An Adaptive neuro-fuzzy backstepping sliding mode controller for finite time stabilization of fractional-order uncertain chaotic systems with time-varying delays

Abstract

In this paper, the design of a fractional-order hyperbolic adaptive neuro-fuzzy backstepping sliding mode controller (HANFBSMC) has been addressed for a class of fractional-order chaotic systems with time-varying delays in their states, control inputs, disturbances and uncertainties. In the proposed controller, adaptive rules are used both in a neuro-fuzzy estimator to estimate the unknown system dynamics, and in updating uncertainty bounds of system. The robust part of the proposed hybrid controller includes backstepping sliding mode controller, in which, the hyperbolic tangential fractional-order sliding surfaces are employed to prevent large tracking errors. Employing backstepping control strategy also extends the flexibility of controller to deal with higher order systems and under more extensive design issues. Adaptive rules based on Lyapunov stability analysis are also employed for tuning of relating robust control parameters according to the estimated upper bounds of the uncertainties. Analysis of stability of this controller has been performed via Lyapunov–Krasovskii theorem and Barbalat s lemma. Besides, finite time reaching to sliding surfaces has been proved. Finally, out performance of the proposed controller has been reflected via stabilization of a fractional-order hyper-chaotic system with time varying delays in its states as well as fractional-order Chen system with time delay in its inputs and states, where both systems experience unknown uncertainties and disturbances.