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 Computing and Applications

Tipp

Weitere Artikel dieser Ausgabe durch Wischen aufrufen

Erschienen in: Neural Computing and Applications 3/2017

24.10.2015 | Original Article

Sampled-data synchronization of randomly coupled reaction–diffusion neural networks with Markovian jumping and mixed delays using multiple integral approach

verfasst von: R. Rakkiyappan, S. Dharani

Erschienen in: Neural Computing and Applications | Ausgabe 3/2017

Einloggen, um Zugang zu erhalten

Abstract

This paper is devoted to investigate the problem of global asymptotic synchronization of an array of N randomly coupled reaction–diffusion neural networks with Markovian jumping parameters and mixed delays using sampled-data control technique. The jump parameters are determined by a continuous-time, discrete-state Markovian chain, and the mixed time delays under consideration comprise both discrete and distributed delays. A multiple integral inequality is proposed firstly in Markovian jump reaction–diffusion neural networks with mixed delays. Through constructing appropriate Lyapunov–Krasovskii functional including multiple integral terms, some novel synchronization criteria in terms of linear matrix inequalities are derived. The obtained LMIs can be easily verified for feasibility through any of the available softwares. Finally, numerical examples with simulations are provided to illustrate the effectiveness of the proposed theoretical results.
Vorheriger Artikel Incorporating global search capability of a genetic algorithm into neural computing to model seismic records and soil test data
Nächster Artikel Hybridization of harmony search with hill climbing for highly constrained nurse rostering problem

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

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

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+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
Literatur
1.
Young S, Scott P, Nasrabadi N (1997) Object recognition using multilayer Hopfield neural network. IEEE Trans Image Process 6:357–372 CrossRef
2.
Atencia M, Joya G, Sandoval F (2005) Dynamical analysis of continuous higher order Hopfield networks for combinatorial optimization. Neural Comput 17:1802–1819 MathSciNetCrossRefMATH
3.
Sheikhan M, Shahnazi R, Garoucy S (2013) Synchronization of general chaotic systems using neural controllers with application to secure communication. Neural Comput Appl 22:361–373 CrossRef
4.
Huang H, Feng G (2009) Synchronization of nonidentical chaotic neural networks with time delays. Neural Netw 22:1841–1845 CrossRefMATH
5.
Li X, Ding C, Zhu Q (2010) Synchronization of stochastic perturbed chaotic neural networks with mixed delays. J Franklin Inst 347:1266–1280 MathSciNetCrossRefMATH
6.
Liang J, Wang Z, Li P (2009) Robust Synchronization of delayed neural networks with both linear and non-linear couplings. Int J Syst Sci 40:973–984 CrossRefMATH
7.
Grassi G, Mascolo S (1999) Synchronizing high dimensional chaotic systems via eigenvalue placement in application to cellular neural networks. Int J Bifurc Chaos 9:705–711 CrossRefMATH
8.
Zhang L (2009) \(H_\infty\) estimation for discrete-time piecewise homogeneous Markov jump linear systems. Automatica 45:2570–2576 MathSciNetCrossRefMATH
9.
Zhang W, Li C, Huang T, Qi J (2014) Global exponential synchronization for coupled switched delayed recurrent neural networks with stochastic perturbation and impulsive effects. Neural Comput Appl 25:1275–1283 CrossRef
10.
Cao J, Wan Y (2014) Matrix measure strategies for stability and synchronization for inertial BAM neural network with time delay. Neural Netw 53:165–172 CrossRefMATH
11.
12.
Gong D, Liu J, Zhou S (2015) Chaotic synchronization for coupled neural networks based on T-S fuzzy theory. Int J Syst Sci 46:681–689 CrossRefMATH
13.
Liu X (2010) Synchronization of linearly coupled neural networks with reaction–diffusion terms and unbounded time delays. Neurocomputing 73:2681–2888 CrossRef
14.
Wang K, Teng Z, Jiang H (2012) Adaptive synchronization in an array of linearly coupled neural networks with reaction–diffusion terms and time delays. Commun Nonlinear Sci Numer Simul 17:3866–3875 MathSciNetCrossRefMATH
15.
Yang X, Cao J, Yang Z (2013) Synchronization of coupled reaction–diffusion neural networks with time-varying delays via pinning-impulsive controller. SIAM J Control Optim 51:3486–3510 MathSciNetCrossRefMATH
16.
Hu C, Jiang H, Teng Z (2010) Impulsive control and synchronization for delayed neural networks with reaction–diffusion terms. IEEE Trans Neural Netw 21:67–81 CrossRef
17.
Liu Z, Peng J (2010) Delay-independent stability of stochastic reaction–diffusion neural networks with Dirichlet boundary conditions. Neural Comput Appl 19:151–158 CrossRef
18.
Wang Y, Cao J (2007) Synchronization of a class of delayed neural networks with reaction–diffusion terms. Phys Lett A 369:201–211 CrossRef
19.
Krasovskii NN, Lidskii EA (1961) Analysis and design of controllers in systems with random attributes. Autom Remote Control 22:1021–1025
20.
Liu Y, Wang Z, Liu X (2008) Exponential synchronization of complex networks with Markovian jump and mixed delays. Phys Lett A 372:3986–3998 MathSciNetCrossRefMATH
21.
Shen H, Xu S, Zhou J, Lu J (2011) Fuzzy \(H_\infty\) filtering for nonlinear Markovian jump neutral systems. Int J Syst Sci 42:767–780 MathSciNetCrossRefMATH
22.
Wang Z, Liu L, Liu X (2010) Exponential stability of a class of stochastic system with Markovian jump parameters and mode-dependent mixed time-delays. IEEE Trans Autom Control 55:1656–1662 CrossRef
23.
Chen B, Huang J, Niu Y (2012) Sliding mode control for Markovian jumping systems with actuator nonlinearities. Int J Syst Sci 43:656–664 MathSciNetCrossRefMATH
24.
Xu S, Chen T, Lam J (2003) Robust \(H_\infty\) filtering for uncertain Markovian jump systems with mode-dependent time delays. IEEE Trans Autom Control 48:900–908 CrossRef
25.
Liu Y (2009) Stochastic asymptotic stability of Markovian jumping neural networks with Markov mode estimation and mode-dependent delays. Phys Lett A 373:3741–3742 MathSciNetCrossRefMATH
26.
Zhang L, Boukas E, Lam J (2008) Analysis and synthesis of Markov jump linear systems with time-varying delays and partially known transition probabilities. IEEE Trans Autom Control 53:2458–2464 MathSciNetCrossRef
27.
Balasubramaniam P, Vembarasan V, Rakkiyappan R (1999) Delay-dependent robust exponential state estimation of Markovian jumping fuzzy Hopfield neural networks with mixed random time-varying. IEEE Trans Circuits Syst I Fundam Theory Appl 46:1144–1150 CrossRefMATH
28.
Wang L, Zhang Z, Wang Y (2008) Stochastic exponential stability of the delayed reaction–diffusion recurrent neural networks with Markovian jumping parameters. Phys Lett A 372:3201–3209 MathSciNetCrossRefMATH
29.
30.
Zheng CD, Zhang H, Wang Z (2014) Exponential synchronization of stochastic chaotic neural networks with mixed time delays and Markovian switching. Neural Comput Appl 25:429–442 CrossRef
31.
Yang X, Cao J, Lu J (2013) Synchronization of randomly coupled neural networks with Markovian jumping and time-delay. IEEE Trans Circuits Syst I Regul Pap 60:363–376 MathSciNetCrossRef
32.
Kao YG, Guo JF, Wang CH, Sun XQ (2012) Delay-dependent robust exponential stability of Markovian jumping reaction–diffusion Cohen-Grossberg neural networks with mixed delays. J Franklin Inst 349:1972–1988 MathSciNetCrossRefMATH
33.
34.
Shi G, Ma Q (2011) Synchronization of stochastic Markovian jump neural networks with reaction–diffusion terms. Neurocomputing 77:275–280 CrossRef
35.
Zhou J, Shen H, Wang Z (2012) Synchronization of delayed reaction–diffusion neural networks with markovian jumping parameters. In: The second international conference on computer application and system modeling
36.
Wang X, Li C, Huang T, Chen L (2014) Impulsive exponential synchronization of randomly coupled neural networks with Markovian jumping and mixed model-dependent time delays. Neural Netw 60:25–32 CrossRefMATH
37.
Zhang CK, He Y, Wu M (2010) Exponential synchronization of neural networks with time-varying mixed delays and sampled-data. Neurocomputing 74:265–273 CrossRef
38.
Li N, Zhang Y, Hu J, Nie Z (2011) Synchronization for general complex dynamical networks with sampled-data. Neurocomputing 74:805–811 CrossRef
39.
Liu YY, Yang GH (2012) Sampled-data \(H_\infty\) control for networked control systems with digital control inputs. Int J Syst Sci 43:1728–1740 MathSciNetCrossRefMATH
40.
41.
Kalpana M, Balasubramaniam P (2013) Stochastic asymptotical synchronization of chaotic Markovian jumping fuzzy cellular neural networks with mixed delays and the Wiener process based on sampled-data control. Chin Phys B 22:078401 CrossRef
42.
Zhang CK, He Y, Wu M (2009) Improved global asymptotical synchronization of chaotic Lur’e systems with sampled-data control. IEEE Trans Circuits Syst II Express Briefs 56:320–324 CrossRef
43.
Wu Z, Shi P, Su H, Chu J (2013) Stochastic synchronization of Markovian jump neural networks with time-varying delay using sampled-data. IEEE Trans Cybern 43:1796–1806 CrossRef
44.
Astrom K, Wittenmark B (1989) Adaptive control. Addison-Wesley, Reading
45.
Mikheev Y, Sobolev V, Fridman E (1988) Asymptotic analysis of digital control systems. Autom Remote Control 49:1175–1180 MathSciNetMATH
46.
Fang M, Park JH (2013) A multiple integral approach to stability of neutral time-delay systems. Appl Math Comput 224:714–718 MathSciNetMATH
47.
Wang J, Zhang H, Wang Z, Wang B (2013) Local exponential synchronization in complex dynamical networks with time-varying delay and hybrid coupling. Appl Math Comput 225:16–32 MathSciNetMATH
48.
Park JH, Lee TH (2015) Synchronization of complex dynamical networks with discontinuous coupling signals. Nonlinear Dyn 79:1353–1362 MathSciNetCrossRefMATH
49.
Fridman E, Seuret A, Richard JP (2004) Robust sampled-data stabilization of linear systems: an input delay approach. Automatica 40:1441–1446 MathSciNetCrossRefMATH
50.
Lu JG (2008) Global exponential stability and periodicity of reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions. Chaos Solitons Fractals 35:116–125 MathSciNetCrossRefMATH
51.
Zhang HG, Ma TD, Huang GB, Wang CX (2010) Robust global exponential synchronization of uncertain chaotic delayed neural networks via dual-stage impulsive control. IEEE Trans Syst Man Cybern B Cybern 40:831–844 CrossRef
52.
Yu W, Cao J, Chen G, Lu J, Han J, Wei W (2009) Local synchronization of a complex network model. IEEE Trans Syst Man Cybern B Cybern 39:230–241 CrossRef
53.
Chen J, Chen X (2001) Special matrices. Tsinghua University Press, Beijing
54.
Tahara S, Fujii T, Yokoyama T (2007) Variable sampling quasi multirate deadbeat control method for single phase PWM inverter in low carrier frequency. In: Power conversion conference (PCC), pp 804–809
55.
Hu B, Michel AN (2000) Stability analysis of digital feedback control systems with time-varying sampling periods. Automatica 36:897–905 MathSciNetCrossRefMATH
56.
57.
58.
Lee T, Park J, Lee S, Kwon O (2013) Robust synchronization of chaotic systems with randomly occurring uncertainties via stochastic sampled-data control. Int J Control 86:107–119 CrossRefMATH
59.
Lee T, Park J, Kwon O, Lee S (2013) Stochastic sampled-data control for state estimation of time-varying delayed neural networks. Neural Netw 46:99–108 CrossRefMATH
60.
Ding S, Wang Z (2015) Stochastic exponential synchronization control of Memristive neural networks with multiple time-varying delays. Neurocomputing 162:16–25 CrossRef
61.
Wang Z, Zhang H, Jiang B (2011) LMI-based approach for global asymptotic stability analysis of recurrent neural networks with various delays and structures. IEEE Trans Neural Netw 22:1032–1045 CrossRef
62.
Wang Z, Liu L, Shan Q-H, Zhang H Stability criteria for recurrent neural networks with time-varying delay based on secondary delay partitioning method. IEEE Trans Neural Netw Learn Syst. doi: 10.​1109/​TNNLS.​2014.​2387434
Metadaten
Titel
Sampled-data synchronization of randomly coupled reaction–diffusion neural networks with Markovian jumping and mixed delays using multiple integral approach
verfasst von
R. Rakkiyappan
S. Dharani
Publikationsdatum
24.10.2015
Verlag
Springer London
Erschienen in
Neural Computing and Applications / Ausgabe 3/2017
Print ISSN: 0941-0643
Elektronische ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-015-2079-5

Weitere Artikel der Ausgabe 3/2017

Neural Computing and Applications 3/2017 Zur Ausgabe

Original Article

Machine learning use in predicting interior spruce wood density utilizing progeny test information

Original Article

Using mixture design and neural networks to build stock selection decision support systems

Commentary

Comments on “Local coupled extreme learning machine”

Original Article

Hybridization of harmony search with hill climbing for highly constrained nurse rostering problem

Original Article

A hybrid model for supplier selection: integration of AHP and multi expression programming (MEP)

Original Article

Extension of Laplace transform–homotopy perturbation method to solve nonlinear differential equations with variable coefficients defined with Robin boundary conditions

Premium Partner