Backstepping-Based Adaptive Control of a Class of Uncertain Incommensurate Fractional-Order Nonlinear Systems With External Disturbance
Xinyao Li, Jinsong He, Changyun Wen, Xiao‐Kang Liu
Abstract
Normally, achieving asymptotic convergence in the presence of unknown arbitrarily bounded external disturbance requires noncontinuous control signals. In this article, an adaptive backstepping controller for a class of incommensurate fractional-order nonlinear systems with parametric uncertainties and external time-varying disturbance is proposed to realize asymptotic perfect output tracking. Appropriate adaptive laws are designed to deal with the uncertainties and unknown bounded disturbance. In the designed adaptive backstepping control scheme, an auxiliary function is adopted to obtain a smooth control signal. It is theoretically shown that asymptotic output tracking to a given reference signal is achieved while ensuring global system stability in the sense that all the closed-loop signals are bounded. Simulation and experimental studies demonstrate the effectiveness of the proposed backstepping control scheme.