Composite Neural Network Learning From Fractional Backstepping

This paper focuses on parameter convergence and precise modeling for fractional-order nonlinear systems with functional uncertainties via using adaptive backstepping neural network control (ABNNC) and composite learning adaptive backstepping neural network control (CLABNNC). In the ABNNC design, a command filter is proposed, and the neural network approximation system is considered to deal with the unknown function, where an adaptation law is designed to ensure tracking errors converge to an arbitrarily small region near the origin under a strict persistent excitation condition that is too strict for the convergence of adaptive parameters. In order to relax this condition, a composite learning adaptation law is established by taking advantage of the tracking error and the prediction error to update the free parameter of the neural network system. The proposed CLABNNC method can not only ensure the convergence of tracking errors, but also achieve the accurate approximation of functional uncertainties under a weaker interval excitation condition. Finally, a numerical simulation example is put forward to demonstrate the effectiveness of our method.