Adaptive NN Tracking Control for Nonlinear Fractional Order Systems With Uncertainty and Input Saturation

In this paper, an adaptive neural network (NN) backstepping control method is designed for a class of uncertain fractional order nonlinear systems with external disturbance and input saturation, in which the fractional Lyapunov stability theory is used to construct the controller. The complicated unknown fractional order nonlinear function is approximated by a radial basis function (RBF) NN in each step, and the virtual control law and parameters update law are presented based on the backstepping algorithm procedures. At the final step, an adaptive RBF NN controller is constructed, in which no knowledge of system uncertainty and the upper bound of the disturbance is required. Then, a theorem is presented to address that the asymptotical convergence of the tracking error can be guaranteed. The effectiveness of the proposed scheme is illustrated by two simulation examples.