Skip to main content
Erschienen in: Neural Processing Letters 6/2022

29.04.2022

Robust Asymptotic Stability and Projective Synchronization of Time-Varying Delayed Fractional Neural Networks Under Parametric Uncertainty

verfasst von: Mengqi Li, Xujun Yang, Qiankun Song, Xiaofeng Chen

Erschienen in: Neural Processing Letters | Ausgabe 6/2022

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this paper, the robust asymptotic stability and projective synchronization of fractional-order time-varying delayed neural networks with uncertain parameters are studied. On account of the homeomorphism mapping theorem, free-weighting method and generalized Halanay inequality, several sufficient conditions of existence, uniqueness and asymptotic stability of the equilibrium point of the addressed models in the form of LMIs are established. In addition, some criteria ensuring the robust asymptotic projective synchronization between the master system and the slave system are deduced based on a suitable controller. Finally, two numerical simulations are designed to illustrate the effectiveness and rationality of the theoretical results.

Sie haben noch keine Lizenz? 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 Wissensvorsprung sichern!

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 Wissensvorsprung sichern!

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 Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Kulish VV, Lage JL (2002) Application of fractional calculus to fluid mechanics. J Fluids Eng 124(3):803–806CrossRef Kulish VV, Lage JL (2002) Application of fractional calculus to fluid mechanics. J Fluids Eng 124(3):803–806CrossRef
2.
Zurück zum Zitat Lundstrom BN, Higgs MH, Spain WJ, Fairhall AL (2008) Fractional differentiation by neocortical pyramidal neurons. Nat Neurosci 11:1335–1342CrossRef Lundstrom BN, Higgs MH, Spain WJ, Fairhall AL (2008) Fractional differentiation by neocortical pyramidal neurons. Nat Neurosci 11:1335–1342CrossRef
3.
Zurück zum Zitat Cao JD, Yuan K, Li HX (2006) Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays. IEEE Trans Neural Netw 17(6):1646–1651CrossRef Cao JD, Yuan K, Li HX (2006) Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays. IEEE Trans Neural Netw 17(6):1646–1651CrossRef
4.
Zurück zum Zitat Huang TW, Li CD, Duan SK, Starzyk JA (2012) Robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects. IEEE Trans Neural Netw Learn Syst 23(6):866–875CrossRef Huang TW, Li CD, Duan SK, Starzyk JA (2012) Robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects. IEEE Trans Neural Netw Learn Syst 23(6):866–875CrossRef
7.
Zurück zum Zitat Podlubny I (1999) Fractional differential equations. Academic Press Podlubny I (1999) Fractional differential equations. Academic Press
8.
Zurück zum Zitat Sabatier J, Moze M, Farges C (2010) LMI stability conditions for fractional order systems. Comput Math Appl 59(5):1594–1609MathSciNetCrossRefMATH Sabatier J, Moze M, Farges C (2010) LMI stability conditions for fractional order systems. Comput Math Appl 59(5):1594–1609MathSciNetCrossRefMATH
9.
Zurück zum Zitat Deng WH, Li CP, Lü JH (2007) Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dyn 48(4):409–416MathSciNetCrossRefMATH Deng WH, Li CP, Lü JH (2007) Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dyn 48(4):409–416MathSciNetCrossRefMATH
10.
Zurück zum Zitat Li Y, Chen YQ, Podlubny I (2009) Mittag-Leffler stability of fractional order nonlinear dynamic systems. Automatica 45(8):1965–1969MathSciNetCrossRefMATH Li Y, Chen YQ, Podlubny I (2009) Mittag-Leffler stability of fractional order nonlinear dynamic systems. Automatica 45(8):1965–1969MathSciNetCrossRefMATH
11.
Zurück zum Zitat Wang H, Yu YG, Wen GG, Zhang S, Yu JZ (2015) Global stability analysis of fractional-order Hopfield neural networks with time delay. Neurocomputing 154:15–23CrossRef Wang H, Yu YG, Wen GG, Zhang S, Yu JZ (2015) Global stability analysis of fractional-order Hopfield neural networks with time delay. Neurocomputing 154:15–23CrossRef
12.
Zurück zum Zitat Song QK, Chen YX, Zhao ZJ, Liu YR, Alsaadi FE (2021) Robust stability of fractional-order quaternion-valued neural networks with neutral delays and parameter uncertainties. Neurocomputing 420:70–81CrossRef Song QK, Chen YX, Zhao ZJ, Liu YR, Alsaadi FE (2021) Robust stability of fractional-order quaternion-valued neural networks with neutral delays and parameter uncertainties. Neurocomputing 420:70–81CrossRef
13.
Zurück zum Zitat Kaslik E, Sivasundaram S (2012) Nonlinear dynamics and chaos in fractional-order neural networks. Neural Netw 32:245–256CrossRefMATH Kaslik E, Sivasundaram S (2012) Nonlinear dynamics and chaos in fractional-order neural networks. Neural Netw 32:245–256CrossRefMATH
14.
Zurück zum Zitat Chen LP, Huang TW (2019) Delay-dependent criterion for asymptotic stability of a class of fractional-order memristive neural networks with time-varying delays. Neural Netw 118:289–299CrossRefMATH Chen LP, Huang TW (2019) Delay-dependent criterion for asymptotic stability of a class of fractional-order memristive neural networks with time-varying delays. Neural Netw 118:289–299CrossRefMATH
15.
Zurück zum Zitat Yang XJ, Song QK, Liu YR, Zhao ZJ (2015) Finite-time stability analysis of fractional-order neural networks with delay. Neurocomputing 152:19–26CrossRef Yang XJ, Song QK, Liu YR, Zhao ZJ (2015) Finite-time stability analysis of fractional-order neural networks with delay. Neurocomputing 152:19–26CrossRef
16.
Zurück zum Zitat Chen JY, Li CD, Yang XJ (2018) Asymptotic stability of delayed fractional-order fuzzy neural networks with impulse effects. J Frankl Inst 355(15):7595–7608MathSciNetCrossRefMATH Chen JY, Li CD, Yang XJ (2018) Asymptotic stability of delayed fractional-order fuzzy neural networks with impulse effects. J Frankl Inst 355(15):7595–7608MathSciNetCrossRefMATH
17.
Zurück zum Zitat Zhu H, He ZS, Zhou SB (2011) Lag synchronization of the fractional-order system via nonlinear observer. Int J Modern Phys B 25(29):3951–3964CrossRefMATH Zhu H, He ZS, Zhou SB (2011) Lag synchronization of the fractional-order system via nonlinear observer. Int J Modern Phys B 25(29):3951–3964CrossRefMATH
18.
Zurück zum Zitat Erjaee GH, Momani S (2008) Phase synchronization in fractional differential chaotic systems. Phys Lett A 372(14):2350–2354CrossRefMATH Erjaee GH, Momani S (2008) Phase synchronization in fractional differential chaotic systems. Phys Lett A 372(14):2350–2354CrossRefMATH
19.
Zurück zum Zitat Bao HB, Park JH, Cao JD (2015) Adaptive synchronization of fractional-order memristor-based neural networks with time delay. Nonlinear Dyn 82(3):1343–1354MathSciNetCrossRefMATH Bao HB, Park JH, Cao JD (2015) Adaptive synchronization of fractional-order memristor-based neural networks with time delay. Nonlinear Dyn 82(3):1343–1354MathSciNetCrossRefMATH
20.
Zurück zum Zitat Liu P, Kong MX, Zeng ZG (2020) Projective synchronization analysis of fractional-order neural networks with mixed time delays. IEEE Trans Cybern 1-11 Liu P, Kong MX, Zeng ZG (2020) Projective synchronization analysis of fractional-order neural networks with mixed time delays. IEEE Trans Cybern 1-11
21.
Zurück zum Zitat Yang XJ, Li CD, Song QK, Chen JY, Huang JJ (2018) Global Mittag-Leffler stability and synchronization analysis of fractional-order quaternion-valued neural networks with linear threshold neurons. Neural Netw 105:88–1033CrossRefMATH Yang XJ, Li CD, Song QK, Chen JY, Huang JJ (2018) Global Mittag-Leffler stability and synchronization analysis of fractional-order quaternion-valued neural networks with linear threshold neurons. Neural Netw 105:88–1033CrossRefMATH
22.
Zurück zum Zitat Xiao JY, Cao JD, Cheng J, Zhong SM, Wen SP (2020) Novel methods to finite-time Mittag-Leffler synchronization problem of fractional-order quaternion-valued neural networks. Inform Sci 526:221–244MathSciNetCrossRefMATH Xiao JY, Cao JD, Cheng J, Zhong SM, Wen SP (2020) Novel methods to finite-time Mittag-Leffler synchronization problem of fractional-order quaternion-valued neural networks. Inform Sci 526:221–244MathSciNetCrossRefMATH
23.
Zurück zum Zitat Li HL, Hu C, Cao JD, Jiang HJ, Alsaedi A (2019) Quasi-projective and complete synchronization of fractional-order complex-valued neural networks with time delays. Neural Netw 118:102–109CrossRefMATH Li HL, Hu C, Cao JD, Jiang HJ, Alsaedi A (2019) Quasi-projective and complete synchronization of fractional-order complex-valued neural networks with time delays. Neural Netw 118:102–109CrossRefMATH
24.
Zurück zum Zitat Wu A, Zeng ZG (2013) Anti-synchronization control of a class of memristive recurrent neural networks. Commun Nonlinear Sci Numer Simul 18(2):373–385MathSciNetCrossRefMATH Wu A, Zeng ZG (2013) Anti-synchronization control of a class of memristive recurrent neural networks. Commun Nonlinear Sci Numer Simul 18(2):373–385MathSciNetCrossRefMATH
25.
Zurück zum Zitat Zhang WW, Sha CL, Cao JD, Wang JL, Wang Y (2021) Adaptive quaternion projective synchronization of fractional order delayed neural networks in quaternion field. Appl Math Comput 400:126045MathSciNetMATH Zhang WW, Sha CL, Cao JD, Wang JL, Wang Y (2021) Adaptive quaternion projective synchronization of fractional order delayed neural networks in quaternion field. Appl Math Comput 400:126045MathSciNetMATH
26.
Zurück zum Zitat Yang SA, Yu J, Hu C, Jiang HJ (2018) Quasi-projective synchronization of fractional-order complex-valued recurrent neural networks. Neural Netw 104:104–113CrossRefMATH Yang SA, Yu J, Hu C, Jiang HJ (2018) Quasi-projective synchronization of fractional-order complex-valued recurrent neural networks. Neural Netw 104:104–113CrossRefMATH
27.
Zurück zum Zitat Bao HB, Cao JD (2015) Projective synchronization of fractional-order memristor-based neural networks. Neural Netw 63:1–9CrossRefMATH Bao HB, Cao JD (2015) Projective synchronization of fractional-order memristor-based neural networks. Neural Netw 63:1–9CrossRefMATH
28.
Zurück zum Zitat Chen JY, Li CD, Yang XJ (2018) Global Mittag-Leffler projective synchronization of nonidentical fractional-order neural networks with delay via sliding mode control. Neurocomput 313:324–332CrossRef Chen JY, Li CD, Yang XJ (2018) Global Mittag-Leffler projective synchronization of nonidentical fractional-order neural networks with delay via sliding mode control. Neurocomput 313:324–332CrossRef
29.
Zurück zum Zitat Chen JR, Jiao LC, Wu JS, Wang XD (2010) Projective synchronization with different scale factors in a driven-response complex network and its application in image encryption. Nonlinear Anal: Real World Appl 11(4):3045–3058CrossRefMATH Chen JR, Jiao LC, Wu JS, Wang XD (2010) Projective synchronization with different scale factors in a driven-response complex network and its application in image encryption. Nonlinear Anal: Real World Appl 11(4):3045–3058CrossRefMATH
30.
Zurück zum Zitat Wu XJ, Wang H, Lu HT (2011) Hyperchaotic secure communication via generalized function projective synchronization. Nonlinear Anal: Real World Appl 12(2):1288–1299MathSciNetCrossRefMATH Wu XJ, Wang H, Lu HT (2011) Hyperchaotic secure communication via generalized function projective synchronization. Nonlinear Anal: Real World Appl 12(2):1288–1299MathSciNetCrossRefMATH
31.
Zurück zum Zitat Li CD, Wu SC, Feng GG, Liao XF (2011) Stabilizing effects of impulses in discrete-time delayed neural networks. IEEE Trans Neural Netw 22(2):323–329CrossRef Li CD, Wu SC, Feng GG, Liao XF (2011) Stabilizing effects of impulses in discrete-time delayed neural networks. IEEE Trans Neural Netw 22(2):323–329CrossRef
32.
Zurück zum Zitat Yang XJ, Li CD, Huang TW, Song QK, Huang JJ (2018) Synchronization of fractional-order memristor-based complex-valued neural networks with uncertain parameters and time delays. Chaos, Solitons & Fractals 110:105–123MathSciNetCrossRefMATH Yang XJ, Li CD, Huang TW, Song QK, Huang JJ (2018) Synchronization of fractional-order memristor-based complex-valued neural networks with uncertain parameters and time delays. Chaos, Solitons & Fractals 110:105–123MathSciNetCrossRefMATH
33.
Zurück zum Zitat Chen XF, Li ZS, Song QK, Hu J (2017) Robust stability analysis of quaternion-valued neural networks with time delays and parameter uncertainties. Neural Netw 91:55–65CrossRefMATH Chen XF, Li ZS, Song QK, Hu J (2017) Robust stability analysis of quaternion-valued neural networks with time delays and parameter uncertainties. Neural Netw 91:55–65CrossRefMATH
34.
Zurück zum Zitat Huang WQ, Song QK, Zhao ZJ (2021) Robust stability for a class of fractional-order complex-valued projective neural networks with neutral-type delays and uncertain parameters. Neurocomputing 450(25):399–410CrossRef Huang WQ, Song QK, Zhao ZJ (2021) Robust stability for a class of fractional-order complex-valued projective neural networks with neutral-type delays and uncertain parameters. Neurocomputing 450(25):399–410CrossRef
35.
Zurück zum Zitat Xie LH, Fu MY (1992) \(H_\infty \) control and quadratic stabilization of systems with parameter uncertainty via output feedback. IEEE Trans Auto Control 37(8):1253–1256MathSciNetCrossRefMATH Xie LH, Fu MY (1992) \(H_\infty \) control and quadratic stabilization of systems with parameter uncertainty via output feedback. IEEE Trans Auto Control 37(8):1253–1256MathSciNetCrossRefMATH
36.
Zurück zum Zitat Liang S, Wu RC, Chen LP (2016) Adaptive pinning synchronization in fractional-order uncertain complex dynamical networks with delay. Phys A: Stat Mech Appl 444:49–62MathSciNetCrossRefMATH Liang S, Wu RC, Chen LP (2016) Adaptive pinning synchronization in fractional-order uncertain complex dynamical networks with delay. Phys A: Stat Mech Appl 444:49–62MathSciNetCrossRefMATH
39.
Zurück zum Zitat Diethelm K, Ford NJ, Freed AD (2002) A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dyn 29:3–22MathSciNetCrossRefMATH Diethelm K, Ford NJ, Freed AD (2002) A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dyn 29:3–22MathSciNetCrossRefMATH
Metadaten
Titel
Robust Asymptotic Stability and Projective Synchronization of Time-Varying Delayed Fractional Neural Networks Under Parametric Uncertainty
verfasst von
Mengqi Li
Xujun Yang
Qiankun Song
Xiaofeng Chen
Publikationsdatum
29.04.2022
Verlag
Springer US
Erschienen in
Neural Processing Letters / Ausgabe 6/2022
Print ISSN: 1370-4621
Elektronische ISSN: 1573-773X
DOI
https://doi.org/10.1007/s11063-022-10825-6

Weitere Artikel der Ausgabe 6/2022

Neural Processing Letters 6/2022 Zur Ausgabe

Neuer Inhalt