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Volume 68, Issue 3


Iterative learning control with pulse compensation for fractional differential systems

Shengda Liu / JinRong Wang
  • Department of Mathematics Guizhou University Guiyang, Guizhou 550025 P. R. China
  • School of Mathematical Sciences Qufu Normal University Qufu Shandong 273165 P. R. China
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/ Yong Zhou
  • Department of Mathematics Xiangtan University Xiangtan, Hunan 411105 P. R. China
  • Nonlinear Analysis and Applied Mathematics (NAAM) Research Group Faculty of Science King Abdulaziz University Jeddah 21589 Saudi arabia
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/ Michal Fečkan
  • Department of Mathematical Analysis and Numerical Mathematics Faculty of Mathematics, Physics and Informatics Comenius University in Bratislava Mlynská dolina 842 48 Bratislava Slovakia
  • Mathematical Institute of Slovak Academy of Sciences Štefánikova 49 814 73 Bratislava Slovakia
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Published Online: 2018-05-18 | DOI: https://doi.org/10.1515/ms-2017-0125


In this paper, we explore PD-type ILC schemes of fractional version with pulse compensation for single-input-single-output fractional differential systems. More precisely, we design a new type of pulse-based ILC schemes involving fractional derivative and sign function for a class of fractional order linear systems with initial state shift. In order to tracking discrepancy incurred by the initial state shift effectively, a new function of pulse compensation is introduced. The effectiveness of the result is illustrated by numerical simulations.

MSC 2010: Primary 26A33, 34A08; Secondary 34K35, 93B05

Keywords: P&Dα-type iterative learning control; pulse compensation; fractional differential systems; sign function

The first and second authors acknowledge the support by NNSF of China (11661016), Training Object of High Level and Innovative Talents of Guizhou Province ((2016)4006), and Foundation of Postgraduate of Guizhou Province (KYJJ2017001); the third author acknowledges the support by NNSF of China (11671339); the fourth author acknowledges the support by the Slovak Grant Agency VEGA No. 2/0153/16 and No. 1/0078/17, and by the Slovak Research and Development Agency under the contract No. APVV-14-0378.


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About the article

Received: 2016-05-12

Accepted: 2017-03-01

Published Online: 2018-05-18

Published in Print: 2018-06-26

Citation Information: Mathematica Slovaca, Volume 68, Issue 3, Pages 563–574, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0125.

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