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

Abstract

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.

Load-frequency control in an islanded microgrid PV/WT/FC/ESS using an optimal self-tuning fractional-order fuzzy controller

“…Reimann, by defining the first fractional derivative, introduced Liouville's work as Reimann-Liouville. In 1967, Caputo presented a usable definition in the field of engineering for fractional derivatives (Atangana, 2017;Luo and Wang, 2017;Podlubny, 1999). In the Riemann-Liouville derivative, the first block is the integrator and the second block is the derivative, but in the Caputo's definition, first the derivative with an integer order and then the fractional integrator is used.…”

Convergence on iterative learning control of Hilfer fractional impulsive evolution equations

“…Li et al [12] discussed the convergence of the iterative control of fractional‐order system in the time domain. Further, it is important to mention a few notable works, such as the Riemann‐Liouville fractional‐order system by Luo and Wang [13]; convergence of open and closed‐loop $$$ P $$$‐type iterative learning control by Liu et al [14]; controllability of ILC system and a detailed analysis between controllability, output controllability, and target path controllability by Leissner et al [15]; and stability analysis of the fractional‐order systems by Badri and Sojoodi [16].…”