Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

An improving integration-enhanced ZNN for solving time-varying polytope distance problems with inequality constraint

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

Abstract

Time-varying polytope distance (TVPD) problems are prevalent in scientific and engineering applications and can be transformed into time-varying quadratic programming (TVQP) problems with both equality and inequality constraints. Concurrently, the noise interferences during the solution process are non-negligible and challenging to eliminate. Although zeroing neural networks (ZNNs) perform well in solving various types of time-varying problems, they still fall short in the suppression of unbounded noises, such as linear noise. To address this limitation, this paper proposes an improving integration-enhanced ZNN (IIEZNN) model for accurately solving TVPD problems under noise environments. Compared with the existing ZNN models, the IIEZNN model has stronger inherent robustness. The stability and robustness of the IIEZNN model are guaranteed by rigorous theoretical analysis. Firstly, the effectiveness of the IIEZNN model is verified via two TVQP examples. Then, the IIEZNN model is generalized to TVPD problem solving and has excellent performance. Specifically, in solving the TVPD under linear noises, the residual error of the IIEZNN model converges to the order of \(10^{-5}\), which is much lower than that of the existing noise-tolerant ZNN model with an order of \(10^{-1}\).

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Data availability

Data will be made available on request.

References

  1. Li Y, Hu X (2022) A differential game approach to intrinsic formation control. Automatica 136(110):077

    MathSciNet  Google Scholar 

  2. Foskey M, Lin MC, Manocha D (2003) Efficient computation of a simplified medial axis. In: Proceedings of the eighth ACM symposium on Solid modeling and applications, pp 96–107

  3. Fuhrmann A, Sobotka G, Groß C (2003) Distance fields for rapid collision detection in physically based modeling. In: Proceedings of GraphiCon, Citeseer 2003:58–65

  4. Tang Z, Zhang Y (2022) Refined self-motion scheme with zero initial velocities and time-varying physical limits via Zhang neurodynamics equivalency. Front Neurorobot 16(945):346

    Google Scholar 

  5. Jin L, Liao B, Liu M, Xiao L, Guo D, Yan X (2017) Different-level simultaneous minimization scheme for fault tolerance of redundant manipulator aided with discrete-time recurrent neural network. Front Neurorobot 11:50

    Article  Google Scholar 

  6. Zhang Y, Li S, Kadry S, Liao B (2019) Recurrent neural network for kinematic control of redundant manipulators with periodic input disturbance and physical constraints. IEEE Trans Cybern 49(12):4194–4205

    Article  Google Scholar 

  7. Zhang Z, Zheng L, Li L, Deng X, Xiao L, Huang G (2018) A new finite-time varying-parameter convergent-differential neural-network for solving nonlinear and nonconvex optimization problems. Neurocomputing 319:74–83

    Article  Google Scholar 

  8. Xiao L, Li L, Tao J, Li W (2023) A predefined-time and anti-noise varying-parameter ZNN model for solving time-varying complex stein equations. Neurocomputing 526:158–168

    Article  Google Scholar 

  9. 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 Cybern 48(11):3135–3148

    Article  Google Scholar 

  10. Sulaiman NA et al (2023) Solving cubic objective function programming problem by modification simplex method. Int J Nonlinear Anal Appl 14(2):159–165

    Google Scholar 

  11. Yang Y (2023) Attitude model predictive control with actuator saturation using an arc-search interior-point method. J Guid Control Dyn 46(4):726–733

    Article  Google Scholar 

  12. Hua C, Cao X, Liao B, Li S (2023) Advances on intelligent algorithms for scientific computing: an overview. Front Neurorobot 17(1190):977

    Google Scholar 

  13. Xiao L, Liao B, Li S, Zhang Z, Ding L, Jin L (2017) Design and analysis of FTZNN applied to the real-time solution of a nonstationary Lyapunov equation and tracking control of a wheeled mobile manipulator. IEEE Trans Industr Inf 14(1):98–105

    Article  Google Scholar 

  14. Nazemi A, Sabeghi A (2019) A novel gradient-based neural network for solving convex second-order cone constrained variational inequality problems. J Comput Appl Math 347:343–356

    Article  MathSciNet  Google Scholar 

  15. Li J, Shi Y, Xuan H (2020) Unified model solving nine types of time-varying problems in the frame of zeroing neural network. IEEE Trans Neural Netw Learn Syst 32(5):1896–1905

    Article  MathSciNet  Google Scholar 

  16. Jin L, Zhang Y, Li S, Zhang Y (2016) Noise-tolerant ZNN models for solving time-varying zero-finding problems: A control-theoretic approach. IEEE Trans Autom Control 62(2):992–997

    Article  MathSciNet  Google Scholar 

  17. Zhou T, Lin X, Wu J, Chen Y, Xie H, Li Y, Fan J, Wu H, Fang L, Dai Q (2021) Large-scale neuromorphic optoelectronic computing with a reconfigurable diffractive processing unit. Nat Photonics 15(5):367–373

    Article  Google Scholar 

  18. 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 

  19. Zhang Y, Li S, Weng J, Liao B (2024) GNN model for time-varying matrix inversion with robust finite-time convergence. IEEE Trans Neural Netw Learn Syst 35(1):559–569

    Article  MathSciNet  Google Scholar 

  20. Xiang Q, Liao B, Xiao L, Lin L, Li S (2019) Discrete-time noise-tolerant Zhang neural network for dynamic matrix pseudoinversion. Soft Comput 23:755–766

    Article  Google Scholar 

  21. Liao B, Wang Y, Li J, Guo D, He Y (2022) Harmonic noise-tolerant ZNN for dynamic matrix pseudoinversion and its application to robot manipulator. Front Neurorobot 16(928):636

    Google Scholar 

  22. Xiao L (2016) A nonlinearly-activated neurodynamic model and its finite-time solution to equality-constrained quadratic optimization with nonstationary coefficients. Appl Soft Comput 40:252–259

    Article  Google Scholar 

  23. Liao B, Zhang Y, Jin L (2016) Taylor \(o(h^{3})\) discretization of ZNN models for dynamic equality-constrained quadratic programming with application to manipulators. IEEE Trans Neural Netw Learn Syst 27(2):225–237

    Article  MathSciNet  Google Scholar 

  24. Li W, Ma X, Luo J, Jin L (2019) A strictly predefined-time convergent neural solution to equality-and inequality-constrained time-variant quadratic programming. IEEE Trans Syst Man Cybern: Syst 51(7):4028–4039

    Article  Google Scholar 

  25. Zhang Z, Kong LD, Zheng L (2018) Power-type varying-parameter RNN for solving TVQP problems: design, analysis, and applications. IEEE trans neural netw learn syst 30(8):2419–2433

    Article  MathSciNet  Google Scholar 

  26. Zhang Z, Li Z, Yang S (2021) A barrier varying-parameter dynamic learning network for solving time-varying quadratic programming problems with multiple constraints. IEEE Trans Cybern 52(9):8781–8792

    Article  Google Scholar 

  27. Zhang K, Zuo W, Chen Y, Meng D, Zhang L (2017) Beyond a gaussian denoiser: residual learning of deep cnn for image denoising. IEEE Trans Image Process 26(7):3142–3155

    Article  MathSciNet  Google Scholar 

  28. Liao B, Zhang Y (2014) Different complex ZFs leading to different complex ZNN models for time-varying complex generalized inverse matrices. IEEE Trans Neural Netw Learn Syst 25(9):1621–1631

    Article  Google Scholar 

  29. Li W, Xiao L, Liao B (2020) A finite-time convergent and noise-rejection recurrent neural network and its discretization for dynamic nonlinear equations solving. IEEE Trans Cybern 50(7):3195–3207

    Article  Google Scholar 

  30. Liao B, Xiang Q, Li S (2019) Bounded Z-type neurodynamics with limited-time convergence and noise tolerance for calculating time-dependent Lyapunov equation. Neurocomputing 325:234–241

    Article  Google Scholar 

  31. Bin Chai MT, Zhang Ke, Wang J (2023) Prescribed time convergence and robust zeroing neural network for solving time-varying linear matrix equation. Int J Comput Math 100(5):1094–1109

    Article  MathSciNet  Google Scholar 

  32. 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 

  33. Stanimirović PS, Katsikis VN, Li S (2019) Integration enhanced and noise tolerant znn for computing various expressions involving outer inverses. Neurocomputing 329:129–143

    Article  Google Scholar 

  34. Xiao L, Zhang Y, Zuo Q, Dai J, Li J, Tang W (2019) A noise-tolerant zeroing neural network for time-dependent complex matrix inversion under various kinds of noises. IEEE Trans Industr Inf 16(6):3757–3766

    Article  Google Scholar 

  35. Zhang Y (2006) A set of nonlinear equations and inequalities arising in robotics and its online solution via a primal neural network. Neurocomputing 70(1–3):513–524

    Article  Google Scholar 

  36. Nazemi A (2018) A capable neural network framework for solving degenerate quadratic optimization problems with an application in image fusion. Neural Process Lett 47:167–192

    Article  Google Scholar 

  37. Zhang Y, Yi C, Guo D, Zheng J (2011) Comparison on Zhang neural dynamics and gradient-based neural dynamics for online solution of nonlinear time-varying equation. Neural Comput Appl 20:1–7

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grants 62066015 and 62006095.

Author information

Authors and Affiliations

  1. College of Computer Science and Engineering, Jishou University, Jishou, 416000, Hunan, China

    Hao Li, Bolin Liao & Cheng Hua

  2. School of Communication and Electronic Engineering, Jishou University, Jishou, 416000, Hunan, China

    Hao Li & Cheng Hua

  3. School of Electronic Information and Electrical Engineering, Changsha university, Changsha, 410073, Hunan, China

    Zhen Zhang

Authors
  1. Hao Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhen Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bolin Liao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Cheng Hua
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bolin Liao.

Ethics declarations

Conflict of interest

All authors declare that they have no conflict of interest.

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, H., Zhang, Z., Liao, B. et al. An improving integration-enhanced ZNN for solving time-varying polytope distance problems with inequality constraint. Neural Comput & Applic 36, 18237–18250 (2024). https://doi.org/10.1007/s00521-024-10100-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-024-10100-w

Keywords

Search

Navigation