Lebesgue-\(p\) norm convergence analysis of PD\(^\alpha\)-type iterative learning control for fractional-order nonlinear systems
type: Item
instance of: scholarly article
title: Lebesgue-\(p\) norm convergence analysis of PD\(^\alpha\)-type iterative learning control for fractional-order nonlinear systems
zbMATH Open document ID: 1417.93151
DOI: 10.1155/2018/5157267
author: Lei Li
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-20T00:00:00Z
review text: Summary: The first-order and second-order PD\(^\alpha\)-type iterative learning control (ILC) schemes are considered for a class of Caputo-type fractional-order nonlinear systems. Due to the imperfection of the \(\lambda\)-norm, the Lebesgue-\(p\) (\(L^p\)) norm is adopted to overcome the disadvantage. First, a generalization of the Gronwall integral inequality with singularity is established. Next, according to the reached generalized Gronwall integral inequality and the generalized Young inequality, the monotonic convergence of the first-order PD-type ILC is investigated, while the convergence of the second-order PD-type ILC is analyzed. The resultant condition shows that both the learning gains and the system dynamics affect the convergence. Finally, numerical simulations are exploited to verify the results.
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 34A08
zbMATH DE Number: 7026604
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/5157267
OpenAlex ID: W2792947331
cites work: Intervalized iterative learning control for monotonic convergence in the sense of sup-norm
cites work: Linear and nonlinear iterative learning control
cites work: Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
cites work: Q3141895
cites work: Fractional-order systems and controls. Fundamentals and applications
cites work: Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers
cites work: Fractional order [proportional derivative] controller for a class of fractional order systems
cites work: Fractional-order iterative learning control for fractional-order linear systems
cites work: A survey on fractional-order iterative learning control
cites work: High-order \(\mathcal{D}^{\alpha}\)-type iterative learning control for fractional-order nonlinear time-delay systems
cites work: Dα‐Type Iterative Learning Control for Fractional‐Order Linear Time‐Delay Systems
cites work: Fractional order nonlinear systems with delay in iterative learning control
cites work: Robust second-order PDα type iterative learning control for a class of uncertain fractional order singular systems
cites work: Fractional order iterative learning control with randomly varying trial lengths
cites work: A note on convergence property of iterative learning controller with respect to sup norm
cites work: Robust optimal design and convergence properties analysis of iterative learning control approaches
cites work: Convergence Properties of Iterative Learning Control Processes in the Sense of the Lebesgue‐P Norm
cites work: Q3159056
cites work: Analysis of fractional differential equations
cites work: Lebesgue‐p NORM Convergence OF Fractional‐Order PID‐Type Iterative Learning Control for Linear Systems
description: scientific article; zbMATH DE number 7026604