Skip to main content
Erschienen in: Neural Computing and Applications 6/2012

01.09.2012 | Original Article

Direct adaptive robust NN control for a class of discrete-time nonlinear strict-feedback SISO systems

verfasst von: Guo-Xing Wen, Yan-Jun Liu, C. L. Philip Chen

Erschienen in: Neural Computing and Applications | Ausgabe 6/2012

Einloggen

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

search-config
loading …

Abstract

In this paper, a direct adaptive neural network control algorithm based on the backstepping technique is proposed for a class of uncertain nonlinear discrete-time systems in the strict-feedback form. The neural networks are utilized to approximate unknown functions, and a stable adaptive neural network controller is synthesized. The fact that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded is proven and the tracking error can converge to a small neighborhood of zero by choosing the design parameters appropriately. Compared with the previous research for discrete-time systems, the proposed algorithm improves the robustness of the systems. A simulation example is employed to illustrate the effectiveness of the proposed algorithm.

Sie haben noch keine Lizenz? 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 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+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!

Literatur
1.
Zurück zum Zitat Park J, Sandberg IW (1991) Universal approximation using radial-basis-function network. Neural Comput 3(2):246–257CrossRef Park J, Sandberg IW (1991) Universal approximation using radial-basis-function network. Neural Comput 3(2):246–257CrossRef
2.
Zurück zum Zitat Wang LX (1992) Fuzzy systems are universal approximators. In: Proceedings of the IEEE international conference fuzzy systems. San Diego, CA, pp 1163–1170 Wang LX (1992) Fuzzy systems are universal approximators. In: Proceedings of the IEEE international conference fuzzy systems. San Diego, CA, pp 1163–1170
3.
Zurück zum Zitat Li TS, Tong SC, Feng G (2010) A novel robust adaptive-fuzzy-tracking control for a class of nonlinear multi-input/multi-output systems. IEEE Trans Fuzzy Syst 18(1):150–160CrossRef Li TS, Tong SC, Feng G (2010) A novel robust adaptive-fuzzy-tracking control for a class of nonlinear multi-input/multi-output systems. IEEE Trans Fuzzy Syst 18(1):150–160CrossRef
4.
Zurück zum Zitat Liu YJ, Tong SC, Wang W (2009) Adaptive fuzzy output tracking control for a class of uncertain nonlinear systems. Fuzzy Sets Syst 160(9):2727–2754MathSciNetMATHCrossRef Liu YJ, Tong SC, Wang W (2009) Adaptive fuzzy output tracking control for a class of uncertain nonlinear systems. Fuzzy Sets Syst 160(9):2727–2754MathSciNetMATHCrossRef
5.
Zurück zum Zitat Chen WS, Jiao LC, Li RH, Li J (2010) Adaptive backstepping fuzzy control for nonlinearly parameterized systems with periodic disturbances. IEEE Trans Fuzzy Syst 18(4):674–685CrossRef Chen WS, Jiao LC, Li RH, Li J (2010) Adaptive backstepping fuzzy control for nonlinearly parameterized systems with periodic disturbances. IEEE Trans Fuzzy Syst 18(4):674–685CrossRef
6.
Zurück zum Zitat Ge SS, Wang C (2004) Adaptive neural control of uncertain MIMO nonlinear systems. IEEE Trans Neural Netw 15(3):674–692CrossRef Ge SS, Wang C (2004) Adaptive neural control of uncertain MIMO nonlinear systems. IEEE Trans Neural Netw 15(3):674–692CrossRef
7.
Zurück zum Zitat Tong SC, Li CY, Li YM (2009) Fuzzy adaptive observer backstepping control for MIMO nonlinear systems. Fuzzy Sets Syst 160(19):2755–2775MathSciNetMATHCrossRef Tong SC, Li CY, Li YM (2009) Fuzzy adaptive observer backstepping control for MIMO nonlinear systems. Fuzzy Sets Syst 160(19):2755–2775MathSciNetMATHCrossRef
8.
Zurück zum Zitat Li ZJ, Chen WD (2008) Adaptive neural-fuzzy control of uncertain constrained multiple coordinated nonholonomic mobile manipulators. Eng Appl Artif Intell 21(7):985–1000CrossRef Li ZJ, Chen WD (2008) Adaptive neural-fuzzy control of uncertain constrained multiple coordinated nonholonomic mobile manipulators. Eng Appl Artif Intell 21(7):985–1000CrossRef
9.
Zurück zum Zitat Li ZJ, Xu CQ (2009) Adaptive fuzzy logic control of dynamic balance and motion for wheeled inverted pendulums. Fuzzy Sets Syst 160(12):1787–1803MATHCrossRef Li ZJ, Xu CQ (2009) Adaptive fuzzy logic control of dynamic balance and motion for wheeled inverted pendulums. Fuzzy Sets Syst 160(12):1787–1803MATHCrossRef
10.
Zurück zum Zitat Chen WS, Li JM (2008) Decentralized output-feedback neural control for systems with unknown interconnections. IEEE Trans Syst Man Cybern B Cybern 38(1):258–266CrossRef Chen WS, Li JM (2008) Decentralized output-feedback neural control for systems with unknown interconnections. IEEE Trans Syst Man Cybern B Cybern 38(1):258–266CrossRef
11.
Zurück zum Zitat Chen WS, Jiao LC (2010) Adaptive tracking for periodically time-varying and nonlinearly parameterized systems using multilayer neural networks. IEEE Trans Neural Netw 21(2):345–351CrossRef Chen WS, Jiao LC (2010) Adaptive tracking for periodically time-varying and nonlinearly parameterized systems using multilayer neural networks. IEEE Trans Neural Netw 21(2):345–351CrossRef
12.
Zurück zum Zitat Tong SC, He XL, Zhang HG (2009) Combined backstepping and small-gain approach to robust adaptive fuzzy output feedback control. IEEE Trans Fuzzy Syst 17(5):1059–1069CrossRef Tong SC, He XL, Zhang HG (2009) Combined backstepping and small-gain approach to robust adaptive fuzzy output feedback control. IEEE Trans Fuzzy Syst 17(5):1059–1069CrossRef
13.
Zurück zum Zitat Tong SC, He XL, Li YM, Zhang HG (2010) Adaptive fuzzy backstepping robust control for uncertain nonlinear systems based on small-gain approach. Fuzzy Sets Syst 161(3):771–796MathSciNetMATHCrossRef Tong SC, He XL, Li YM, Zhang HG (2010) Adaptive fuzzy backstepping robust control for uncertain nonlinear systems based on small-gain approach. Fuzzy Sets Syst 161(3):771–796MathSciNetMATHCrossRef
14.
Zurück zum Zitat Li HX, Tong SC (2003) A hybrid adaptive fuzzy control for a class of nonlinear MIMO systems. IEEE Trans Fuzzy Syst 11(1):24–34CrossRef Li HX, Tong SC (2003) A hybrid adaptive fuzzy control for a class of nonlinear MIMO systems. IEEE Trans Fuzzy Syst 11(1):24–34CrossRef
15.
Zurück zum Zitat Zhang HG, Cai LL, Bien Z (2000) A fuzzy basis function vector-based multivariable adaptive fuzzy controller for nonlinear systems. Trans Syst Man Cybern B Cybern 30(1):210–217CrossRef Zhang HG, Cai LL, Bien Z (2000) A fuzzy basis function vector-based multivariable adaptive fuzzy controller for nonlinear systems. Trans Syst Man Cybern B Cybern 30(1):210–217CrossRef
17.
Zurück zum Zitat Liu YJ, Wang W (2007) Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems. Inf Sci 177(18):3901–3917MATHCrossRef Liu YJ, Wang W (2007) Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems. Inf Sci 177(18):3901–3917MATHCrossRef
18.
Zurück zum Zitat Ge SS, Lee TH, Li GY, Zhang J (2003) Adaptive NN control for aclass of discrete-time nonlinear systems. Int J Control 76(4):334–354MathSciNetMATHCrossRef Ge SS, Lee TH, Li GY, Zhang J (2003) Adaptive NN control for aclass of discrete-time nonlinear systems. Int J Control 76(4):334–354MathSciNetMATHCrossRef
19.
Zurück zum Zitat Yang CG, Ge SS, Xiang C, Chai TY, Lee TH (2008) Output feedback NN control for two classes of discrete-time systems with unknown control directions in a unified approach. IEEE Trans Neural Netw 19(11):1873–1886CrossRef Yang CG, Ge SS, Xiang C, Chai TY, Lee TH (2008) Output feedback NN control for two classes of discrete-time systems with unknown control directions in a unified approach. IEEE Trans Neural Netw 19(11):1873–1886CrossRef
20.
Zurück zum Zitat Zhang J, Ge SS, Lee TL (2005) Output feedback control of a class of discrete MIMO nonlinear systems with triangular form inputs. IEEE Trans Neural Netw 16(6):1491–1503CrossRef Zhang J, Ge SS, Lee TL (2005) Output feedback control of a class of discrete MIMO nonlinear systems with triangular form inputs. IEEE Trans Neural Netw 16(6):1491–1503CrossRef
21.
Zurück zum Zitat Ge SS, Li GY, Lee TH (2003) Adaptive NN control for a class of strict-feedback discrete-time nonlinear systems. Automatica 39(5):807–819MathSciNetMATHCrossRef Ge SS, Li GY, Lee TH (2003) Adaptive NN control for a class of strict-feedback discrete-time nonlinear systems. Automatica 39(5):807–819MathSciNetMATHCrossRef
22.
Zurück zum Zitat Ge SS, Zhang J, Lee TH (2004) State feedback neural network control of a class of discrete MIMO nonlinear systems with disturbances. IEEE Trans Syst Man Cybern B Cybern 34(4):1630–1645CrossRef Ge SS, Zhang J, Lee TH (2004) State feedback neural network control of a class of discrete MIMO nonlinear systems with disturbances. IEEE Trans Syst Man Cybern B Cybern 34(4):1630–1645CrossRef
23.
Zurück zum Zitat Ge SS, Li GY, Zhang J, Lee TH (2004) Direct adaptive control for a class of MIMO nonlinear systems using neural networks. IEEE Trans Autom Control 49(11):2001–2006MathSciNetCrossRef Ge SS, Li GY, Zhang J, Lee TH (2004) Direct adaptive control for a class of MIMO nonlinear systems using neural networks. IEEE Trans Autom Control 49(11):2001–2006MathSciNetCrossRef
24.
Zurück zum Zitat Liu YJ, Wen GX, Tong SC (2010) Direct adaptive NN control for a class of discrete-time nonlinear strict-feedback systems. Neurocomputing 73(13–15):2498–2505CrossRef Liu YJ, Wen GX, Tong SC (2010) Direct adaptive NN control for a class of discrete-time nonlinear strict-feedback systems. Neurocomputing 73(13–15):2498–2505CrossRef
25.
Zurück zum Zitat Diaz DV, Tang Y (2004) Adaptive robust fuzzy control of nonlinear systems. IEEE Trans Syst Man Cyber B Cybern 34(3):1596–1601CrossRef Diaz DV, Tang Y (2004) Adaptive robust fuzzy control of nonlinear systems. IEEE Trans Syst Man Cyber B Cybern 34(3):1596–1601CrossRef
26.
Zurück zum Zitat Ge SS, Wang J (2002) Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems. IEEE Trans Neural Netw 13(6):1409–1419CrossRef Ge SS, Wang J (2002) Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems. IEEE Trans Neural Netw 13(6):1409–1419CrossRef
27.
Zurück zum Zitat Liu YJ, Wang W, Tong SC, Liu YS (2010) Robust adaptive tracking control for nonlinear systems based on bounds of fuzzy approximation parameters. IEEE Trans Syst Man Cybern A Syst Hum 40(1):170–184CrossRef Liu YJ, Wang W, Tong SC, Liu YS (2010) Robust adaptive tracking control for nonlinear systems based on bounds of fuzzy approximation parameters. IEEE Trans Syst Man Cybern A Syst Hum 40(1):170–184CrossRef
Metadaten
Titel
Direct adaptive robust NN control for a class of discrete-time nonlinear strict-feedback SISO systems
verfasst von
Guo-Xing Wen
Yan-Jun Liu
C. L. Philip Chen
Publikationsdatum
01.09.2012
Verlag
Springer-Verlag
Erschienen in
Neural Computing and Applications / Ausgabe 6/2012
Print ISSN: 0941-0643
Elektronische ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-011-0596-4

Weitere Artikel der Ausgabe 6/2012

Neural Computing and Applications 6/2012 Zur Ausgabe

Premium Partner