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On the iterative learning control of fractional impulsive evolution equations in Banach spaces
Author(s) -
Yu Xiulan,
Debbouche Amar,
Wang JinRong
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3726
Subject(s) - iterative learning control , mathematics , banach space , convergence (economics) , type (biology) , norm (philosophy) , iterative method , mathematical analysis , pure mathematics , control (management) , mathematical optimization , computer science , artificial intelligence , ecology , political science , law , economics , biology , economic growth
In this paper, we study P ‐type, P I α ‐type, and D ‐type iterative learning control for fractional impulsive evolution equations in Banach spaces. We present triple convergence results for open‐loop iterative learning schemes in the sense of λ ‐norm through rigorous analysis. The proposed iterative learning control schemes are effective to fractional hybrid infinite‐dimensional distributed parameter systems. Finally, an example is given to illustrate our theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.