Adaptive Discrete-time Fuzzy Sliding Mode Control For a Class of Chaotic Systems

Abstract

In this paper, we propose an adaptive discrete-time fuzzy sliding mode control for a class of chaotic systems. For this aim, a discrete sliding mode controller and a fuzzy system are combined to achieve an adequate control. The Laypunov stability theorem is used to testify the asymptotic stability of the whole system and the consequence parameters of the adaptive fuzzy system are tuned on-line by adaptive laws. The simulation example of the 3D Henon chaotic model is giving to confirm the effectiveness and the robustness of the proposed method.

Stabilizing periodic orbits of Chua’s system using adaptive fuzzy sliding mode controller

“…Because the terms w F and w Fp are of the order of the minimum approximation error and from the Universal Approximation Theorem (Wang, 1994), Wang expected that w F and w Fp should be very small if not equal to 0 in the adaptive fuzzy system (Medhaffar et al , 2017). Therefore, the choice of the following adaptive law: yields to: …”

“…It is claimed that this union will lead to new control algorithms that exploit the advantages of both paradigms, providing a platform for the design of nonlinear systems with incorporation of human knowledge. In the past years, several research works using the concept of fuzzy logic and especially fuzzy approximators together with SMC have been developed for controlling chaos (Medhaffar et al , 2017; Alfi et al , 2018; Abadi and Balochian, 2017).…”