Controlling a Time-Varying Unified Chaotic System via Interval Type 2 Fuzzy Sliding-Mode Technique

In this paper, a decoupled interval type-2 fuzzy sliding-mode controller (IT2FSMC) is proposed for controlling a time-varying unified chaotic system. This technique, a fusion of the interval type-2 fuzzy logic control (IT2FLC) method and the sliding-mode control (SMC) method, inherits the benefits of both methods. In the sense of Lyapunov stability, the objective of the proposed controller is to assure the system approaching to the asymptotic stability of the closed-loop controlled system. The simulations include regulating the states of a time-varying unified chaotic system to the origin and tracking a predefined orbit extracted from the unforced Chen's chaotic system. The simulation results, from the viewpoint of the integral of the absolute error (IAE), the integral of time multiplied by the absolute error (ITAE), and the integral of square error (ISE), demonstrate that the IT2FSMC can achieve better control performance in comparison with that of the conventional fuzzy sliding-mode control (FSMC).

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