RETRACTED: Adaptive fuzzy backstepping control of fractional-order chaotic systems with input saturation

An adaptive fuzzy backstepping control method is proposed for uncertain fractional-order chaotic systems subject to system constraints, including unknown external disturbance and input saturation in this article. The system constraints are resolved by modeling the saturation limiter as portions of unknown functions and a backstepping recursive algorithm is proposed. In each step, the system unknown nonlinearity is approximated by a fuzzy logic system, and fuzzy parameters are updated by the corresponding fractional-order adaptation laws online. In the end, an adaptive fuzzy controller that assures the convergence of tracking error is designed. Formal proof and two simulations are applied for confirming the effectiveness of the designed controller.