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Published in: Neural Processing Letters 3/2022

23-04-2022

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

Authors: Jiawei Luo, Hui Yang

Published in: Neural Processing Letters | Issue 3/2022

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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.
Literature
1.
go back to reference 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 CrossRef 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 CrossRef
2.
go back to reference 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 CrossRef 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 CrossRef
3.
go back to reference 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 CrossRef 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 CrossRef
4.
go back to reference 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 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
5.
go back to reference 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 MathSciNetCrossRef 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 MathSciNetCrossRef
6.
go back to reference 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 CrossRef 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 CrossRef
7.
go back to reference 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 CrossRef 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 CrossRef
8.
go back to reference 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 MathSciNetCrossRef 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 MathSciNetCrossRef
9.
go back to reference Li S, Liu B, Chen B, Lou Y (2013) Neural network based mobile phone localization using Bluetooth connectivity. Neural Comput Appl 23:667–675 CrossRef Li S, Liu B, Chen B, Lou Y (2013) Neural network based mobile phone localization using Bluetooth connectivity. Neural Comput Appl 23:667–675 CrossRef
11.
go back to reference 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 CrossRef 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 CrossRef
12.
go back to reference 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 CrossRef 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 CrossRef
13.
go back to reference 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 CrossRef 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 CrossRef
14.
go back to reference 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 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.
go back to reference 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 CrossRef 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 CrossRef
16.
go back to reference 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 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
17.
go back to reference 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 CrossRef 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 CrossRef
18.
go back to reference 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 MathSciNetCrossRef 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 MathSciNetCrossRef
19.
go back to reference 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 CrossRef 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 CrossRef
20.
go back to reference 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 CrossRef 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 CrossRef
21.
go back to reference 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 CrossRef 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 CrossRef
22.
go back to reference 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 MathSciNetCrossRef 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 MathSciNetCrossRef
23.
go back to reference 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 MathSciNetCrossRef 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 MathSciNetCrossRef
24.
go back to reference Jin L, Li S, Liao B, Zhang Z (2017) Zeroing neural networks: a survey. Neurocomputing 267:597–604 CrossRef Jin L, Li S, Liao B, Zhang Z (2017) Zeroing neural networks: a survey. Neurocomputing 267:597–604 CrossRef
25.
go back to reference 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 MathSciNetCrossRef 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 MathSciNetCrossRef
26.
go back to reference 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 MathSciNetCrossRef 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 MathSciNetCrossRef
27.
go back to reference 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 MathSciNetCrossRef 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 MathSciNetCrossRef
28.
go back to reference 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 CrossRef 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 CrossRef
29.
go back to reference 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 MathSciNetCrossRef 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 MathSciNetCrossRef
30.
go back to reference 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 CrossRef 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 CrossRef
31.
go back to reference 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 CrossRef 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 CrossRef
32.
go back to reference 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 CrossRef 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 CrossRef
33.
go back to reference 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 MathSciNetCrossRef 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 MathSciNetCrossRef
34.
go back to reference 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 MathSciNetCrossRef 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 MathSciNetCrossRef
35.
go back to reference 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 MathSciNetCrossRef 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 MathSciNetCrossRef
36.
go back to reference 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 MathSciNetCrossRef 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 MathSciNetCrossRef
37.
go back to reference 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 MathSciNetCrossRef 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 MathSciNetCrossRef
38.
go back to reference Zuo Z, Tie L (2016) Distributed robust finite-time nonlinear consensus protocols for multi-agent systems. Int J Syst Sci 47(6):1366–1375 MathSciNetCrossRef Zuo Z, Tie L (2016) Distributed robust finite-time nonlinear consensus protocols for multi-agent systems. Int J Syst Sci 47(6):1366–1375 MathSciNetCrossRef
39.
go back to reference 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 CrossRef 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 CrossRef
40.
go back to reference 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 CrossRef 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 CrossRef
41.
go back to reference 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 CrossRef 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 CrossRef
42.
go back to reference 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 CrossRef 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 CrossRef
Metadata
Title
A Robust Zeroing Neural Network Model Activated by the Special Nonlinear Function for Solving Time-Variant Linear System in Predefined-Time
Authors
Jiawei Luo
Hui Yang
Publication date
23-04-2022
Publisher
Springer US
Published in
Neural Processing Letters / Issue 3/2022
Print ISSN: 1370-4621
Electronic ISSN: 1573-773X
DOI
https://doi.org/10.1007/s11063-021-10726-0

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