Adaptive Control of a Class of Incommensurate Fractional Order Nonlinear Systems With Input Dead-Zone

This paper develops a new adaptive control scheme for a class of incommensurate fractional order nonlinear systems with external disturbances and input dead-zone. Based on the backstepping algorithm, the radial basis function neural network (RBF NN) is used to approximate the unknown nonlinear uncertainties in each step of the backstepping, and the fractional order parameters update laws for RBF NN are proposed as well as the fractional order nonlinear disturbance estimator to estimate the external disturbances. The adaptive RBF NN controller is designed based on the frequency distributed model of fractional integrator for the fractional order systems, and the stability of the closed loop system is proved. Finally, three simulation examples are given to verify the effectiveness and robustness of the proposed method.