Study on iterative learning control for Riemann-Liouville type fractional-order systems

Abstract

In this paper, we explore P-type and D-type learning laws for two classes of RiemannLiouville fractional-order controlled systems to track the varying reference accurately by adopting a few iterations in a finite time interval. Firstly, we establish open and closed-loop P-type convergence results in the sense of (1−α ,λ) -weighted norm ‖ ·‖1−α,λ for Riemann-Liouville fractional-order system of order 0 < α < 1 with initial state learning. Secondly, we establish open and closed-loop D-type convergence results in the sense of λ -weighted norm ‖ · ‖λ for Riemann-Liouville fractional-order system of order 1 < α < 2 with initial state learning. Finally, two numerical examples are given to illustrate our theoretical results. Mathematics subject classification (2010): 34A37, 93C15, 93C40.