Convergence analysis of fractional-order iterative learning control

Abstract

The classical time domain and frequency domain analysis of iterative learning control (ILC) are extended to a type of time domain analysis of fractional order iterative learning control (FOILC) for fractional order nonlinear systems. A novel FOILC scheme is proposed, which leads to simpler convergence condition. The equivalence of the above two FOILC schemes is shown for the constant learning gain cases, which leads to two further developments: the learnable domain of an adaptive FOILC for the uncertain fractional order systems, and a desirable band-stop FOILC scheme. Several examples are provided to illustrate the presented results.