Skip to main content
SpringerLink
Log in

Decentralized adaptive neural control of nonlinear systems with unknown time delays

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In this paper, a novel decentralized adaptive neural control scheme is proposed for a class of uncertain multi-input and multi-output (MIMO) nonlinear time-delay systems. RBF neural networks (NNs) are used to tackle unknown nonlinear functions, then the decentralized adaptive NN tracking controller is constructed by combining Lyapunov–Krasovskii functions and the dynamic surface control (DSC) technique along with the minimal-learning-parameters (MLP) algorithm. The proposed controller guarantees semi-global uniform ultimate boundedness (SGUUB) of all the signals in the closed-loop large-scale system, while the tracking errors converge to a small neighborhood of the origin. An advantage of the proposed control scheme lies in that the number of adaptive parameters for each subsystem is reduced to one, and three problems of “computational explosion,” “dimension curse” and “controller singularity” are solved, respectively. Finally, a numerical simulation is presented to demonstrate the effectiveness and performance 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

Similar content being viewed by others

References

  1. Polycarpou, M.: Stable adaptive neural control scheme for nonlinear systems. IEEE Trans. Autom. Control 41, 447–451 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  2. Sun, F.-C., Sun, Z.-Q., Woo, P.-Y.: Stable neural-network-based adaptive control for sampled-data nonlinear systems. IEEE Trans. Neural Netw. 9(5), 956–968 (1998)

    Article  Google Scholar 

  3. Ge, S.S., Hang, C.C., Zhang, T.: Stable Adaptive Neural Network Control. Kluwer Academic, Norwell (2002)

    MATH  Google Scholar 

  4. Wang, C., Hill, D.J.: Learning from neural control. IEEE Trans. Neural Netw. 17(1), 130–146 (2006)

    Article  Google Scholar 

  5. Hou, Z.-G., Gupta, M., Nikiforum, P.N., Tan, M., Cheng, L.: A recurrent neural network for hierarchical control of interconnected dynamic systems. IEEE Trans. Neural Netw. 18(2), 466–481 (2007)

    Article  Google Scholar 

  6. Liu, Y.J., Wang, W.: Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems. Inf. Sci. 177, 3901–3917 (2007)

    Article  MATH  Google Scholar 

  7. Liu, Y.J., Wang, Z.F.: Adaptive fuzzy controller design of nonlinear systems with unknown gain sign. Nonlinear Dyn. 58(4), 687–695 (2009)

    Article  MATH  Google Scholar 

  8. Li, T.S., Wang, D., Chen, N.X.: Adaptive fuzzy control of uncertain MIMO nonlinear systems in block-triangular forms. Nonlinear Dyn. 63(1), 105–123 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  9. Liu, Y.J., Tong, S.C., Wang, W.: Adaptive fuzzy output tracking control for a class of uncertain nonlinear systems. Fuzzy Sets Syst. 160(19), 2727–2754 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  10. Liu, Y.J., Wang, W., Tong, S.C., Liu, Y.S.: Robust adaptive tracking control for nonlinear systems based on bounds of fuzzy approximation parameters. IEEE Trans. Syst. Man Cybern., Part A, Syst. Hum. 40(1), 170–184 (2010)

    Article  Google Scholar 

  11. Tong, S.C., Li, Y.M.: Observer-based fuzzy adaptive control for strict-feedback nonlinear systems. Fuzzy Sets Syst. 160(12), 1749–1764 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  12. Tong, S.C., Li, C.Y., Li, Y.M.: Fuzzy adaptive observer backstepping control for MIMO nonlinear systems. Fuzzy Sets Syst. 160(19), 2755–2775 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  13. Tong, S.C., Liu, C.L., Li, Y.M.: Fuzzy adaptive decentralized control for large-scale nonlinear systems with dynamical uncertainties. IEEE Trans. Fuzzy Syst. 18(5), 845–861 (2010)

    Article  Google Scholar 

  14. Tong, S.C., He, X.L., Zhang, H.G.: A combined backstepping and small-gain approach to robust adaptive fuzzy output feedback control. IEEE Trans. Fuzzy Syst. 17(5), 1059–1069 (2009)

    Article  Google Scholar 

  15. Kwan, C., Lewis, F.L.: Robust backstepping control of nonlinear systems using neural networks. IEEE Trans. Syst. Man Cybern., Part A 30, 753–766 (2000)

    Article  Google Scholar 

  16. Zhou, J., Meng, J.E., Zurada, J.M.: Adaptive neural network control of uncertain nonlinear systems with nonsmooth actuator nonlinearities. Neurocomputing 70(4–6), 1062–1070 (2007)

    Google Scholar 

  17. Chen, W.S., Li, J.M.: Decentralized output-feedback neural control for systems with unknown interconnections. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 38(1), 258–266 (2008)

    Article  Google Scholar 

  18. Chen, W.S.: Adaptive backstepping dynamic surface control for systems with periodic disturbances using neural networks. IET Control Theory Appl. 3(10), 1383–1394 (2009)

    Article  MathSciNet  Google Scholar 

  19. Chen, W.S., Li, J.M.: Globally decentralized adaptive backstepping neural network tracking control for unknown nonlinear interconnected systems. Asian J. Control 12(1), 96–102 (2010)

    MathSciNet  Google Scholar 

  20. Liu, Y.J., Tong, S.C., Li, Y.M.: Adaptive neural network tracking control for a class of non-linear systems. Int. J. Syst. Sci. 40(2), 143–158 (2010)

    Article  MathSciNet  Google Scholar 

  21. Liu, Y.J., Wen, G.X., Tong, S.C.: Direct adaptive NN control for a class of discrete-time nonlinear strict-feedback systems. Neurocomputing 73(13–15), 2498–2505 (2010)

    Article  Google Scholar 

  22. Wang, R., Liu, Y.J., Tong, S.C.: Decentralized control of uncertain nonlinear stochastic systems based on DSC. Nonlinear Dyn. 64(4), 305–314 (2011)

    Article  MathSciNet  Google Scholar 

  23. Zhou, N., Liu, Y.J., Tong, S.C.: Adaptive fuzzy output feedback control of uncertain nonlinear systems with nonsymmetric dead-zone input. Nonlinear Dyn. 63(4), 771–778 (2011)

    Article  MathSciNet  Google Scholar 

  24. Yang, Y.S., Li, T.S., Wang, X.F.: Robust adaptive neural network control for strict-feedback nonlinear systems via small-gain approaches. Lect. Notes Comput. Sci. 3972, 888–897 (2006)

    Article  Google Scholar 

  25. Yang, Y.S., Wang, X.F.: Adaptive NN tracking control for a class of uncertain nonlinear systems using radial-basis-function neural networks. Neurocomputing 70, 932–941 (2007)

    Article  Google Scholar 

  26. Wang, D., Huang, J.: Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form. IEEE Trans. Neural Netw. 16(1), 195–202 (2005)

    Article  Google Scholar 

  27. Li, T.S., Feng, G., Wang, D.: Neural-network-based simple adaptive control of uncertain MIMO nonlinear systems. IET Control Theory Appl. 4(9), 1543–1557 (2010)

    Article  MathSciNet  Google Scholar 

  28. Li, T.S., Wang, D., Feng, G., Tong, S.C.: A DSC approach to robust adaptive NN tracking control for strict-feedback nonlinear systems. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 40(3), 915–923 (2010)

    Article  Google Scholar 

  29. Huang, H., Feng, G., Cao, J.: Robust state estimation for uncertain neural networks with time-varying delay. IEEE Trans. Neural Netw. 19(8), 1329–1339 (2008)

    Article  Google Scholar 

  30. Wang, Z.S., Zhang, H.G., Yu, W.: Robust exponential stability analysis of neural networks with multiple time delays. Neurocomputing 70(13–15), 2534–2543 (2007)

    Article  Google Scholar 

  31. Wang, Z.S., Zhang, H.G.: Global asymptotic stability of reaction-diffusion Cohen–Grossberg neural networks with continuously distributed delays. IEEE Trans. Neural Netw. 21(1), 39–49 (2010)

    Article  Google Scholar 

  32. Ge, S.S., Hong, F., Lee, T.H.: Adaptive neural network control of nonlinear systems with unknown time delays. IEEE Trans. Autom. Control 48(11), 2004–2010 (2003)

    Article  MathSciNet  Google Scholar 

  33. Ge, S.S., Hong, F.: Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients. IEEE Trans. Syst. Man Cybern., Part B 34(1), 499–516 (2004)

    Article  MathSciNet  Google Scholar 

  34. Hong, F., Ge, S.S., Lee, T.H.: Practical adaptive neural control of nonlinear systems with unknown time delays. IEEE Trans. Syst. Man Cybern., Part B 35(4), 849–854 (2005)

    Article  Google Scholar 

  35. Wang, M., Chen, B., Shi, P.: Adaptive neural control for a class of perturbed strict-feedback nonlinear time-delay systems. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 38(3), 721–730 (2008)

    Article  Google Scholar 

  36. Ho, W.C., Li, J., Niu, Y.: Adaptive neural control for a class of nonlinearly parametric time-delay systems. IEEE Trans. Neural Netw. 16(3), 625–635 (2005)

    Article  Google Scholar 

  37. Yoo, S.J., Park, J.B., Choi, Y.H.: Adaptive neural dynamic surface control of nonlinear time-delay systems with model uncertainties. In: Proc of the 2006 American Control Conference, MN, June 14–16, pp. 3140–3145 (2006)

    Google Scholar 

  38. Lin, W., Qian, C.: Adaptive control of nonlinearly parameterized systems: the smooth feedback case. IEEE Trans. Autom. Control 47(8), 1249–1266 (2002)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Navigation College, Dalian Maritime University, Dalian, 116026, China

    Tieshan Li, Ronghui Li & Junfang Li

  2. Shanghai Jiao Tong University, Shanghai, 200240, China

    Tieshan Li

Authors
  1. Tieshan Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ronghui Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Junfang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tieshan Li.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, T., Li, R. & Li, J. Decentralized adaptive neural control of nonlinear systems with unknown time delays. Nonlinear Dyn 67, 2017–2026 (2012). https://doi.org/10.1007/s11071-011-0126-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-011-0126-z

Keywords

Search

Navigation