Convergence Analysis of Iterative Learning Control for Stocastic Semilinear Generalized Distributed Parameter Systems

Zhaoqiang Ge

doi:doi:10.11648/j.sd.20251305.14

Research Article |

| Peer-Reviewed

Convergence Analysis of Iterative Learning Control for Stocastic Semilinear Generalized Distributed Parameter Systems

Zhaoqiang Ge^*

Published in Science Discovery (Volume 13, Issue 5)

Received: 6 September 2025 Accepted: 29 September 2025 Published: 29 October 2025

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

The iterative learning control problem of generalized distributed parameter systems is one of the important issues in the research of generalized distributed parameter systems. In this paper convergence analysis of P-type iterative learning control for stochastic semilinear generalized distributed parameter systems is discussed in the sense of integral solution by GE-semigroup theory in separable Hilbert spaces. Firstly, the basic concepts of GE-semigroup and integral solution are presented, along with a description of the iterative learning control problem for stochastic semilinear generalized distributed parameter systems under P-type learning law. Secondly, some sufficient conditions are obtained, by which the input tracking and output tracking errors can converge to be bounded in the mean square sense. At the same time, we have also obtained sufficient conditions for the input tracking and output tracking errors of the semilinear generalized distributed parameter system to converge uniformly to zero.

Published in	Science Discovery (Volume 13, Issue 5)
DOI	10.11648/j.sd.20251305.14
Page(s)	101-107
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Convergence Analysis, Iterative Learning Control, Stochastic Semilinear Generalized Distributed Parameter Systems, Integral Solution, GE-semigroup

References

[1]	葛照强, 朱广田, 冯德兴. Hilbert空间中广义分布参数系统的精确能控性 [J]. 中国科学: 信息科学, 2009, 39(11): 1210-1216.
[2]	葛照强, 朱广田, 冯德兴. 广义算子半群与广义分布参数系统的适定性 [J]. 中国科学: 数学, 2010, 40(5): 477-495.
[3]	葛照强, 冯德兴. Banach空间中时变广义分布参数系统的可解性 [J]. 中国科学: 信息科学, 2013, 43: 386-406.
[4]	Ge Z Q, Feng D X. Solvability of a time-varying singular distributed parameter system in Banach space [J]. Sci Sin Inform, 2013, 56: 128201:1-128201:14.
[5]	葛照强, 冯德兴. 非线性时变广义分布参数系统的适定性 [J]. 中国科学: 数学, 2014, 44: 1277-1298.
[6]	Liaskos K B, Pantelous A A, Stratis I G. Linear stochastic degenerate Sobolev equations and applications [J]. Int J Control, 2015, 88: 2538-2553. https://doi.org/10.1080/00207179.2015.1048482
[7]	Zhang Y, Li Y, Su J. Singular distributed parameter system iterative learning control with forgetting factor with time delay [J]. International Journal of u- and e- Service, Science and Technology, 2016, 9(7): 1-8. https://doi.org/10.14257/ijuness.2016.9.7.01
[8]	Dai X S, Zhou X Y, Tian S P, Ye H T. Iterative learning control for MIMO singular distributed parameter systems. IEEE Access, 2017, 5: 24094-24104. https://doi.org/10.1109/ACCESS.2017.2768480
[9]	葛照强, 冯德兴. 广义分布参数系统与广义集中参数系统耦合系统的极点配置问题 [J]. 中国科学: 信息科学, 2017, 47: 326-336.
[10]	Jiang Y S, Zhang Q L, Li L. State feedback control on singular distributed parameter system with parabolic-elliptic type [C]. In: Proceeding of 28th Chinese Control and Decision Conference (CCDC), 2017. 261-265.
[11]	Jiang Y S, Liu C, Zhang Q L, Zhang T Y. Two side observer for singular distributed parameter systems [J]. System & Control Letters, 2019, 124: 112-120.
[12]	Ge Z Q, Ge X C, Zhang J F. Approximate controllability and approximate observability of singular distributed parameter systems [J]. IEEE Transaction on Automatic Control, 2020, 65: 2294-2299. https://doi.org/10.1109/TAC.2019.2920215
[13]	Jacob B, Morris K. On solvability of dissipative partial differential-algebraic equation [J]. IEEE Control System Letters, 2022, 6: 3188-3193.
[14]	Bortolan M C, Brito M C A, Dantas F. Weii-posedness of linear singular evolution equation in Banach space: theoretical results [J]. Anal Math, 2025, 51: 99-128.
[15]	Zhou X, Dai X, Tian S, Mei S. Iterative learning control for a class of singular distributed parameter systems [C]. In: Proceedings of 6th data driven control and learning system, 2017. 42-47.
[16]	Zhou X Y, Dai X S, Wang D X, Qi M M. Iterative learning control for MIMO singular distributed parameter system with parabolic type [C]. In: Proceedings of 2017 Chinese Automation Congress (CAC), 2017. 4093-4098.
[17]	Lan Z M, Zhang Y J, Chen M J. Iterative learning controller design for nonlinear generalized distributed parameter system with correction factor [J]. Engineering Intelligent Systems, 2018, 2-3: 139-145.
[18]	Zhang Y J, Li Y H, Chen M J. Iterative learning control for linear generalized distributed parameter system [J]. Neurai Computing and Applications, 2019, 31: 4503-4512. https://doi.org/10.1007/s00521
[19]	Chen M J, Zhang Y J. Iterative learning control of descrete generalized distributed parameter [C]. In: Xu Z, Choo K K R, Dehghantanha A, Parizi R, Hammoudeh M (eds). Cyber Security Intelligence and Analysis. CSIA 2019. Advance in Intelligent Systems and Computing, vol 298. Spring, 2020, 407-414.
[20]	De X S, Zhou X Y. Mixed PD-type iterative learning control algorithm for a class of parabolic singular distributed parameter systems [J]. IEEE Access, 2021, 9: 12180-12190. https://doi.org/10.1109/ACCESS.2021.3050481
[21]	Li G, Hou L, Lu Y. D-type iterative learning control for open container motion system with sloshing contains [J]. IEEE Access, 2021, 9: 136666-136673. https://doi.org/10.1109/ACCESS.2021.3117730
[22]	Liaskos K B, Stratis I G, Pantelous A A. Stochastic degenerate Sobolev equation: Well posedness and exact controllability [J]. Math Meth Appl Sci, 2018, 41: 1025-1032.
[23]	Ge Z Q. GE-evolution operator method for controllability of time varying stochastic descriptor systems in Hilbert spaces [J]. IMA Journal of Mathematical Control and Information, 2022, 39: 80-92. https://doi.org/10.1093/imamci/dnab038
[24]	Ge Z Q. GE-semigroup method for controllability of stochastic descriptor linear systems [J]. Sci China Inf Sci, 2023, 66: 139201, 1-2. https://doi.org/10.1007/s11432-020-3288-x
[25]	Ge Z Q. Controllability of semilinear stochastic generalized system in Hilbert spaces by GE-evolution operator method [J]. Mathematics, 2023, 11: 743, 1-26. https://doi.org/10.3390/math11030743
[26]	Ge Z Q. Controllability of semilinear integrodifferential degenerate Sobolev equations [J]. J Syst Sci Complex, 2024, 37: 1923-1936. https://doi.org/10.1007/s11424-024-3181-5

Cite This Article

Plain Text BibTeX RIS

APA Style

Ge, Z. (2025). Convergence Analysis of Iterative Learning Control for Stocastic Semilinear Generalized Distributed Parameter Systems. Science Discovery, 13(5), 101-107. https://doi.org/10.11648/j.sd.20251305.14

Copy | Download

ACS Style

Ge, Z. Convergence Analysis of Iterative Learning Control for Stocastic Semilinear Generalized Distributed Parameter Systems. Sci. Discov. 2025, 13(5), 101-107. doi: 10.11648/j.sd.20251305.14

Copy | Download

AMA Style

Ge Z. Convergence Analysis of Iterative Learning Control for Stocastic Semilinear Generalized Distributed Parameter Systems. Sci Discov. 2025;13(5):101-107. doi: 10.11648/j.sd.20251305.14

Copy | Download

@article{10.11648/j.sd.20251305.14,
  author = {Zhaoqiang Ge},
  title = {Convergence Analysis of Iterative Learning Control for Stocastic Semilinear Generalized Distributed Parameter Systems
},
  journal = {Science Discovery},
  volume = {13},
  number = {5},
  pages = {101-107},
  doi = {10.11648/j.sd.20251305.14},
  url = {https://doi.org/10.11648/j.sd.20251305.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sd.20251305.14},
  abstract = {The iterative learning control problem of generalized distributed parameter systems is one of the important issues in the research of generalized distributed parameter systems. In this paper convergence analysis of P-type iterative learning control for stochastic semilinear generalized distributed parameter systems is discussed in the sense of integral solution by GE-semigroup theory in separable Hilbert spaces. Firstly, the basic concepts of GE-semigroup and integral solution are presented, along with a description of the iterative learning control problem for stochastic semilinear generalized distributed parameter systems under P-type learning law. Secondly, some sufficient conditions are obtained, by which the input tracking and output tracking errors can converge to be bounded in the mean square sense. At the same time, we have also obtained sufficient conditions for the input tracking and output tracking errors of the semilinear generalized distributed parameter system to converge uniformly to zero.
},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Convergence Analysis of Iterative Learning Control for Stocastic Semilinear Generalized Distributed Parameter Systems

AU  - Zhaoqiang Ge
Y1  - 2025/10/29
PY  - 2025
N1  - https://doi.org/10.11648/j.sd.20251305.14
DO  - 10.11648/j.sd.20251305.14
T2  - Science Discovery
JF  - Science Discovery
JO  - Science Discovery
SP  - 101
EP  - 107
PB  - Science Publishing Group
SN  - 2331-0650
UR  - https://doi.org/10.11648/j.sd.20251305.14
AB  - The iterative learning control problem of generalized distributed parameter systems is one of the important issues in the research of generalized distributed parameter systems. In this paper convergence analysis of P-type iterative learning control for stochastic semilinear generalized distributed parameter systems is discussed in the sense of integral solution by GE-semigroup theory in separable Hilbert spaces. Firstly, the basic concepts of GE-semigroup and integral solution are presented, along with a description of the iterative learning control problem for stochastic semilinear generalized distributed parameter systems under P-type learning law. Secondly, some sufficient conditions are obtained, by which the input tracking and output tracking errors can converge to be bounded in the mean square sense. At the same time, we have also obtained sufficient conditions for the input tracking and output tracking errors of the semilinear generalized distributed parameter system to converge uniformly to zero.

VL  - 13
IS  - 5
ER  -

Copy | Download

Author Information

Zhaoqiang Ge

School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, China

Contact Email

http://orcid.org/0000-0002-1550-096X

Download PDF

Submit an Article

Sections

Plain Text BibTeX RIS

APA Style

Ge, Z. (2025). Convergence Analysis of Iterative Learning Control for Stocastic Semilinear Generalized Distributed Parameter Systems. Science Discovery, 13(5), 101-107. https://doi.org/10.11648/j.sd.20251305.14

Copy | Download

ACS Style

Ge, Z. Convergence Analysis of Iterative Learning Control for Stocastic Semilinear Generalized Distributed Parameter Systems. Sci. Discov. 2025, 13(5), 101-107. doi: 10.11648/j.sd.20251305.14

Copy | Download

AMA Style

Ge Z. Convergence Analysis of Iterative Learning Control for Stocastic Semilinear Generalized Distributed Parameter Systems. Sci Discov. 2025;13(5):101-107. doi: 10.11648/j.sd.20251305.14

Copy | Download

@article{10.11648/j.sd.20251305.14,
  author = {Zhaoqiang Ge},
  title = {Convergence Analysis of Iterative Learning Control for Stocastic Semilinear Generalized Distributed Parameter Systems
},
  journal = {Science Discovery},
  volume = {13},
  number = {5},
  pages = {101-107},
  doi = {10.11648/j.sd.20251305.14},
  url = {https://doi.org/10.11648/j.sd.20251305.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sd.20251305.14},
  abstract = {The iterative learning control problem of generalized distributed parameter systems is one of the important issues in the research of generalized distributed parameter systems. In this paper convergence analysis of P-type iterative learning control for stochastic semilinear generalized distributed parameter systems is discussed in the sense of integral solution by GE-semigroup theory in separable Hilbert spaces. Firstly, the basic concepts of GE-semigroup and integral solution are presented, along with a description of the iterative learning control problem for stochastic semilinear generalized distributed parameter systems under P-type learning law. Secondly, some sufficient conditions are obtained, by which the input tracking and output tracking errors can converge to be bounded in the mean square sense. At the same time, we have also obtained sufficient conditions for the input tracking and output tracking errors of the semilinear generalized distributed parameter system to converge uniformly to zero.
},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Convergence Analysis of Iterative Learning Control for Stocastic Semilinear Generalized Distributed Parameter Systems

AU  - Zhaoqiang Ge
Y1  - 2025/10/29
PY  - 2025
N1  - https://doi.org/10.11648/j.sd.20251305.14
DO  - 10.11648/j.sd.20251305.14
T2  - Science Discovery
JF  - Science Discovery
JO  - Science Discovery
SP  - 101
EP  - 107
PB  - Science Publishing Group
SN  - 2331-0650
UR  - https://doi.org/10.11648/j.sd.20251305.14
AB  - The iterative learning control problem of generalized distributed parameter systems is one of the important issues in the research of generalized distributed parameter systems. In this paper convergence analysis of P-type iterative learning control for stochastic semilinear generalized distributed parameter systems is discussed in the sense of integral solution by GE-semigroup theory in separable Hilbert spaces. Firstly, the basic concepts of GE-semigroup and integral solution are presented, along with a description of the iterative learning control problem for stochastic semilinear generalized distributed parameter systems under P-type learning law. Secondly, some sufficient conditions are obtained, by which the input tracking and output tracking errors can converge to be bounded in the mean square sense. At the same time, we have also obtained sufficient conditions for the input tracking and output tracking errors of the semilinear generalized distributed parameter system to converge uniformly to zero.

VL  - 13
IS  - 5
ER  -

Copy | Download