Skip to main content
Erschienen in: Neural Processing Letters 3/2020

05.02.2020

Finite-Time and Fixed-Time Non-chattering Control for Inertial Neural Networks with Discontinuous Activations and Proportional Delay

verfasst von: Dengguo Xu, Xinsong Yang, Rongqiang Tang

Erschienen in: Neural Processing Letters | Ausgabe 3/2020

Einloggen

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

search-config
loading …

Abstract

Based on the framework of Filippov solutions, this paper considers synchronization of inertial neural networks (INNs) with discontinuous activation functions and proportional delay. By designing several non-chattering controllers, both finite-time and fixed-time synchronization are studied. The designed controllers are simple to be implemented and can overcome the effects of both nonidentical uncertainties of Filippov solutions and the proportional delay without inducing any chattering. By designing new Lyapunov functionals and utilizing 1-norm methods, several sufficient conditions are obtained to ensure that the INNs achieve drive-response synchronization in finite time and fixed time, respectively. Moreover, the settling time is estimated for the two types of synchronization. Simulations are provided to illustrate the effectiveness of theoretical analysis.

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 Utkin V (1977) Variable structure systems with sliding modes. IEEE Trans Autom Control 22:212–222MathSciNetMATH Utkin V (1977) Variable structure systems with sliding modes. IEEE Trans Autom Control 22:212–222MathSciNetMATH
2.
Zurück zum Zitat Marco M, Forti M, Nistri P, Pancioni L (2016) Discontinuous neural networks for finite-time solution of time-dependent linear equations. IEEE Trans Cyber 46(11):2509–2520 Marco M, Forti M, Nistri P, Pancioni L (2016) Discontinuous neural networks for finite-time solution of time-dependent linear equations. IEEE Trans Cyber 46(11):2509–2520
3.
Zurück zum Zitat Nie X, Zheng WX (2016) Dynamical behaviors of multiple equilibria in competitive neural networks with discontinuous nonmonotonic piecewise linear activation functions. IEEE Trans Cyber 46(3):679–693 Nie X, Zheng WX (2016) Dynamical behaviors of multiple equilibria in competitive neural networks with discontinuous nonmonotonic piecewise linear activation functions. IEEE Trans Cyber 46(3):679–693
4.
Zurück zum Zitat Forti M, Nistri P (2003) Global convergence of neural networks with discontinuous neuron activations. IEEE Trans Circ Syst I Reg Pap 50(11):1421–1435MathSciNetMATH Forti M, Nistri P (2003) Global convergence of neural networks with discontinuous neuron activations. IEEE Trans Circ Syst I Reg Pap 50(11):1421–1435MathSciNetMATH
5.
Zurück zum Zitat Forti M, Nistri P, Papini D (2005) Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain. IEEE Trans Neural Netw 16(6):1449–1463 Forti M, Nistri P, Papini D (2005) Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain. IEEE Trans Neural Netw 16(6):1449–1463
6.
Zurück zum Zitat Huang C, Lu J, Ho DWC, Zhai G, Cao J (2020) Stabilization of probabilistic Boolean networks via pinning control strategy. Inf Sci 510:205–217MathSciNet Huang C, Lu J, Ho DWC, Zhai G, Cao J (2020) Stabilization of probabilistic Boolean networks via pinning control strategy. Inf Sci 510:205–217MathSciNet
8.
Zurück zum Zitat Forti M, Nistri P, Quincampoix M (2004) Generalized neural network for nonsmooth nonlinear programming problems. IEEE Trans Circ Syst I Reg Pap 51:1741–1754MathSciNetMATH Forti M, Nistri P, Quincampoix M (2004) Generalized neural network for nonsmooth nonlinear programming problems. IEEE Trans Circ Syst I Reg Pap 51:1741–1754MathSciNetMATH
9.
Zurück zum Zitat Yang X, Cao J, Xu C, Feng J (2018) Finite-time stabilization of switched dynamical networks with quantized couplings via quantized controller. Sci China Technol Sci 61(2):299–308 Yang X, Cao J, Xu C, Feng J (2018) Finite-time stabilization of switched dynamical networks with quantized couplings via quantized controller. Sci China Technol Sci 61(2):299–308
10.
Zurück zum Zitat Wang G, Shen Y, Yin Q (2015) Synchronization analysis of coupled stochastic neural networks with on-off coupling and time-delay. Neural Process Lett 42(2):501–515 Wang G, Shen Y, Yin Q (2015) Synchronization analysis of coupled stochastic neural networks with on-off coupling and time-delay. Neural Process Lett 42(2):501–515
11.
Zurück zum Zitat Song Y, Sun W (2017) Adaptive synchronization of stochastic memristor-based neural networks with mixed delays. Neural Process Lett 46(3):969–990 Song Y, Sun W (2017) Adaptive synchronization of stochastic memristor-based neural networks with mixed delays. Neural Process Lett 46(3):969–990
12.
Zurück zum Zitat Li Y, Lou J, Wang Z, Alsaadi FE (2018) Synchronization of dynamical networks with nonlinearly coupling function under hybrid pinning impulsive controllers. J Frankl Inst 355(14):6520–6530MathSciNetMATH Li Y, Lou J, Wang Z, Alsaadi FE (2018) Synchronization of dynamical networks with nonlinearly coupling function under hybrid pinning impulsive controllers. J Frankl Inst 355(14):6520–6530MathSciNetMATH
13.
Zurück zum Zitat Liu X, Chen T, Cao J, Lu W (2011) Dissipativity and quasi-synchronization for neural networks with discontinuous activations and parameter mismatches. Neural Netw 24:1013–1021MATH Liu X, Chen T, Cao J, Lu W (2011) Dissipativity and quasi-synchronization for neural networks with discontinuous activations and parameter mismatches. Neural Netw 24:1013–1021MATH
14.
Zurück zum Zitat Yang J, Lu J, Lou J, Liu Y (2020) Synchronization of drive-response Boolean control networks with impulsive disturbances. Appl Math Comput 364:124679MathSciNetMATH Yang J, Lu J, Lou J, Liu Y (2020) Synchronization of drive-response Boolean control networks with impulsive disturbances. Appl Math Comput 364:124679MathSciNetMATH
15.
Zurück zum Zitat Liu X, Cao J, Yu W (2012) Filippov systems and quasi-synchronization control for switched networks. Chaos 22:033110MathSciNetMATH Liu X, Cao J, Yu W (2012) Filippov systems and quasi-synchronization control for switched networks. Chaos 22:033110MathSciNetMATH
16.
Zurück zum Zitat Yang X, Cao J (2013) Exponential synchronization of delayed neural networks with discontinuous activations. IEEE Trans Circ Syst I Reg Pap 60(9):2431–2439MathSciNet Yang X, Cao J (2013) Exponential synchronization of delayed neural networks with discontinuous activations. IEEE Trans Circ Syst I Reg Pap 60(9):2431–2439MathSciNet
18.
Zurück zum Zitat Wu E, Yang X, Xu C, Alsaadi FE, Hayat T (2018) Finite-time synchronization of complex-valued delayed neural networks with discontinuous activations. Asian J Control 20(6):2237–2247MathSciNetMATH Wu E, Yang X, Xu C, Alsaadi FE, Hayat T (2018) Finite-time synchronization of complex-valued delayed neural networks with discontinuous activations. Asian J Control 20(6):2237–2247MathSciNetMATH
19.
Zurück zum Zitat Babcock KL, Westervelt RM (1986) Stability and dynamics of simple electronic neural networks with added inertia. Phys D 28(1–3):464–469 Babcock KL, Westervelt RM (1986) Stability and dynamics of simple electronic neural networks with added inertia. Phys D 28(1–3):464–469
20.
Zurück zum Zitat Wheeler DW, Schieve WC (1997) Stability and chaos in an inertial two neuron system. Phys D 105(4):267–284MATH Wheeler DW, Schieve WC (1997) Stability and chaos in an inertial two neuron system. Phys D 105(4):267–284MATH
21.
Zurück zum Zitat Cao J, Wan Y (2014) Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays. Neural Netw 53(5):165–172MATH Cao J, Wan Y (2014) Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays. Neural Netw 53(5):165–172MATH
22.
Zurück zum Zitat Hu J, Cao J, Alofi A, AL-Mazrooei A, Elaiw A (2015) Pinning synchronization of coupled inertial delayed neural networks. Cogn Neurodyn 9(3):35–42 Hu J, Cao J, Alofi A, AL-Mazrooei A, Elaiw A (2015) Pinning synchronization of coupled inertial delayed neural networks. Cogn Neurodyn 9(3):35–42
24.
Zurück zum Zitat Li X, Li X, Hu C (2017) Some new results on stability and synchronization for delayed inertial neural networks based on non-reduced order method. Neural Netw 96:91–100MATH Li X, Li X, Hu C (2017) Some new results on stability and synchronization for delayed inertial neural networks based on non-reduced order method. Neural Netw 96:91–100MATH
25.
26.
Zurück zum Zitat Yang X, Wu Z, Cao J (2013) Finite-time synchronization of complex networks with nonidentical discontinuous nodes. Nonlinear Dyn 73(4):2313–2327MathSciNetMATH Yang X, Wu Z, Cao J (2013) Finite-time synchronization of complex networks with nonidentical discontinuous nodes. Nonlinear Dyn 73(4):2313–2327MathSciNetMATH
27.
Zurück zum Zitat Xu C, Yang X, Lu J, Feng J, Alsaadi FE, Hayat T (2018) Finite-time synchronization of networks via quantized intermittent pinning control. IEEE Trans Cyber 48(10):3021–3027 Xu C, Yang X, Lu J, Feng J, Alsaadi FE, Hayat T (2018) Finite-time synchronization of networks via quantized intermittent pinning control. IEEE Trans Cyber 48(10):3021–3027
28.
Zurück zum Zitat Yang X, Lu J (2016) Finite-time synchronization of coupled networks with Markovian topology and impulsive effects. IEEE Trans Autom Control 61(8):2256–2261MathSciNetMATH Yang X, Lu J (2016) Finite-time synchronization of coupled networks with Markovian topology and impulsive effects. IEEE Trans Autom Control 61(8):2256–2261MathSciNetMATH
29.
Zurück zum Zitat Yang X, Song Q, Liang J, He B (2015) Finite-time synchronization of coupled discontinuous neural networks with mixed delays and nonidentical perturbations. J Frankl Inst 352(10):4382–4406MathSciNetMATH Yang X, Song Q, Liang J, He B (2015) Finite-time synchronization of coupled discontinuous neural networks with mixed delays and nonidentical perturbations. J Frankl Inst 352(10):4382–4406MathSciNetMATH
30.
Zurück zum Zitat Yang X, Ho DWC (2016) Synchronization of delayed memristive neural networks: robust analysis approach. IEEE Trans Cyber 46(12):3377–3387 Yang X, Ho DWC (2016) Synchronization of delayed memristive neural networks: robust analysis approach. IEEE Trans Cyber 46(12):3377–3387
31.
Zurück zum Zitat Yang X, Ho DWC, Lu J, Song Q (2015) Finite-time cluster synchronization of T–S fuzzy complex networks with discontinuous subsystems and random coupling delays. IEEE Trans Fuzzy Syst 23(6):2302–2316 Yang X, Ho DWC, Lu J, Song Q (2015) Finite-time cluster synchronization of T–S fuzzy complex networks with discontinuous subsystems and random coupling delays. IEEE Trans Fuzzy Syst 23(6):2302–2316
32.
Zurück zum Zitat Yang X (2014) Can neural networks with arbitrary delays be finite-timely synchronized? Neurocomputing 143(2):275–281 Yang X (2014) Can neural networks with arbitrary delays be finite-timely synchronized? Neurocomputing 143(2):275–281
33.
Zurück zum Zitat Wei R, Cao J, Alsaedi A (2018) Finite-time and fixed-time synchronization analysis of inertial memristive neural networks with time-varying delays. Cogn Neurodyn 12(1):121–134 Wei R, Cao J, Alsaedi A (2018) Finite-time and fixed-time synchronization analysis of inertial memristive neural networks with time-varying delays. Cogn Neurodyn 12(1):121–134
34.
Zurück zum Zitat Huang D, Jiang M, Jian J (2017) Finite-time synchronization of inertial memristive neural networks with time-varying delays via sampled-date control. Neurocomputing 266(29):527–539 Huang D, Jiang M, Jian J (2017) Finite-time synchronization of inertial memristive neural networks with time-varying delays via sampled-date control. Neurocomputing 266(29):527–539
35.
Zurück zum Zitat Cui N, Jiang H, Hu C, Alsaedi A (2017) Finite-time synchronization of inertial neural networks. J Assoc Arab Univ Basic Appl Sci 24:300–309 Cui N, Jiang H, Hu C, Alsaedi A (2017) Finite-time synchronization of inertial neural networks. J Assoc Arab Univ Basic Appl Sci 24:300–309
36.
Zurück zum Zitat Polyakov A (2012) Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Autom Control 57(8):2106–2110MathSciNetMATH Polyakov A (2012) Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Autom Control 57(8):2106–2110MathSciNetMATH
37.
Zurück zum Zitat Yang X, Lam J, Ho DWC, Feng Z (2017) Fixed-time synchronization of complex networks with impulsive effects via non-chattering control. IEEE Trans Autom Control 62(11):5511–5521MATH Yang X, Lam J, Ho DWC, Feng Z (2017) Fixed-time synchronization of complex networks with impulsive effects via non-chattering control. IEEE Trans Autom Control 62(11):5511–5521MATH
38.
Zurück zum Zitat Zhang W, Yang X, Li C (2019) Fixed-time stochastic synchronization of complex networks via continuous control. IEEE Trans Cyber 498:3099–3104 Zhang W, Yang X, Li C (2019) Fixed-time stochastic synchronization of complex networks via continuous control. IEEE Trans Cyber 498:3099–3104
39.
Zurück zum Zitat Cao J, Li R (2017) Fixed-time synchronization of delayed memristor-based recurrent neural networks. Sci China Inf Sci 60:032201 Cao J, Li R (2017) Fixed-time synchronization of delayed memristor-based recurrent neural networks. Sci China Inf Sci 60:032201
40.
Zurück zum Zitat Ji G, Hu C, Yu J, Jiang H (2018) Finite-time and fixed-time synchronization of discontinuous complex networks: a unified control framework design. J Frankl Inst 355(11):4665–4685MathSciNetMATH Ji G, Hu C, Yu J, Jiang H (2018) Finite-time and fixed-time synchronization of discontinuous complex networks: a unified control framework design. J Frankl Inst 355(11):4665–4685MathSciNetMATH
41.
Zurück zum Zitat Zhu X, Yang X, Alsaadi FE, Hayat T (2018) Fixed-time synchronization of coupled discontinuous neural networks with nonidentical perturbations. Neural Process Lett 48(2):1161–1174 Zhu X, Yang X, Alsaadi FE, Hayat T (2018) Fixed-time synchronization of coupled discontinuous neural networks with nonidentical perturbations. Neural Process Lett 48(2):1161–1174
43.
Zurück zum Zitat Dovrolis C, Stiliadisd D, Ramanathan P (1999) Proportional differentiated services: delay differentiation and packet scheduling. ACM Sigcomm Comput Commun 29(4):109–120 Dovrolis C, Stiliadisd D, Ramanathan P (1999) Proportional differentiated services: delay differentiation and packet scheduling. ACM Sigcomm Comput Commun 29(4):109–120
44.
Zurück zum Zitat Lee S, Lui J, Yau D (2004) A proportional-delay diffserv-enabled web server: admission control and dynamic adaptation. IEEE Trans Parallel Distrib Syst 15(5):385–400 Lee S, Lui J, Yau D (2004) A proportional-delay diffserv-enabled web server: admission control and dynamic adaptation. IEEE Trans Parallel Distrib Syst 15(5):385–400
45.
Zurück zum Zitat Zhou A, Liu M, Li Z, Dutkiewicz E (2012) Cross-layer design for proportional delay differentiation and network utility maximization in multi-hop wireless networks. IEEE Trans Wirel Commun 11(4):1446–1455 Zhou A, Liu M, Li Z, Dutkiewicz E (2012) Cross-layer design for proportional delay differentiation and network utility maximization in multi-hop wireless networks. IEEE Trans Wirel Commun 11(4):1446–1455
46.
Zurück zum Zitat Yang G (2019) Exponential stability of positive recurrent neural networks with multi-proportional delays. Neural Process Lett 49(1):67–78 Yang G (2019) Exponential stability of positive recurrent neural networks with multi-proportional delays. Neural Process Lett 49(1):67–78
47.
Zurück zum Zitat Guan K, Yang J (2019) Global asymptotic stabilization of cellular neural networks with proportional delay via impulsive control. Neural Process Lett 50(2):1969–1992 Guan K, Yang J (2019) Global asymptotic stabilization of cellular neural networks with proportional delay via impulsive control. Neural Process Lett 50(2):1969–1992
48.
Zurück zum Zitat Huang Z, Bin H, Cao J, Wang B (2018) Synchronizing neural networks with proportional delays based on a class of \(q\)-type allowable time scales. IEEE Trans Neural Netw Learn Syst 29(8):3418–3428MathSciNet Huang Z, Bin H, Cao J, Wang B (2018) Synchronizing neural networks with proportional delays based on a class of \(q\)-type allowable time scales. IEEE Trans Neural Netw Learn Syst 29(8):3418–3428MathSciNet
49.
Zurück zum Zitat Wang W (2018) Finite-time synchronization for a class of fuzzy cellular neural networks with time-varying coefficients and proportional delays. Fuzzy Set Syst 338(1):40–49MathSciNetMATH Wang W (2018) Finite-time synchronization for a class of fuzzy cellular neural networks with time-varying coefficients and proportional delays. Fuzzy Set Syst 338(1):40–49MathSciNetMATH
50.
Zurück zum Zitat Filippov AF (1988) Differential equations with discontinuous righthand sides. Kluwer Academic Publishers, Boston Filippov AF (1988) Differential equations with discontinuous righthand sides. Kluwer Academic Publishers, Boston
51.
Zurück zum Zitat Warga J (1984) Optimization and nonsmooth analysis. American Scientist, PhiladelphiaMATH Warga J (1984) Optimization and nonsmooth analysis. American Scientist, PhiladelphiaMATH
52.
Zurück zum Zitat Hardy GH, Littlewood JE, Pólya G (1934) Inequalities. Cambridge Mathematical Library, CambridgeMATH Hardy GH, Littlewood JE, Pólya G (1934) Inequalities. Cambridge Mathematical Library, CambridgeMATH
Metadaten
Titel
Finite-Time and Fixed-Time Non-chattering Control for Inertial Neural Networks with Discontinuous Activations and Proportional Delay
verfasst von
Dengguo Xu
Xinsong Yang
Rongqiang Tang
Publikationsdatum
05.02.2020
Verlag
Springer US
Erschienen in
Neural Processing Letters / Ausgabe 3/2020
Print ISSN: 1370-4621
Elektronische ISSN: 1573-773X
DOI
https://doi.org/10.1007/s11063-020-10199-7

Weitere Artikel der Ausgabe 3/2020

Neural Processing Letters 3/2020 Zur Ausgabe

Neuer Inhalt