Lebesgue-p Norm Convergence Analysis of PDα-Type Iterative Learning Control for Fractional-Order Nonlinear Systems

Lebesgue-p Norm Convergence Analysis of PDα-Type Iterative Learning Control for Fractional-Order Nonlinear Systems

The first-order and second-order PDα-type iterative learning control (ILC) schemes are considered for a class of Caputo-type fractional-order nonlinear systems. Due to the imperfection of the λ-norm, the Lebesgue-p (Lp) norm is adopted to overcome the disadvantage. First, a generalization of the Gro...

Full description

Bibliographic Details
Main Author: Lei Li
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2018/5157267
id doaj-b8136968cfe14ae99d50c5f6d402fd5c
record_format Article
spelling doaj-b8136968cfe14ae99d50c5f6d402fd5c2020-11-25T00:06:27ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/51572675157267Lebesgue-p Norm Convergence Analysis of PDα-Type Iterative Learning Control for Fractional-Order Nonlinear SystemsLei Li0Department of Applied Mathematics, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, ChinaThe first-order and second-order PDα-type iterative learning control (ILC) schemes are considered for a class of Caputo-type fractional-order nonlinear systems. Due to the imperfection of the λ-norm, the Lebesgue-p (Lp) 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 PDα-type ILC is investigated, while the convergence of the second-order PDα-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.http://dx.doi.org/10.1155/2018/5157267
collection DOAJ
language English
format Article
sources DOAJ
author Lei Li
spellingShingle Lei Li
Lebesgue-p Norm Convergence Analysis of PDα-Type Iterative Learning Control for Fractional-Order Nonlinear Systems
Discrete Dynamics in Nature and Society
author_facet Lei Li
author_sort Lei Li
title Lebesgue-p Norm Convergence Analysis of PDα-Type Iterative Learning Control for Fractional-Order Nonlinear Systems
title_short Lebesgue-p Norm Convergence Analysis of PDα-Type Iterative Learning Control for Fractional-Order Nonlinear Systems
title_full Lebesgue-p Norm Convergence Analysis of PDα-Type Iterative Learning Control for Fractional-Order Nonlinear Systems
title_fullStr Lebesgue-p Norm Convergence Analysis of PDα-Type Iterative Learning Control for Fractional-Order Nonlinear Systems
title_full_unstemmed Lebesgue-p Norm Convergence Analysis of PDα-Type Iterative Learning Control for Fractional-Order Nonlinear Systems
title_sort lebesgue-p norm convergence analysis of pdα-type iterative learning control for fractional-order nonlinear systems
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2018-01-01
description The first-order and second-order PDα-type iterative learning control (ILC) schemes are considered for a class of Caputo-type fractional-order nonlinear systems. Due to the imperfection of the λ-norm, the Lebesgue-p (Lp) 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 PDα-type ILC is investigated, while the convergence of the second-order PDα-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.
url http://dx.doi.org/10.1155/2018/5157267
work_keys_str_mv AT leili lebesguepnormconvergenceanalysisofpdatypeiterativelearningcontrolforfractionalordernonlinearsystems
_version_ 1725421917606772736

Similar Items