Skip to main content

Advertisement

SpringerLink
Log in

A novel varying-parameter periodic rhythm neural network for solving time-varying matrix equation in finite energy noise environment and its application to robot arm

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

Solving matrix equation with noise interference is a challenging problem in mathematical and engineering applications. Unlike the traditional recurrent neural network, a novel varying-parameter periodic rhythm neural network (VP-PRNN) is proposed and used to solve the time-varying matrix equation in finite energy noise environment online. Particularly, VP-PRNN can enable the state solution to converge to the theoretical solution rapidly and robustly, which is also proved by theoretical analysis. Four kinds of noise are used to test the system, which proves the effectiveness of VP-PRNN. Compared with the zeroing neural network and circadian rhythms learning network with fixed parameters, VP-PRNN with variable parameters shows superior convergence performance in the disturbance of finite energy noise.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Data availability

The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.

References

  1. Brahma S, Datta B (2009) An optimization approach for minimum norm and robust partial quadratic eigenvalue assignment problems for vibrating structures. J Sound Vib 324(3–5):471–489

    Article  Google Scholar 

  2. Calvetti D, Reichel L (1996) Application of adi iterative methods to the restoration of noisy images. SIAM J Matrix Anal Appl 17(1):165–186

    Article  MathSciNet  MATH  Google Scholar 

  3. Papyan V, Elad M (2015) Multi-scale patch-based image restoration. IEEE Trans Image Process 25(1):249–261

    Article  MathSciNet  MATH  Google Scholar 

  4. Knoll F, Holler M, Koesters T, Otazo R, Bredies K, Sodickson DK (2016) Joint mr-pet reconstruction using a multi-channel image regularizer. IEEE Trans Med Imag 36(1):1–16

    Article  Google Scholar 

  5. Ding B, Wen G, Ma C, Yang X (2017) Evaluation of target segmentation on sar target recognition. In: 2017 4th International Conference on Information, Cybernetics and Computational Social Systems (ICCSS), pp. 663–667 . IEEE

  6. Chen X, Chen B, Guan J, Huang Y, He Y (2018) Space-range-doppler focus-based low-observable moving target detection using frequency diverse array mimo radar. IEEE Access 6:43892–43904

    Article  Google Scholar 

  7. Ahmad AS (2017) Brain inspired cognitive artificial intelligence for knowledge extraction and intelligent instrumentation system. In: 2017 International Symposium on Electronics and Smart Devices (ISESD), pp. 352–356. IEEE

  8. Park J-H, Uhm T-Y, Bae G-D, Choi Y-H (2018) Stability evaluation of outdoor unmanned security robot in terrain information. In: 2018 18th International Conference on Control, Automation and Systems (ICCAS), pp. 955–957. IEEE

  9. Lee J-W, Park G-T, Shin J-S, Woo J-W (2017) Industrial robot calibration method using denavit-hatenberg parameters. In: 2017 17th International Conference on Control, Automation and Systems (ICCAS), pp. 1834–1837. IEEE

  10. Ma Z, Yu S, Han Y, Guo D (2021) Zeroing neural network for bound-constrained time-varying nonlinear equation solving and its application to mobile robot manipulators. Neural Comput Appl 33(21):14231–14245

    Article  Google Scholar 

  11. Miao P, Wu D, Shen Y, Zhang Z (2019) Discrete-time neural network with two classes of bias noises for solving time-variant matrix inversion and application to robot tracking. Neural Comput Appl 31(9):4879–4890

    Article  Google Scholar 

  12. Song Z, Lu Z, Wu J, Xiao X, Wang G (2022) Improved znd model for solving dynamic linear complex matrix equation and its application. Neural Comput Appl 34(23):21035–21048

    Article  Google Scholar 

  13. Bartels RH, Stewart GW (1972) Solution of the matrix equation ax+ xb= c [f4]. Commun ACM 15(9):820–826

    Article  MATH  Google Scholar 

  14. Ding F, Chen T (2005) Gradient based iterative algorithms for solving a class of matrix equations. IEEE Trans Automat Control 50(8):1216–1221

    Article  MathSciNet  MATH  Google Scholar 

  15. Zhang H, Yin H (2017) On the best convergence factors of iterative methods of matrix equations based on the gradient and least squares searches. In: 2017 36th Chinese Control Conference (CCC), pp. 111–115 . IEEE

  16. Li S, Chen S, Liu B (2013) Accelerating a recurrent neural network to finite-time convergence for solving time-varying sylvester equation by using a sign-bi-power activation function. Neural Process Lett 37:189–205

    Article  Google Scholar 

  17. Mao M, Li J, Jin L, Li S, Zhang Y (2016) Enhanced discrete-time zhang neural network for time-variant matrix inversion in the presence of bias noises. Neurocomputing 207:220–230

    Article  Google Scholar 

  18. Zuo Q, Li K, Xiao L, Wang Y, Li K (2021) On generalized zeroing neural network under discrete and distributed time delays and its application to dynamic lyapunov equation. IEEE Trans Syst Man Cybernet Syst 52(8):5114–5126

    Article  Google Scholar 

  19. Madankan A (2010) Recurrent neural network for solving linear matrix equation. In: 2010 International Conference on Electronics and Information Engineering, vol. 2, pp. 2–70. IEEE

  20. Xiao L, Zhang Y, Dai J, Zuo Q, Wang S (2020) Comprehensive analysis of a new varying parameter zeroing neural network for time varying matrix inversion. IEEE Trans Ind Inform 17(3):1604–1613

    Article  Google Scholar 

  21. Xiao L, Liao B, Li S, Chen K (2018) Nonlinear recurrent neural networks for finite-time solution of general time-varying linear matrix equations. Neural Netw 98:102–113

    Article  MATH  Google Scholar 

  22. Gong J, Jin J (2021) A better robustness and fast convergence zeroing neural network for solving dynamic nonlinear equations. Neural Comput Appl 35:77–87

    Article  Google Scholar 

  23. Luo Y, Deng X, Wu J, Liu Y, Zhang Z (2021) A new finite-time circadian rhythms learning network for solving nonlinear and nonconvex optimization problems with periodic noises. IEEE Trans Cybernet 52(11):12514–12524

    Article  Google Scholar 

  24. Jin L, Zhang Y, Li S (2015) Integration-enhanced zhang neural network for real-time-varying matrix inversion in the presence of various kinds of noises. IEEE Trans Neural Netw Learn Syst 27(12):2615–2627

    Article  Google Scholar 

  25. Wang S, Dai S, Wang K (2015) Gradient-based neural network for online solution of lyapunov matrix equation with li activation function. In: 4th International Conference on Information Technology and Management Innovation, pp. 955–959. Atlantis Press

  26. Yi C, Chen Y, Lan X (2013) Comparison on neural solvers for the lyapunov matrix equation with stationary & nonstationary coefficients. Appl Math Model 37(4):2495–2502

    Article  MathSciNet  MATH  Google Scholar 

  27. Yan J, Jin L, Zhang R, Li H, Zhang J, Lu H (2019) Zeroing-type recurrent neural network for solving time-dependent lyapunov equation with noise rejection. In: 2019 IEEE 8th Data Driven Control and Learning Systems Conference (DDCLS), pp. 366–371 . IEEE

  28. Xiao L, Liao B, Luo J, Ding L (2017) A convergence-enhanced gradient neural network for solving sylvester equation. In: 2017 36th Chinese Control Conference (CCC), pp. 3910–3913. IEEE

  29. Wang J (1993) A recurrent neural network for real-time matrix inversion. Appl Math Comput 55(1):89–100

    Article  MathSciNet  MATH  Google Scholar 

  30. Xiao L, Zhang Y, Dai J, Li J, Li W (2019) New noise-tolerant znn models with predefined-time convergence for time-variant sylvester equation solving. IEEE Trans Syst Man Cybernet Syst 51(6):3629–3640

    Article  Google Scholar 

  31. Zhang Y, Ge SS (2005) Design and analysis of a general recurrent neural network model for time-varying matrix inversion. IEEE Trans Neural Netw 16(6):1477–1490

    Article  Google Scholar 

  32. Xiao L, Ding S, Mao M, Zhang Y, Liao B (2014) Finite-time convergence analysis and verification of improved znn for real-time matrix inversion. In: 2014 4th IEEE International Conference on Information Science and Technology, pp. 286–289. IEEE

  33. Zhang Z, Zheng L, Weng J, Mao Y, Lu W, Xiao L (2018) A new varying-parameter recurrent neural-network for online solution of time-varying sylvester equation. IEEE Trans Cybernet 48(11):3135–3148

    Article  Google Scholar 

  34. Xiao L, He Y, Dai J, Liu X, Liao B, Tan H (2020) A variable-parameter noise-tolerant zeroing neural network for time-variant matrix inversion with guaranteed robustness. IEEE Trans Neural Netw Learn Syst 33(4):1535–1545

    Article  MathSciNet  Google Scholar 

  35. Xiao L, Li S, Lin F-J, Tan Z, Khan AH (2018) Zeroing neural dynamics for control design: comprehensive analysis on stability, robustness, and convergence speed. IEEE Trans Ind Inform 15(5):2605–2616

    Article  Google Scholar 

  36. Xiao L, Song W, Li X, Jia L, Sun J, Wang Y (2021) Design and analysis of a noise-resistant znn model for settling time-variant linear matrix inequality in predefined-time. IEEE Trans Ind Inform 18(10):6840–6847

    Article  Google Scholar 

  37. Zhang Z, Deng X, Kong L, Li S (2019) A circadian rhythms learning network for resisting cognitive periodic noises of time-varying dynamic system and applications to robots. IEEE Trans Cognit Dev Syst 12(3):575–587

    Article  Google Scholar 

  38. Zhang Y, Li S, Kadry S, Liao B (2018) Recurrent neural network for kinematic control of redundant manipulators with periodic input disturbance and physical constraints. IEEE Trans Cybernet 49(12):4194–4205

    Article  Google Scholar 

  39. Lokvenc J, Drtina R (2017) Asynchronous machine set for electrical laboratories part 1: Noise load. In: 2017 European Conference on Electrical Engineering and Computer Science (EECS), pp. 295–299. IEEE

  40. Sharma MK, Vig R (2014) Server noise: health hazard and its reduction using active noise control. In: 2014 Recent Advances in Engineering and Computational Sciences (RAECS), pp. 1–5. IEEE

  41. Lindner B, Garcıa-Ojalvo J, Neiman A, Schimansky-Geier L (2004) Effects of noise in excitable systems. Phys Rep 392(6):321–424

    Article  Google Scholar 

  42. Zhu J, Liu X (2018) Measuring spike timing distance in the hindmarsh-rose neurons. Cognit Neurodyn 12:225–234

    Article  Google Scholar 

  43. Zeng K, Huang J, Dong M (2014) White gaussian noise energy estimation and wavelet multi-threshold de-noising for heart sound signals. Circuits Syst Signal Process 33:2987–3002

    Article  Google Scholar 

  44. Wen M, Basar E, Li Q, Zheng B, Zhang M (2017) Multiple-mode orthogonal frequency division multiplexing with index modulation. IEEE Trans Commun 65(9):3892–3906

    Article  Google Scholar 

  45. Vieira TP, Tenório DF, da Costa JPC, de Freitas EP, Del Galdo G, de Sousa Júnior RT (2017) Model order selection and eigen similarity based framework for detection and identification of network attacks. J Netw Comput Appl 90:26–41

    Article  Google Scholar 

  46. Lv J, Wang F (2015) Image laplace denoising based on sparse representation. In: 2015 International Conference on Computational Intelligence and Communication Networks (CICN), pp. 373–377. IEEE

  47. Wang Z, Chang J, Zhang S, Sun B, Jiang S, Luo S, Jia C, Liu Y, Liu X, Lv G et al (2014) An adaptive rayleigh noise elimination method in raman distributed temperature sensors using anti-stokes signal only. Opt Quant Electron 46:821–827

    Article  Google Scholar 

  48. Sai Suneel A, Shiyamala S (2021) Peak detection based energy detection of a spectrum under rayleigh fading noise environment. J Ambient Intel Human Comput 12:4237–4245

    Article  Google Scholar 

  49. Li S, Zhou M, Luo X (2017) Modified primal-dual neural networks for motion control of redundant manipulators with dynamic rejection of harmonic noises. IEEE Trans Neural Netw Learn Syst 29(10):4791–4801

    Article  MathSciNet  Google Scholar 

  50. Zhang Z, Ye L, Chen B, Luo Y (2023) An anti-interference dynamic integral neural network for solving the time-varying linear matrix equation with periodic noises. Neurocomputing 534:29–44

    Article  Google Scholar 

  51. Shen L, Wu J, Yang S (2011) Initial position estimation in srm using bootstrap circuit without predefined inductance parameters. IEEE Trans Power Electron 26(9):2449–2456

    Article  Google Scholar 

  52. Zhang Y, Ruan G, Li K, Yang Y (2010) Robustness analysis of the Zhang neural network for online time-varying quadratic optimization. J Phys A Math Theor 43(24):245202

    Article  MathSciNet  MATH  Google Scholar 

  53. Guo L, Li Y, Wang T, Wang H, Wang H (2017) Analysis and detection on noise characteristics of ac power transmission and transformation project in different voltage levels. In: 2017 2nd International Conference on Power and Renewable Energy (ICPRE), pp. 336–340. IEEE

  54. Girgis RS, Bernesjo M, Anger J (2009) Comprehensive analysis of load noise of power transformers. In: 2009 IEEE Power & Energy Society General Meeting, pp. 1–7. IEEE

  55. Huang Chuangxia, Liu Bingwen, Yang Hedi, Cao Jinde (2022) Positive almost periodicity on SICNNs incorporating mixed delays and D operator. Nonlinear Anal Model Control 27(4):719–739

    MathSciNet  MATH  Google Scholar 

  56. Wang W (2022) Further results on mean-square exponential Input-to-State stability of stochastic delayed Cohen-Grossberg neural networks. Neural Processing Letters, 1–13

Download references

Funding

This work was supported in part by the National Natural Science Foundation of China under Grants 62173176, 61863028, 81660299, and 61503177, and in part by the Science and Technology Department of Jiangxi Province of China under Grants 2020ABC03A39, 20161ACB21007, 20171BBE50071, and 20171BAB202033.

Author information

Author notes

  1. Chunquan Li and Boyu Zheng contributed equally to this work.

Authors and Affiliations

  1. School of Information Engineering, Nanchang University, Nanchang, 330031, China

    Chunquan Li, Boyu Zheng, Qingling Ou, Qianqian Wang, Chong Yue & Limin Chen

  2. School of Automation Science and Engineering, South China University of Technology, Guangzhou, 510640, China

    Zhijun Zhang

  3. State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, China

    Junzhi Yu

  4. State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, BIC-ESAT, College of Engineering, Peking University, Beijing, 100871, China

    Junzhi Yu

  5. Department of Systems and Computer Engineering, Carleton University, Ottawa, ON K1S 5B6, Canada

    Peter X. Liu

Authors
  1. Chunquan Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Boyu Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qingling Ou
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Qianqian Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Chong Yue
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Limin Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Zhijun Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Junzhi Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Peter X. Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Limin Chen.

Ethics declarations

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, C., Zheng, B., Ou, Q. et al. A novel varying-parameter periodic rhythm neural network for solving time-varying matrix equation in finite energy noise environment and its application to robot arm. Neural Comput & Applic 35, 22577–22593 (2023). https://doi.org/10.1007/s00521-023-08895-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-023-08895-1

Keywords

Search

Navigation