Composite Learning Backstepping Control Of Fractional Order Neural Network

In the conventional neural network adaptive control,a persistent excitation condition,which ensures the convergence of parameters,must be satisfied.This paper is derived from fractional backstepping,focusing on parameter convergence and precise modeling for fractional-order nonlinear systems with functional uncertainties through the neural network backstepping control and the composite learning neural network backstepping control.In the neural network backstepping control design,a command filter is proposed,and the neural network approximation system is considered to deal with the unknown function,where an adaptive law is designed to ensure the convergence of the tracking error under the persistent excitation.In order to overcome the strict condition,a composite learning law is established by taking advantage of the tracking error and the prediction error to update the neural network free parameter.The proposed the composite learning neural network backstepping control can not only ensure the convergence of tracking error,but also obtain accurate unknown function estimation under the condition of an interval excitation.Finally,a simulation example is presented to demonstrate the effectiveness of the proposed method.There are three chapters in this paper.The specific contents are as follows:Chapter 1:Preliminaries.Firstly,the definition of Caputo fractional calculus and some basic lemmas are reviewed,and then the neural network approximation system is described.Chapter 2:The neural network backstepping control and composite learning neural network backstepping control.First,a fractional-order system with function uncertainty is given.Secondly,the controller is designed and the stability is analyzed by the neural backstepping network control,so as to ensure the convergence of the tracking error and the bounded system parameters.Finally,the composite learning neural network backstepping control is designed based on the composite learning technology,the composite learning law is established,the stability of the system is guaranteed by the Lyapunov criterion,and the accurate approximation of the function is achieved with this method.Chapter 3:Comparision analysis of control performance between the neural network backstepping control and composite learning neural network backstepping control.Compared with the neural network backstepping control,the composite learning neural network backstepping control can not only achieve better control performance,but also achieve fast parameter convergence.