Adaptive Fuzzy Output Tracking Control of a Class of Uncertain Fractional Order Systems Subject to Unknown Disturbance

In this paper, a novel adaptive fuzzy backstepping control method is designed for a class of incommensurate fractional-order nonlinear systems with unknown nonlinearities and external disturbance, in which the frequency distributed model is employed so that the indirect Lyapunov method can be used to design the controller. In each step of the backstepping, the complicated unknown nonlinear function coming from a fractional differential function is approximated using a fuzzy logic system, and the virtual control law and parameters update law are designed, in which the order of the parameters update law cannot be fixed to the system order and more degree of freedom can be obtained. In the last step, an adaptive fuzzy controller is given, which can ensure the convergence of the tracking error. Compared with the previous methods, the proposed backstepping method is first adopted to solve the tracking problem of incommensurate order systems with unknown nonlinearities and external disturbance, in which the stabilization and tracking can be achieved. Two careful simulation studies are provided to illustrate the effectiveness of this novel scheme.