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Erschienen in: Neural Computing and Applications 1/2023

04.01.2021 | S.I. : Information, Intelligence, Systems and Applications

A better robustness and fast convergence zeroing neural network for solving dynamic nonlinear equations

verfasst von: Jianqiang Gong, Jie Jin

Erschienen in: Neural Computing and Applications | Ausgabe 1/2023

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Abstract

In this paper, a better fast convergence zeroing neural network (BFCZNN) model with a new activation function (AF) for solving dynamic nonlinear equations (DNE) and applying to control of robot manipulator is presented. The proposed BFCZNN model not only finds the solutions of DNE in fixed time, but also has better robustness than most of the previously reported studies. The numerical simulation results of the proposed BFCZNN and the previously reported robust nonlinear zeroing neural network (RNZNN) for solving third-order DNE in the same condition are presented to demonstrate the better robustness of our new BFCZNN model. Moreover, a successful kinematic control of robot manipulator of our new BFCZNN model is used to verify the realistic availability of the proposed BFCZNN model.

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Literatur
1.
Zurück zum Zitat Guo D, Zhang Y (2015) ZNN for solving online time-varying linear matrix–vector inequality via equality conversion. Appl Math Comput 259:327–338MathSciNetMATH Guo D, Zhang Y (2015) ZNN for solving online time-varying linear matrix–vector inequality via equality conversion. Appl Math Comput 259:327–338MathSciNetMATH
2.
Zurück zum Zitat Xiao L, Zhang Y (2014) Solving time-varying inverse kinematics problem of wheeled mobile manipulators using Zhang neural network with exponential convergence. Nonlinear Dyn 76(2):1543–1559CrossRef Xiao L, Zhang Y (2014) Solving time-varying inverse kinematics problem of wheeled mobile manipulators using Zhang neural network with exponential convergence. Nonlinear Dyn 76(2):1543–1559CrossRef
3.
Zurück zum Zitat Li S, Zhang Y, Jin L (2017) Kinematic control of redundant manipulators using neural networks. IEEE Trans Neural Netw Learn Syst 28(10):2243–2254MathSciNetCrossRef Li S, Zhang Y, Jin L (2017) Kinematic control of redundant manipulators using neural networks. IEEE Trans Neural Netw Learn Syst 28(10):2243–2254MathSciNetCrossRef
4.
Zurück zum Zitat Ngoc PHA, Anh TT (2019) Stability of nonlinear Volterra equations and applications. Appl Math Comput 341:1–14MathSciNetMATH Ngoc PHA, Anh TT (2019) Stability of nonlinear Volterra equations and applications. Appl Math Comput 341:1–14MathSciNetMATH
5.
Zurück zum Zitat Peng J, Wang J, Wang Y (2011) Neural network based robust hybrid control for robotic system: an H∞ approach. Nonlinear Dyn 65(4):421–431MathSciNetCrossRefMATH Peng J, Wang J, Wang Y (2011) Neural network based robust hybrid control for robotic system: an H∞ approach. Nonlinear Dyn 65(4):421–431MathSciNetCrossRefMATH
6.
Zurück zum Zitat Jin L, Zhang Y (2015) Discrete-time Zhang neural network for online time-varying nonlinear optimization with application to manipulator motion generation. IEEE Trans Neural Netw Learn Syst 26(7):1525–1531MathSciNetCrossRef Jin L, Zhang Y (2015) Discrete-time Zhang neural network for online time-varying nonlinear optimization with application to manipulator motion generation. IEEE Trans Neural Netw Learn Syst 26(7):1525–1531MathSciNetCrossRef
7.
Zurück zum Zitat Chun C (2006) Construction of Newton-like iteration methods for solving nonlinear equations. Numerische Mathematik 104(3):297–315MathSciNetCrossRefMATH Chun C (2006) Construction of Newton-like iteration methods for solving nonlinear equations. Numerische Mathematik 104(3):297–315MathSciNetCrossRefMATH
8.
Zurück zum Zitat Abbasbandy S (2003) Improving Newton-Raphson method for nonlinear equations by modified Adomian decomposition method. Appl Math Comput 145(2–3):887–893MathSciNetMATH Abbasbandy S (2003) Improving Newton-Raphson method for nonlinear equations by modified Adomian decomposition method. Appl Math Comput 145(2–3):887–893MathSciNetMATH
9.
Zurück zum Zitat Sharma JR (2005) A composite third order Newton-Steffensen method for solving nonlinear equations. Appl Mathe Comput 169(1):242–246MathSciNetCrossRefMATH Sharma JR (2005) A composite third order Newton-Steffensen method for solving nonlinear equations. Appl Mathe Comput 169(1):242–246MathSciNetCrossRefMATH
10.
Zurück zum Zitat Ujevic N (2006) A method for solving nonlinear equations. Applied Mathematics and Computation, 174(2): 1416-1426 Ujevic N (2006) A method for solving nonlinear equations. Applied Mathematics and Computation, 174(2): 1416-1426
11.
Zurück zum Zitat Wang J, Chen L, Guo Q (2017) Iterative solution of the dynamic responses of locally nonlinear structures with drift. Nonlinear Dyn 88(3):1551–1564CrossRef Wang J, Chen L, Guo Q (2017) Iterative solution of the dynamic responses of locally nonlinear structures with drift. Nonlinear Dyn 88(3):1551–1564CrossRef
12.
Zurück zum Zitat Y. Tang, L. Jiang, Y. Hou and R. Wang, (2017) "Contactless Fingerprint Image Enhancement Algorithm Based on Hessian Matrix and STFT," 2017 2nd International Conference on Multimedia and Image Processing (ICMIP), Wuhan, pp. 156-160, doi: https://doi.org/10.1109/ICMIP.2017.65 Y. Tang, L. Jiang, Y. Hou and R. Wang, (2017) "Contactless Fingerprint Image Enhancement Algorithm Based on Hessian Matrix and STFT," 2017 2nd International Conference on Multimedia and Image Processing (ICMIP), Wuhan, pp. 156-160, doi: https://​doi.​org/​10.​1109/​ICMIP.​2017.​65
13.
Zurück zum Zitat Amiri A, Cordero A, Darvishi MT et al (2019) A fast algorithm to solve systems of nonlinear equations. J Comput Appl Math 354:242–258MathSciNetCrossRefMATH Amiri A, Cordero A, Darvishi MT et al (2019) A fast algorithm to solve systems of nonlinear equations. J Comput Appl Math 354:242–258MathSciNetCrossRefMATH
14.
15.
Zurück zum Zitat Birgin EG, Martínez JM (2019) A Newton-like method with mixed factorizations and cubic regularization for unconstrained minimization. Comput Optim Appl 73(3):707–753MathSciNetCrossRefMATH Birgin EG, Martínez JM (2019) A Newton-like method with mixed factorizations and cubic regularization for unconstrained minimization. Comput Optim Appl 73(3):707–753MathSciNetCrossRefMATH
16.
Zurück zum Zitat Saheya B, Chen GQ, Sui YK et al (2016) A new Newton-like method for solving nonlinear equations. SpringerPlus 5(1):1269CrossRef Saheya B, Chen GQ, Sui YK et al (2016) A new Newton-like method for solving nonlinear equations. SpringerPlus 5(1):1269CrossRef
17.
Zurück zum Zitat Sharma JR, Arora H (2016) Improved Newton-like methods for solving systems of nonlinear equations. Sema J 74(2):1–17MathSciNet Sharma JR, Arora H (2016) Improved Newton-like methods for solving systems of nonlinear equations. Sema J 74(2):1–17MathSciNet
18.
Zurück zum Zitat Madhu K, Jayaraman J (2016) Some higher order Newton-like methods for solving system of nonlinear equations and its applications. Int J Appl Comput Math 1–18:2016 Madhu K, Jayaraman J (2016) Some higher order Newton-like methods for solving system of nonlinear equations and its applications. Int J Appl Comput Math 1–18:2016
19.
Zurück zum Zitat Ding F, Zhang H (2014) Brief Paper - Gradient-based iterative algorithm for a class of the coupled matrix equations related to control systems. IET Control Theory Appl 8(15):1588–1595MathSciNetCrossRef Ding F, Zhang H (2014) Brief Paper - Gradient-based iterative algorithm for a class of the coupled matrix equations related to control systems. IET Control Theory Appl 8(15):1588–1595MathSciNetCrossRef
20.
Zurück zum Zitat Zhang Z, Li Z, Zhang Y et al (2015) Neural-Dynamic-method-based dual-arm CMG scheme with time-varying constraints applied to humanoid robots. IEEE Trans Neural Netw Learn Syst 26(12):3251–3262MathSciNetCrossRef Zhang Z, Li Z, Zhang Y et al (2015) Neural-Dynamic-method-based dual-arm CMG scheme with time-varying constraints applied to humanoid robots. IEEE Trans Neural Netw Learn Syst 26(12):3251–3262MathSciNetCrossRef
21.
Zurück zum Zitat Li S, Zhang Y, Jin L (2017) Kinematic control of redundant manipulators using neural networks. IEEE Trans Neural Netw Learn Syst 28(10):2243–2254MathSciNetCrossRef Li S, Zhang Y, Jin L (2017) Kinematic control of redundant manipulators using neural networks. IEEE Trans Neural Netw Learn Syst 28(10):2243–2254MathSciNetCrossRef
22.
Zurück zum Zitat Xiao L, Liao B, Li S et al (2018) 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 Ind Inform 14(5):98–105CrossRef Xiao L, Liao B, Li S et al (2018) 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 Ind Inform 14(5):98–105CrossRef
23.
Zurück zum Zitat 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):1477–1490CrossRef 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):1477–1490CrossRef
24.
Zurück zum Zitat Chen K, Yi C (2016) Robustness analysis of a hybrid of recursive neural dynamics for online matrix inversion. Appl Math Comput 273:969–975MathSciNetMATH Chen K, Yi C (2016) Robustness analysis of a hybrid of recursive neural dynamics for online matrix inversion. Appl Math Comput 273:969–975MathSciNetMATH
25.
Zurück zum Zitat Chen K (2013) Recurrent implicit dynamics for online matrix inversion. Appl Math Comput 219:10218–10224MathSciNetMATH Chen K (2013) Recurrent implicit dynamics for online matrix inversion. Appl Math Comput 219:10218–10224MathSciNetMATH
26.
Zurück zum Zitat Zhang Y, Ge SS (2005) Design and analysis of a general recurrent neural network model for time-varying matrix inversion. IEEE Trans Neural Netw 16:1477–1490CrossRef Zhang Y, Ge SS (2005) Design and analysis of a general recurrent neural network model for time-varying matrix inversion. IEEE Trans Neural Netw 16:1477–1490CrossRef
27.
Zurück zum Zitat Li S, Chen S, Liu B (2013) Accelerating a recurrent neural network finite time convergence for solving time-varying Sylvester equation by using signbi-power activation function. Neural Proc Lett 37:189–205CrossRef Li S, Chen S, Liu B (2013) Accelerating a recurrent neural network finite time convergence for solving time-varying Sylvester equation by using signbi-power activation function. Neural Proc Lett 37:189–205CrossRef
28.
Zurück zum Zitat Xiao L, Liao B (2016) A convergence-accelerated Zhang neural network and its solution application to Lyapunov equation. Neurocomputing 193:213–218CrossRef Xiao L, Liao B (2016) A convergence-accelerated Zhang neural network and its solution application to Lyapunov equation. Neurocomputing 193:213–218CrossRef
29.
Zurück zum Zitat 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 350:108–116CrossRef 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 350:108–116CrossRef
31.
Zurück zum Zitat Xiao L, Zhang Y (2014) A new performance index for the repetitive motion of mobile manipulators. IEEE Trans Cybern 44(2):280–292CrossRef Xiao L, Zhang Y (2014) A new performance index for the repetitive motion of mobile manipulators. IEEE Trans Cybern 44(2):280–292CrossRef
32.
Zurück zum Zitat Shi Y, Jin L, Li S, Qiang J (2020) Proposing, developing and verification of a novel discrete-time zeroing neural network for solving future augmented Sylvester matrix equation. J Franklin Institute 357(6):636–3655MathSciNetCrossRefMATH Shi Y, Jin L, Li S, Qiang J (2020) Proposing, developing and verification of a novel discrete-time zeroing neural network for solving future augmented Sylvester matrix equation. J Franklin Institute 357(6):636–3655MathSciNetCrossRefMATH
33.
Zurück zum Zitat Shi Y, Zhang Y (2020) New discrete-time models of zeroing neural network solving systems of time-variant linear and nonlinear inequalities. IEEE Trans Syst Man Cybern: Syst 50(2):565–576MathSciNetCrossRef Shi Y, Zhang Y (2020) New discrete-time models of zeroing neural network solving systems of time-variant linear and nonlinear inequalities. IEEE Trans Syst Man Cybern: Syst 50(2):565–576MathSciNetCrossRef
34.
Zurück zum Zitat Y. Shi, L. Jin, S. Li, J. Li, J. (2020) Qiang, D. K. Gerontitis, Novel Discrete-Time Recurrent Neural Networks Handling Discrete-Form Time-Variant Multi-Augmented Sylvester Matrix Problems and Manipulator Application, IEEE Transactions on Neural Networks and Learning Systems, doi: https://doi.org/10.1109/TNNLS.2020.3028136. Y. Shi, L. Jin, S. Li, J. Li, J. (2020) Qiang, D. K. Gerontitis, Novel Discrete-Time Recurrent Neural Networks Handling Discrete-Form Time-Variant Multi-Augmented Sylvester Matrix Problems and Manipulator Application, IEEE Transactions on Neural Networks and Learning Systems, doi: https://​doi.​org/​10.​1109/​TNNLS.​2020.​3028136.
35.
Zurück zum Zitat Xiao L, Zhang Y (2014) A new performance index for the repetitive motion of mobile manipulators. IEEE Trans Cybern 44(2):280–292CrossRef Xiao L, Zhang Y (2014) A new performance index for the repetitive motion of mobile manipulators. IEEE Trans Cybern 44(2):280–292CrossRef
36.
Zurück zum Zitat Jin J, Zhao L, Li M et al (2020) Improved zeroing neural networks for finite time solving nonlinear equations. Neural Comput Appl 32:4151–4160CrossRef Jin J, Zhao L, Li M et al (2020) Improved zeroing neural networks for finite time solving nonlinear equations. Neural Comput Appl 32:4151–4160CrossRef
37.
Zurück zum Zitat Xiao L (2019) A finite-time convergent Zhang neural network and its application to real-time matrix square root finding. Neural Comput Appl 31:793–800CrossRef Xiao L (2019) A finite-time convergent Zhang neural network and its application to real-time matrix square root finding. Neural Comput Appl 31:793–800CrossRef
Metadaten
Titel
A better robustness and fast convergence zeroing neural network for solving dynamic nonlinear equations
verfasst von
Jianqiang Gong
Jie Jin
Publikationsdatum
04.01.2021
Verlag
Springer London
Erschienen in
Neural Computing and Applications / Ausgabe 1/2023
Print ISSN: 0941-0643
Elektronische ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-020-05617-9

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