Adaptive Fractional-Order Backstepping Control for a General Class of Nonlinear Uncertain Integer-Order Systems

In this article, we consider the adaptive fractional-order backstepping control problem for a class of high-order integer-order systems with uncertainties and unknown external disturbance. To obtain enhanced control performance, fractional-order calculus is integrated within the conventional backstepping controller design procedure. Theoretical proof is provided based on the Lyapunov stability theorem to ensure the global stability of the closed-loop system in the sense that all the closed-loop signals are uniformly ultimately bounded and the output tracking error to a reference signal converges to an adjustable arbitrarily small range by tuning certain design parameters. Both numerical simulation and experimental results verify the efficacy of the proposed adaptive fractional-order backstepping control scheme.