Robust Control of Nonlinear Fractional-Order Systems with Unknown Upper Bound of Uncertainties and External Disturbance

Abstract

This paper investigates the asymptotic stabilization of nonlinear fractional-order systems under unknown upper bounds on external disturbances and uncertainties. The upper bound of uncertainties is a nonlinear function of the pseudostates norm with unknown coefficients. Based on the robust fractional-order sliding mode control, the states of the nonlinear fractional-order system under unknown upper bounds on external disturbances and uncertainties have been stabled. Adaptive control laws estimate the upper bound of external disturbances and uncertainties. In all cases, the stability proof is obtained using the Lyapunov theorem to show the convergence of the sliding surface to zero. Also, by introducing a suitable sliding surface, the chattering phenomenon is eliminated. Finally, the effectiveness of the proposed fractional-order controller is demonstrated using practical examples. The simulation results show the proposed controller has a proper performance in the presence of external disturbance and uncertainties.