Adaptive Backstepping Control of a Class of Incommensurate Fractional Order Nonlinear MIMO Systems With Unknown Disturbance

In this paper, a new adaptive backstepping control scheme for a class of incommensurate fractional order nonlinear multiple-input multiple-output (MIMO) systems with unknown nonlinearities and external disturbance is presented. In each step of the backstepping, the radial basis function neural network (RBF NN) is utilized to approximate the unknown nonlinear uncertainties, and the incommensurate fractional order parameters update laws are designed based on backstepping algorithm. Using the frequency distributed model of fractional integrator and Lyapunov stability theory for the fractional order systems, the adaptive RBF NN controller is designed and the stability of the closed loop system is proved. Two simulation examples are given to verify the effectiveness and robustness of the proposed method.