Iterative learning control with initial state learning for fractional order nonlinear systems

This paper presents a P-type iterative learning control (ILC) scheme with initial state learning for a class of α(0≤α<1) fractional-order nonlinear systems. By introducing the λλ-norm and using a generalized Gronwall inequality, the sufficient condition for the robust convergence of the tracking errors with respect to initial positioning errors under P-type ILC is obtained. Based on this convergence condition, the learning gain of the initial learning and input learning updating law can be determined. Unlike the existing methods, the ILC scheme will not fix the initial value on the expected condition at the beginning of each iteration. Finally, the validity of the methods are verified by a numerical example.