FUZZY SLIDING-MODE CONTROL OF FRACTIONAL-ORDER CHAOTIC SYSTEMS SUBJECT TO UNCERTAIN CONTROL COEFFICIENTS AND INPUT SATURATION

Abstract

In this paper, a novel fuzzy sliding-mode backstepping control approach is put forward to tackle the tracking control issue of fractional-order chaotic nonlinear systems subject to uncertain control coefficient and input saturation. First, a kind of sliding surface with nonlinear term of exponential monotonic attenuation is introduced to facilitate the fast error convergence and the chaos effect suppression. Subsequently, fuzzy logic systems and Nussbaum gains are synthesized to cope with the entire uncertainties including unknown control coefficients. Furthermore, dynamic surface technique is utilized to circumvent the occurrence of “complexity explosion” during the overall backstepping control procedure. By means of the proposed control scheme, system state is guaranteed to maintain close to the sliding surface without any reaching phrase, and whereafter the tracking error converges to a sufficiently small residual set containing the origin. Finally, the comparison between the proposed control scheme and an alternative existing chaos control approach is given through numerical simulation, which further confirms the validity of the obtained results and the superiority of the proposed strategy.