of IFSMC is proved by Lyapunov stability condition. The numerical results and analysis show the efficiency of the IFSMC with regards to synchronization control of uncertain chaotic systems having challenging external disturbances in terms of robustness, minimum tracking error.