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A Robust Zeroing Neural Network Model Activated by the Special Nonlinear Function for Solving Time-Variant Linear System in Predefined-Time

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Abstract

The time-varying linear equations resolved by the Zeroing neural network (ZNN) models play very important roles in many areas. The traditional ZNN can only achieve the simple finite-time convergence problem, which makes ZNN very easy to be disturbed in the noisy environment. Since the initial state of ZNN is unknown, the finite time convergence depends on its initial state, so the ZNN models activated by the traditional nonlinear activations cannot deal with the different noise interference. To solve the above problems, a novel Power plus Sign activation function (PpSAF) is designed to activate the ZNN model. The predefined-time robust ZNN (PTR-ZNN) model activated by the simple and special nonlinear PpSAF is used to solve the time-variant linear system equations. Through theoretical analysis and simulation comparison of the system expected convergence time and noise tolerance performance, the numerical experiments present that the PTR-ZNN model possesses the predefined-time convergence and strong noise-tolerance performance, and also prove its superiority in solving time-varying linear system equations.

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References

  1. Li W (2018) A recurrent neural network with explicitly definable convergence time for solving time-variant linear matrix equations. IEEE Trans Ind Inf 14(12):5289–5298

    Article  Google Scholar 

  2. Li W, Ma X, Luo J, Jin L (2021) A strictly predefined-time convergent neural solution to equality- and inequality-constrained time-variant quadratic programming. IEEE Trans Syst Man Cybern 51(7):4028–4039

    Article  Google Scholar 

  3. 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 

  4. Zhang Z, Zheng L, Yang H, Qu X (2019) Design and analysis of a novel integral recurrent neural network for solving time-varying sylvester equation. IEEE Trans Cybern 16(6):1477–1490

    Google Scholar 

  5. Dong L, Zhong X, Sun C, He H (2017) Adaptive event-triggered control based on heuristic dynamic programming for nonlinear discrete-time systems. IEEE Trans Neural Netw Learning Syst 28(7):1594–1605

    Article  MathSciNet  Google Scholar 

  6. Chen D, Zhang Y (2018) Robust zeroing neural-dynamics and its time-varying disturbances suppression model applied to mobile robot manipulators. IEEE Trans Neural Netw Learning Syst 29(9):4385–4397

    Article  Google Scholar 

  7. Jin Long, Zhang Yunong, Li Shuai, Zhang Yinyan (2016) Modified ZNN for time-varying quadratic programming with inherent tolerance to noises and its application to kinematic redundancy resolution of robot manipulators. IEEE Trans Ind Ele 63(11):6978–6988

    Article  Google Scholar 

  8. Xiao L (2016) A new design formula exploited for accelerating Zhang neural network and its application to time-varying matrix inversion. Theor Comput Sci 647:50–58

    Article  MathSciNet  Google Scholar 

  9. Li S, Liu B, Chen B, Lou Y (2013) Neural network based mobile phone localization using Bluetooth connectivity. Neural Comput Appl 23:667–675

    Article  Google Scholar 

  10. Xiao L (2017) A finite-time convergent Zhang neural network and its application to real-time matrix square root finding. Neural Comput Appl. https://doi.org/10.1007/s00521-017-3010-z

  11. Li S, Cui H, Li Y, Liu B, Lou Y (2013) Decentralized control of collaborative redundant manipulators with partial command coverage via locally connected recurrent neural networks. Neural Comput Appl 23:1051–1060

    Article  Google Scholar 

  12. 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 

  13. Xiao L, Zhang Y (2014) From different Zhang functions to various ZNN models accelerated to finite-time convergence for time-varying linear matrix equation. Neural Process Lett 39:309–326

    Article  Google Scholar 

  14. Guo D, Zhang Y (2012) Zhang neural network, Getz-Marsden dynamic system, and discrete-time algorithms for time-varying matrix inversion with application to robots’ kinematic control. Neurocomputing 97:22–32

  15. Li W, Su Z, Tan Z (2019) A variable-gain finite-time convergent recurrent neural network for time-variant quadratic programming with unknown noises endured. IEEE Trans Ind Inf 15(9):5330–5340

    Article  Google Scholar 

  16. Zhang Y, Zhang Y, Chen D, Xiao Z, Yan X (2016) From Davidenko method to Zhang dynamics for nonlinear equation systems solving. IEEE Trans Syst Man Cybern 99:1–14

    Google Scholar 

  17. Jin L, Zhang Y, Qiao T, Tan M, Zhang Y (2016) Tracking control of modified Lorenz nonlinear system using ZG neural dynamics with additive input or mixed inputs. Neurocomputing 196:82–94

    Article  Google Scholar 

  18. Dai J, Jia L, Xiao L (2021) Design and analysis of two prescribed-time and robust ZNN models with application to time-variant Stein matrix equation. IEEE Trans Neural Netw Learning Syst 32(4):1668–1677

    Article  MathSciNet  Google Scholar 

  19. Li S, Li Y, Wang Z (2013) A class of finite-time dual neural networks for solving quadratic programming problems and its k-winners-take-all application. Neural Netw 39:27–39

    Article  Google Scholar 

  20. Feng J, Qin S, Shi F, Zhao X (2018) A recurrent neural network with finite-time convergence for convex quadratic bilevel programming problems. Neural Comput Appl 30(11):3399–3408

    Article  Google Scholar 

  21. Tan Z, Hu Y, Xiao L, Chen K (2019) Robustness analysis and robotic application of combined function sctivated RNN for time-varying matrix pseudo inversion. IEEE Access 7:33434–33440

    Article  Google Scholar 

  22. Qiu B, Zhang Y, Yang Z (2018) New discrete-time ZNN models for least-squares solution of dynamic linear equation system with time-varying rank-deficient coefficient. IEEE Trans Neural Netw Learning Syst 29(11):5767–5776

    Article  MathSciNet  Google Scholar 

  23. Xiao L, Li K, Duan M (2019) Computing time-varying quadratic optimization with finite-time convergence and noise tolerance: a unified framework for zeroing neural network. IEEE Trans Neural Netw Learning Syst 30(11):3360–3369

    Article  MathSciNet  Google Scholar 

  24. Jin L, Li S, Liao B, Zhang Z (2017) Zeroing neural networks: a survey. Neurocomputing 267:597–604

    Article  Google Scholar 

  25. Liu J, Zhang Y, Yu Y, Sun C (2020) Fixed-time leader-follower consensus of networked nonlinear systems via event/self-triggered control. IEEE Trans Neural Netw Learn Syst 31(11):5029–5037

    Article  MathSciNet  Google Scholar 

  26. Liu J, Zhang Y, Sun C, Yu Y (2019) Fixed-time consensus of multi-agent systems with input delay and uncertain disturbances via event-triggered control. Inf Sci 480:261–272

    Article  MathSciNet  Google Scholar 

  27. Liu J, Yu Y, Sun J, Sun C (2018) Distributed event-triggered fixed-time consensus for leader-follower multiagent systems with nonlinear dynamics and uncertain disturbances. Int J Robust Nonlinear Control 28(11):3543–3559

    Article  MathSciNet  Google Scholar 

  28. Liang H, Guo X, Pan Y, Huang T (2021) Event-triggered fuzzy bipartite tracking control for network systems based on distributed reduced-order observers. IEEE Transa Fuzzy Syst 29(6):1601–1614

    Article  Google Scholar 

  29. Liang H, Liu G, Zhang H, Huang T (2020) Neural-network-based event-triggered adaptive control of nonaffine nonlinear multiagent systems with dynamic uncertainties. IEEE Trans Neural Netw Learn Syst 32(5):2239–2250

    Article  MathSciNet  Google Scholar 

  30. Liang H, Zhang Y, Huang T, Ma H (2020) Prescribed performance cooperative control for multiagent systems with input quantization. IEEE Trans Cybern 50(5):1810–1819

    Article  Google Scholar 

  31. Yu F, Liu L, Xiao L, Li K, Cai S (2019) A robust and fixed-time zeroing neural dynamics for computing time-variant nonlinear equation using a novel nonlinear activation function. Neurocomputing 350:108–116

    Article  Google Scholar 

  32. Li W, Liao B, Xiao L, Lu R (2019) A recurrent neural network with predefined-time convergence and improved noise tolerance for dynamic matrix square root finding. Neurocomputing 337:262–273

    Article  Google Scholar 

  33. Xu F, Li Z, Nie Z, Shao H, Guo D (2018) Zeroing neural network for solving time-varying linear equation and inequality systems. IEEE Trans Neural Netw Learning Syst 30(8):2346–2357

    Article  MathSciNet  Google Scholar 

  34. Li J, Zhang Y, Mao M (2019) General square-pattern discretization formulas via second-order derivative elimination for zeroing neural network illustrated by future optimization. IEEE Trans Neural Netw Learning Syst 30(3):891–901

    Article  MathSciNet  Google Scholar 

  35. Tan Z, Li W, Xia L, Hu Y (2020) New varying-parameter ZNN models with finite-time convergence and noise suppression for time-varying matrix moore-penrose inversion. IEEE Trans Neural Netw Learning Syst 31(8):2980–2992

    Article  MathSciNet  Google Scholar 

  36. Xiao L, Dai J, Lu R, Li S, Li J, Wang S (2020) Design and comprehensive analysis of a noise-tolerant ZNN model with limited-time convergence for time-dependent nonlinear minimization. IEEE Trans Neural Netw Learning Syst 31(12):5339–5348

    Article  MathSciNet  Google Scholar 

  37. Zuo Z, Tie L (2014) A new class of finite-time nonlinear consensus protocols for multi-agent systems. Int J Control 87(2):363–370

    Article  MathSciNet  Google Scholar 

  38. Zuo Z, Tie L (2016) Distributed robust finite-time nonlinear consensus protocols for multi-agent systems. Int J Syst Sci 47(6):1366–1375

    Article  MathSciNet  Google Scholar 

  39. Xiao L, Zhang Z, Li S (2019) Solving time-varying system of nonlinear equations by finite-time recurrent neural networks with application to motion tracking of robot manipulators. IEEE Trans Syst Man Cybern Syst 49(11):2210–2220

    Article  Google Scholar 

  40. Luo J, Li K, Yang H, Yang J (2020) Comparison on inverse-free method and psuedoinverse method for fault-tolerant planning of redundant manipulator. IEEE Access 8:178796–178804

    Article  Google Scholar 

  41. Xiao L, Tao J, Dai J, Wang Y, Jia L, He Y (2021) A parameter-changing and complex-valued zeroing neural-network for finding solution of time-varying complex linear matrix equations in finite time. IEEE Trans Ind Inform 17(10):6634–6643

    Article  Google Scholar 

  42. Zhang Y, Li Z (2009) Zhang neural network for online solution of time-varying convex quadratic program subject to time-varying linear-equality constraints. Phys Lett A 373(18):1639–1643

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (NSFC) under grants (61733005,61673172); by the Science and Technology Research Project in Jiangxi Education Department under grants GJJ207310 and the Teaching Reform Research Topic of Higher Education in Jiangxi province grants JXJG20653.

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Authors and Affiliations

  1. School of Electrical and Automation Engineering, The Key Laboratory of Advanced Control and Optimization of Jiangxi Province, East China Jiaotong University, Nanchang, 330013, China

    Jiawei Luo & Hui Yang

  2. Jiangxi Vocational College of Industry and Engineering, Pingxiang, China

    Jiawei Luo

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  1. Jiawei Luo
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  2. Hui Yang
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Correspondence to Hui Yang.

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Luo, J., Yang, H. A Robust Zeroing Neural Network Model Activated by the Special Nonlinear Function for Solving Time-Variant Linear System in Predefined-Time. Neural Process Lett 54, 2201–2217 (2022). https://doi.org/10.1007/s11063-021-10726-0

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