Adaptive Fuzzy Backstepping Control of Fractional-Order Nonlinear Systems

Backstepping control is effective for integer-order nonlinear systems with triangular structures. Nevertheless, it is hard to be applied to fractional-order nonlinear systems as the fractional-order derivative of a compound function is very complicated. In this paper, we develop an adaptive fuzzy backstepping control method for a class of uncertain fractional-order nonlinear systems with unknown external disturbances. In each step, a complicated unknown nonlinear function produced by differentiating a compound function with a fractional order is approximated by a fuzzy logic system, and a virtual control law is designed based on the fractional Lyapunov stability criterion. At the last step, an adaptive fuzzy controller that ensures convergence of the tracking error is constructed. The effectiveness of the proposed method has been verified by two simulation examples.