The control problem of a class of uncertain fractional-order nonlinear systems with strict feedback form are studied. According to the backstepping control principle, firstly in each step, the fuzzy logic system is used to approximate the unknown part of the system, and then a fractional integral sliding mode surface is constructed, and the virtual controller design of each step is carried out according to the sliding mode control theory. Secondly, a filter is designed to solve the problem of “explosion of complexity” caused by repeated derivative of the virtual controller in the backstepping control. Based on the Lyapunov fractional stability theory, the stability analysis of the error dynamic system is carried out to ensure that the tracking error eventually converges to a neighborhood with an adjustable neighborhood near the origin. Finally, a simulation example is given to verify the effectiveness of the method.

fuzzy logic system; sliding mode control; backstepping control; fractional-order nonlinear system