Iterative Learning Control And Stability For Fractional Order Nonlinear Systems With Delay

In this paper, we discuss iterative learning control (ILC) scheme and stability for a class of fractional-order nonlinear systems with delay. By introducing the λ-norm, maximum norm and using Gronwall inequality, the sufficient condition for the robust convergence of the tracking errors and control input is obtained. Based on this convergence, the ILC updating laws can be determined. Then a sufficient condition for uniform stability of neutral fractional neural networks with delay is given by using the definition of norm and uniform stability.The article structure is as follows:In the first chapter, some background knowledge of fractional differential, iterative learning control and neural networks is introduced, and the preliminary knowledge which is necessary in the paper is given.In the second chapter, we discuss a P-type iterative learning control (ILC) scheme for a class of fractional-order nonlinear systems with delay. By introducing the λ-norm and using Gronwall inequality, the sufficient condition for the robust convergence of the tracking errors and control input is obtained. Based on this convergence, the P-type ILC updating laws can be determined.In the third chapter, we present a PDα-type iterative learning control for the fractional-order nonlinear systems with delay. By introducing the A-norm and the maximum norm, the convergence of the tracking errors under PDα-type iterative learning control is obtained. The PDα-type iterative learning control updating laws are considered.In the fourth chapter, we discuss stability of neutral fractional neural networks with delay. Then a sufficient condition for uniform stability of neutral fractional neural networks with delay is given by using the definition of norm and uniform stability.