Skip to main content
Fachgebiete
Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Weitere Formate
Webinare Technik
Webinare Wirtschaft
Kongresse
Veranstaltungskalender
Podcasts
Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen beantragen
Erweiterte Suche
Anmelden
nach oben
Neural Processing Letters

Tipp

Weitere Artikel dieser Ausgabe durch Wischen aufrufen

Erschienen in: Neural Processing Letters 5/2021

28.06.2021

A faster and better robustness zeroing neural network for solving dynamic Sylvester equation

verfasst von: Jianqiang Gong, Jie Jin

Erschienen in: Neural Processing Letters | Ausgabe 5/2021

Einloggen, um Zugang zu erhalten

Abstract

In this paper, a new zeroing neural network (NZNN) with a new activation function (AF) is presented and investigated for solving dynamic Sylvester equation (DSE). The proposed NZNN not only finds the solutions of the DSE in fixed-time but also has better robustness, and its superior effectiveness and robustness are proved by rigorous mathematical analysis. Numerical simulation results of the proposed NZNN, the original zeroing neural network activated by other recently reported AFs and the existing robust nonlinear ZNN (RNZNN) for solving second-order dynamic Sylvester equation and third-order dynamic Sylvester equation are provided for the purpose of comparison. Comparing with the existing ZNN models, the proposed NZNN has better robustness and faster convergence performance for solving DSE in the same noise environment. Moreover, a successful robot manipulator trajectory tracking example in noise-disturbed environment using the proposed NZNN is also applied for illustrating its further practical applications.
Vorheriger Artikel Continuous-Time Varying Complex QR Decomposition via Zeroing Neural Dynamics
Nächster Artikel Finite Time Synchronization of Delayed Quaternion Valued Neural Networks with Fractional Order

Sie möchten Zugang zu diesem Inhalt erhalten? Dann informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt 90 Tage mit der neuen Mini-Lizenz testen!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe



 


Jetzt 90 Tage mit der neuen Mini-Lizenz testen!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt 90 Tage mit der neuen Mini-Lizenz testen!

Jetzt informieren
Literatur
1.
Darouach M (2006) Solution to Sylvester equation associated to linear descriptor systems. Syst Control Lett 55(10):835–838 MathSciNetCrossRef
2.
Wei Q, Dobigeon N, J. Y. T (2015) Fast fusion of multi-band images based on solving a Sylvester equation. IEEE Trans on Image Processing 24(11): 4109–4121
3.
Castelan EB, Silva VG (2005) On the solution of a Sylvester equation appearing in descriptor systems control theory. Syst Control Lett 54(109–117):2005 MathSciNetMATH
4.
Li X, Yu J, Li S, Shao Z, Ni L (2019) A non-linear and noise-tolerant znn model and its application to static and time-varying matrix square root finding. Neural Process Lett 50:1687–1703 CrossRef
5.
Bartels RH, Stewart GW (1972) Solution of the matrix equation AX + XB = C. Commun ACM 15(9):820–826 CrossRef
6.
Li S, Li Y (2014) Nonlinearly activated neural network for solving time-varying complex Sylvester equation. IEEE Trans on Cybern 44(8):1397–1407 CrossRef
7.
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. Inf Process Lett 37(2):189–205 CrossRef
8.
Mathews JH, Fink KD (2004) Numerical methods using MATLAB. Pretice Hall, New Jersey
9.
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 MathSciNetCrossRef
10.
Xiao L (2019) A finite-time convergent Zhang neural network and its application to real-time matrix square root finding. Neural Comput Appl 31(2):793–800 CrossRef
11.
Jin L, Li S, Hu B, Liu M, Yu J (2018) Noise-suppressing neural algorithm for solving time-varying system of linear equations: a control-based approach. IEEE Trans Industr Inf 15(1):236–246 CrossRef
12.
Zhang Y, Jiang D, Wang J (2002) A recurrent neural network for solving Sylvester equation with time-varying coefficients. IEEE Trans Neural Network 13(5):1053–1063 CrossRef
13.
Jin L, Zhang Y, Li S (2017) Noise-Tolerant ZNN models for solving time-varying zero-finding problems: a control-theoretic approach. IEEE Trans Autom Control 62(2):992–997 MathSciNetCrossRef
14.
15.
Yi C, Chen Y, Lu Z (2011) Improved gradient-based neural networks for online solution of Lyapunov matrix equation. Inf Process Lett 111(16):780–786 MathSciNetCrossRef
16.
Yi C, Chen Y, Lan X (2013) Comparison on neural solvers for the Lyapunov matrix equation with stationary & nonstationary coefficients. Appl Math Modell 37(4):2495–2502 MathSciNetCrossRef
17.
Ding F, Chen T (2015) Iterative least squares solutions of coupled Sylvester matrix equations. Syst Control Lett 54:95–107 MathSciNetCrossRef
18.
Jin J, Zhao L, Li M, Yu F, Xi Z (2020) Improved zeroing neural networks for finite time solving nonlinear equations. Neural Comput Appl 32(2):4151–4160 CrossRef
19.
Jin J, Gong J (2021) An interference-tolerant fast convergence zeroing neural network for Dynamic Matrix Inversion and its application to mobile manipulator path tracking. Alex Eng J 60:659–669 CrossRef
20.
Zhang Y, Peng H.F (2007) Zhang neural network for linear time-varying equation solving and its robotic application. International conference on machine learning and cybernetics, pp 3543–3548
21.
Zhang Y, Chen K, Li X, Yi C, Zhu H (2008) Simulink modeling and comparison of Zhang neural networks and gradient neural networks for time-varying Lyapunov equation solving. Proc IEEE Int Confon Nat Comput 3:521–525
22.
Xiao L, Zhang Y (2013) Acceleration-level repetitive motion planning and its experimental verification on a six-link planar robotmanipulator. IEEE Trans Control Syst Technol 21(3):906–914 CrossRef
23.
24.
Xiao L, Zhang Y (2014) Solving time-varying inverse kinematics problem of wheeled mobile manipulators using Zhang neural network with exponential convergence. Nonlinear Dyn 76:1543–1559 CrossRef
25.
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
26.
Xiao L (2015) A finite-time convergent neural dynamics for online solution of time-varying linear complex matrix equation. Neurocomputing 167:254–259 CrossRef
27.
28.
Jin J, Xiao L, Lu M, Li J (2019) Design and Analysis of Two FTRNN models with application to time-varying Sylvester equation. IEEE Access 7:58945–58950 CrossRef
29.
Xiao L, Zhang Y, Hu Z, Dai J (2019) Performance benefits of robust nonlinear zeroing neural network for finding accurate solution of Lyapunov equation in presence of various noises. IEEE Trans Ind Inf 15(9):5161–5171 CrossRef
30.
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
31.
Xiao L, Zhang Y (2014) A new performance index for the repetitive motion of mobile manipulators. IEEE Trans Cybern 44(2):280–292 CrossRef
32.
33.
Zhang YN, Ding YQ, Qiu B, Zhang Y, Li XD (2017) Signum-function array activated ZNN with easier circuit implementation and finite-time convergence for linear systems solving. Inf Process Lett 124(2017):30–34 MathSciNetCrossRef
34.
Xiao L, Li K, Tan ZG, Zhang ZJ, Liao BL, Chen K, Jin L, Li S (2019) Nonlinear gradient neural network for solving system of linear equations. Inf Process Lett 142:35–40 MathSciNetCrossRef
Metadaten
Titel
A faster and better robustness zeroing neural network for solving dynamic Sylvester equation
verfasst von
Jianqiang Gong
Jie Jin
Publikationsdatum
28.06.2021
Verlag
Springer US
Erschienen in
Neural Processing Letters / Ausgabe 5/2021
Print ISSN: 1370-4621
Elektronische ISSN: 1573-773X
DOI
https://doi.org/10.1007/s11063-021-10516-8

Weitere Artikel der Ausgabe 5/2021

Neural Processing Letters 5/2021 Zur Ausgabe

OriginalPaper

The Study of Sailors’ Brain Activity Difference Before and After Sailing Using Activated Functional Connectivity Pattern

OriginalPaper

Opportunistic Activity Recognition in IoT Sensor Ecosystems via Multimodal Transfer Learning

OriginalPaper

CSCNN: Cost-Sensitive Convolutional Neural Network for Encrypted Traffic Classification

OriginalPaper

Common Spatial Pattern with L21-Norm

Correction

Correction to: Recent Deep Learning Techniques, Challenges and Its Applications for Medical Healthcare System: A Review

OriginalPaper

Cross-Domain Polarity Models to Evaluate User eXperience in E-learning