Adaptive neuro-fuzzy backstepping dynamic surface control for uncertain fractional-order nonlinear systems

Abstract In this paper, a fractional-order backstepping dynamic surface control (DSC) method is developed to cope with the stabilization problem for fractional-order nonlinear systems with uncertainties and external disturbances. In each step, a neuro-fuzzy network system is employed to approximate the unknown nonlinear function existing in fractional-order subsystem. Furthermore, a modified fractional-order filter is designed to avoid the problem of explosion of complexity caused by the recursive procedure. Then based on the fractional-order Lyapunov stability theory, the corresponding adaptive backstepping DSC controller is proposed to guarantee the stability of the fractional-order closed-loop systems. Finally, three examples are given in simulation part to demonstrate the validity of the proposed control method.

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