Skip to main content
SpringerLink
Log in

RBFN-based decentralized adaptive control of a class of large-scale non-affine nonlinear systems

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

For a class of large-scale decentralized nonlinear systems with strong interconnections, a radial basis function neural network (RBFN) adaptive control scheme is proposed. The system is composed of a class of non-affine nonlinear subsystems, which are implicit function and smooth with respect to control input. Based on implicit function theorem, inverse function theorem and the design idea of pseudo-control, a novel control algorithm is proposed. Two neural networks are used to approximate unknown nonlinearities in the subsystem and unknown interconnection function, respectively. The stability is proved rigidly. The result of simulation validates the effectiveness of the proposed scheme.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Spooner JT, Passino KM (1996) Adaptive control of a class of decentralized nonlinear system. IEEE Trans Automat Control 41(2):280–284

    Article  MATH  MathSciNet  Google Scholar 

  2. Siljak DD (1985) Decentralized control of complex systems. Academic, Boston

    Google Scholar 

  3. Ioannou PA (1986) Decentralized adaptive control of interconnected systems. IEEE Trans Automat Control AC-31:291–298

    Article  MathSciNet  Google Scholar 

  4. Fu LC (1992) Robust adaptive decentralized control of robot manipulators. Automatic Control IEEE Trans 37:106–110

    Article  Google Scholar 

  5. Sheikholeslam S, Desor CA (1993) Indirect adaptive control of a class of interconnected nonlinear dynamical systems. Int J Control 57(3):742–765

    Article  Google Scholar 

  6. Wen C (1994) Decentralized adaptive regulation. IEEE Trans Automat Control 39:2163–2166

    Article  MATH  MathSciNet  Google Scholar 

  7. Tang Y, Tomizuka M, Guerrero G (2000) Decentralized robust control of mechanical systems. IEEE Trans Automat Control 45(4):2163–2166

    Article  MathSciNet  Google Scholar 

  8. Huang SN, Shao HH (1995) Robust stability analysis of uncertain large-scale systems. Control Comput 23(1):1–5

    MATH  Google Scholar 

  9. Seraji H (1989) Decentralized adaptive control of manipulators: theory, simulation, and experimentation. IEEE Trans Robot Automat 5:183–201

    Article  Google Scholar 

  10. Huang SN, Shao HH (1995) Stability analysis of large-scale systems with delays. Syst Control Lett 25:75–78

    Article  MATH  MathSciNet  Google Scholar 

  11. Lewis FL, Yesildirek A, Liu K (1996) Multilayer neural-net robot controller with guaranteed tracking performance. IEEE Trans Neural Netw 7(2):388–399

    Article  Google Scholar 

  12. Yesildirek A, Lewis FL (1995) Feedback linearization using neural networks. Automatica 3(11):1659–1664

    Article  MathSciNet  Google Scholar 

  13. Calise AJ, Hovakimyan N (2001) Adaptive output feedback control of nonlinear system using neural networks. Automatica 37:1201–1211

    Article  MATH  MathSciNet  Google Scholar 

  14. Johnson E, Calise AJ (2000) Feedback linearization with neural network augmentation applied to X-33 attitude control. Guidance Navigation and Control Conference, AIAA-2000-4157

  15. Ge SS, Huang CC (1997) Direct adaptive neural network control of nonlinear systems. In: Proceedings of the American Control conference, Albuqerque, New Mexico, pp 1568–1572

  16. Ge SS, Huang CC (1999) Adaptive neural network control of nonlinear systems by state and output feedback. IEEE Trans Syst Man Cybern B 29(6):818–828

    Article  Google Scholar 

  17. Zhang T, Ge SS, Hang CC (1999) Design and performance analysis of a direct controller for nonlinear systems. Automatica 35:1809–1817

    Article  MATH  MathSciNet  Google Scholar 

  18. Zhang T, Ge SS, Hang CC (1997) Neural-based direct adaptive control for a class of general nonlinear systems. Int J Syst Sci 28:1011–1020

    Article  MATH  Google Scholar 

  19. Spooner JT, Passino KM (1999) Decentralized adaptive control of nonlinear systems using radial basis neural networks. Trans Automat Control 44(11):2050–2057

    Article  MATH  MathSciNet  Google Scholar 

  20. Huang S, Tan KK (2003) Decentralized control design for large-scale systems with strong interconnections using neural networks. IEEE Trans Automa Control 48(5):805–810

    Article  MathSciNet  Google Scholar 

  21. Johnson E, Calise AJ (2000) Feedback linearization with Neural network augmentation applied to X-33 attitude control. Guidance navigation and control conference,AIAA-2000-4157

  22. Huang SN, Tan KK (2006) Nonlinear adaptive control of interconnected systems using neural networks. IEEE Trans Neural Netw 17(1):243–246

    Article  MATH  Google Scholar 

  23. Nardi F, Hovakimyan N (2006) Decentralized control of large-scale systems using single hidden layer neural networks. In: Proceedings of the American control conference,Arilington, June 2001, pp 3123–3127

  24. Huang SN, Tan KK (2005) Decentralized control of a class of large-scale nonlinear systems using neural networks. Automatica 41:1645–1649

    Article  MATH  MathSciNet  Google Scholar 

  25. Lang S (1983) Real analysis. Addison-Wesley, Reading

    Google Scholar 

  26. Slotine JJE, Li WP (1991) Applied nonlinear control. Prentice Hall, Englewood Cliffs

    MATH  Google Scholar 

  27. Polycarpou MM (1996) Stable adaptive neural control scheme for nonlinear system. IEEE Tran Autom Control 41(3):447–451

    Article  MATH  MathSciNet  Google Scholar 

  28. Girosi F, Poggio T (1989) Networks and the best approximation property. Artif Intell Lab Memo 1164 Mass Inst Technol, Cambridge

  29. Gupta MM, Rao DH (1996) Neural-control system: theory and applications. IEEE Neural Netw Council N Y 41(3):447–451

    Google Scholar 

Download references

Acknowledgments

This research is supported by the research fund granted by the Doctoral Foundation of Qingdao University of Science and Technology.

Author information

Authors and Affiliations

  1. Department of Automatic Control, Qingdao University of Science and Technology, Qingdao, China

    Tong Zhao

Authors
  1. Tong Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tong Zhao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhao, T. RBFN-based decentralized adaptive control of a class of large-scale non-affine nonlinear systems. Neural Comput & Applic 17, 357–364 (2008). https://doi.org/10.1007/s00521-007-0125-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-007-0125-7

Keywords

Search

Navigation