Title: Second-order P-type iterative learning control for fractional order non-linear time-delay systems

Authors: Yong-Hong Lan; Xiao Liu

Addresses: School of Information Engineering, Xiangtan University, Xiangtan, Hunan 411105, China ' School of Information Engineering, Xiangtan University, Xiangtan, Hunan 411105, China

Abstract: This paper presents a second-order P-type iterative learning control (ILC) scheme for a class of fractional-order non-linear time-delay systems with fractional order α (0 ≤ α < 1). First, by analysing the control and learning processes, a discrete system for P-type ILC is established and the ILC design problem is then converted to a stabilisation problem for such a discrete system. Next, by introducing the (Λ, ξ)-norm and using a generalised Gronwall-Bellman lemma, the sufficient condition for the convergence of the control input and the tracking errors is obtained. Finally, the validity of the method is verified by a numerical example.

Keywords: nonlinear systems; time-delay systems; iterative learning control; ILC; Gronwall-Bellman lemma; fractional-order systems; stabilisation.

DOI: 10.1504/IJCSE.2016.077732

International Journal of Computational Science and Engineering, 2016 Vol.13 No.1, pp.48 - 55

Received: 13 Nov 2013
Accepted: 02 Mar 2014
Published online: 14 Jul 2016 *

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