Skip to main content
SpringerLink
Log in

Decentralized model reference adaptive control for interconnected time delay systems with delay in state and compensation of long delay in input by nested prediction

  • Regular Papers
  • Control Theory and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This paper investigates the problem of decentralized model reference adaptive control (MRAC) for a class of stable large scale interconnected systems. The interconnections are nonlinear with time varying delays which are bounded by polynomials with unknown gains. Also, it is assumed that both state and input delays are present. To overcome the input delay effect, a nested predictor based approach is adopted to predict the future states. The uniformly bounded stability of the closed loop system is proved by employing a suitable Lyapunov function. The effectiveness of the proposed approaches is illustrated by a numerical example.

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. S.-I. Han and J.-M. Lee, “Prescribed performance fuzzy backstepping control for nonlinear large-scale systems,” International Journal of Control, Automation and Systems, vol. 13, no. 6, pp. 1508–1520, December 2015. [click]

    Article  Google Scholar 

  2. S. Kamoun and M. Kamoun, “A new decentralized implicit adaptive regulator for large-scale systems described by discrete-time state-space mathematical models,” International Journal of Control, Automation and Systems, vol. 14, no. 3, pp. 733–742, June 2016. [click]

    Article  Google Scholar 

  3. M. Kamali, J. Askari, and F. Sheikholeslam, “An adaptive controller design for linear state-delay systems with actuator failures,” International Journal of Control, Automation and Systems, vol. 12, no. 3, pp. 599–608, June 2014. [click]

    Article  Google Scholar 

  4. B. Mirkin, P.-O. Gutman, and Y. Shtessel, “Decentralized continuous MRAC with local asymptotic sliding modes of nonlinear delayed interconnected systems,” Journal of the Franklin Institute, vol. 351, no. 4, pp. 2076–2088, April 2014. [click]

    Article  MathSciNet  Google Scholar 

  5. H. Wu, “Decentralized adaptive robust tracking and model following for large-scale systems including delayed state perturbations in the interconnections,” Journal of Optimization Theory and Applications, vol. 137, no.1, pp. 231–253, April 2008.

    Article  MathSciNet  MATH  Google Scholar 

  6. H.-T. Yau and J.-J. Yan, “Robust decentralized adaptive control for uncertain large-scale delayed systems with input nonlinearities,” Chaos, Solitons & Fractals, vol. 39, no. 4, pp. 1515–1521, February 2009. [click]

    Article  MathSciNet  MATH  Google Scholar 

  7. H. Wu, “Decentralized adaptive robust control for a class of large-scale systems including delayed state perturbations in the interconnections,” IEEE Trans. on Automatic Control, vol. 47, no. 10, pp. 1745–1751, October 2002. [click]

    Article  MathSciNet  Google Scholar 

  8. J.-J. Yan, “Memoryless adaptive decentralized sliding mode control for uncertain large-scale systems with time varying delays,” Journal of Dynamic Systems, Measurement, and Control, vol. 125, no. 2, pp. 172–176, June 2003. [click]

    Article  Google Scholar 

  9. Y.-J. Liu and S. Tong, “Adaptive fuzzy control for a class of unknown nonlinear dynamical systems,” Fuzzy Sets and Systems, vol. 263, pp. 49–70, March 2015. [click]

    Article  MathSciNet  MATH  Google Scholar 

  10. S. Tong, H.-X. Li, and G. Chen, “Adaptive fuzzy decentralized control fora class of large-scale nonlinear systems,” IEEE Trans. on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 34, no. 1, pp. 770–775, February 2004. [click]

    Article  Google Scholar 

  11. Y.-J. Liu and S. Tong, “Adaptive fuzzy identification and control for a class of nonlinear pure-feedback MIMO systems with unknown dead zones,” IEEE Trans. on Fuzzy Systems, vol. 23, no. 5, pp. 1387–1398, October 2015. [click]

    Article  Google Scholar 

  12. S. Tong, P. Shi, and H. Al-Madfai, “Robust fuzzy decentralized control for nonlinear large-scale systems with parametric uncertainties,” Journal of Intelligent & Fuzzy Systems, vol. 19, no. 2, pp. 85–101, 2008.

    MATH  Google Scholar 

  13. X.-G. Yan, S. K. Spurgeon, and C. Edwards, “Global timedelay dependent decentralised sliding mode control using only output information,” Proc. of the 48th IEEE Conf. on Decision and Control, pp. 6709–6714, 2009.

    Google Scholar 

  14. H. Wu, “Decentralized adaptive robust control of uncertain large-scale non-linear dynamical systems with timevarying delays,” IET Control Theory & Applications, vol. 6, no. 5, pp. 629–640, March 2012. [click]

    Article  MathSciNet  Google Scholar 

  15. C.-C. Hua, J. Leng, and X.-P. Guan, “Decentralized MRAC for large-scale interconnected systems with time-varying delays and applications to chemical reactor systems,” Journal of Process Control, vol. 22, no. 10, pp. 1985–1996, December 2012.

    Article  Google Scholar 

  16. O. J. Smith, “A controller to overcome dead time,” ISA Journal, vol. 6, no. 2, pp. 28–33, 1959.

    Google Scholar 

  17. A. Z. Manitius and A. W. Olbrot, “Finite spectrum assignment problem for systems with delays,” IEEE Trans. on Automatic Control, vol. 24, no. 4, pp. 541–552, August 1979. [click]

    Article  MathSciNet  MATH  Google Scholar 

  18. Z. Artstein, “Linear systems with delayed controls: a reduction,” IEEE Trans. on Automatic Control, vol. 27, no. 4, pp. 869–879, August 1982. [click]

    Article  MathSciNet  MATH  Google Scholar 

  19. B. Zhou, Z.-Y. Li, W. X. Zheng, and G.-R. Duan, “Stabilization of some linear systems with both state and input delays,” Systems & Control Letters, vol. 61, no. 10, pp. 989–998, October 2012. [click]

    Article  MathSciNet  MATH  Google Scholar 

  20. B. Zhou, “Input delay compensation of linear systems with both state and input delays by nested prediction,” Automatica, vol. 50, no. 5, pp. 1434–1443, May 2014. [click]

    Article  MathSciNet  MATH  Google Scholar 

  21. B. Mirkin and P.-O. Gutman, “Adaptive following of perturbed plants with input and state delays,” Proc. of IEEE International Conf. on Control and Automation (ICCA), pp. 865–870, 2011. [click]

    Google Scholar 

  22. Y.-J. Liu and S. Tong, “Adaptive fuzzy control for a class of nonlinear discrete-time systems with backlash,” IEEE Trans. on Fuzzy Systems, vol. 22, no.5, pp. 1359–1365, October 2014. [click]

    Article  Google Scholar 

  23. Y.-J. Liu, L. Tang, S. Tong, C. Chen, and D.-J. Li, “Reinforcement learning design-based adaptive tracking control with less learning parameters for nonlinear discrete-time MIMO systems,” IEEE Trans. on Neural Networks and Learning Systems, vol. 26, no. 1, pp. 165–176, Jan 2015. [click]

    Article  MathSciNet  Google Scholar 

  24. S.-C. Tong, X.-L. He, and H.-G. Zhang, “A combined backstepping and small-gain approach to robust adaptive fuzzy output feedback control,” IEEE Trans. on Fuzzy Systems, vol. 17, no. 5, pp. 1059–1069, October 2009. [click]

    Article  Google Scholar 

  25. C. Hua, X. Guan, and P. Shi, “Decentralized robust model reference adaptive control for interconnected time-delay systems,” Journal of Computational and Applied Mathematics, vol. 193, no. 2, pp. 383–396, September 2006.

    Article  MathSciNet  MATH  Google Scholar 

  26. R. L. Finney, G. B. Thomas, and M. D. Weir, Calculus and Analytic Geometry, Addison-Wesley, 1992.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

    Seyed Hamid Hashemipour

  2. Electrical Engineering Faculty, Shahid Rajaee Teacher Training University, Tehran, Iran

    Nastaran Vasegh

  3. Electrical Engineering Faculty, K. N. Toosi University of Technology, Tehran, Iran

    Ali Khaki Sedigh

Authors
  1. Seyed Hamid Hashemipour
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nastaran Vasegh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ali Khaki Sedigh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nastaran Vasegh.

Additional information

Recommended by Associate Editor Yingmin Jia under the direction of Editor Myo Taeg Lim.

Seyed Hamid Hashemipour was born on September 1983 in Langeroud, Iran. He obtained his B.Sc. degree in Electrical Engineering from the Lahijan Branch, IAU in 2005 and masters in Control Engineering from Tabriz University in 2007 and he is currently a Ph.D. student at the Science and Research Branch, IAU. The main areas of his interest are adaptive control, nonlinear control, time delayed systems analysis, controller tuning, multivariable control and process control.

Nastaran Vasegh received her B.S degree in Electronic Engineering in 2001, and both her M.S. degree in 2004 and the Ph.D. degree in 2008 in Control Engineering from K. N. Toosi University of Technology. She is the head of Control Engineering Department at Shahid Rajaee Teacher Training University. Her current research interests are in the areas of time delayed systems analysis and control, nonlinear control, and control applications in power systems.

Ali Khaki Sedigh is currently a professor of control systems with the Department of Electrical Engineering, K. N. Toosi University of Technology, Tehran, Iran. He obtained an honors degree in mathematics in 1983, a master’s degree in control systems in 1985 and a Ph.D. in control systems in 1988, all in the UK. He is the author and co-author of about 112 journal papers, 180 international conference papers and has published 14 books in the area of control systems. His main research interests are adaptive and robust multivariable control systems, complex systems and chaos control, research ethics and the history of control.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hashemipour, S.H., Vasegh, N. & Sedigh, A.K. Decentralized model reference adaptive control for interconnected time delay systems with delay in state and compensation of long delay in input by nested prediction. Int. J. Control Autom. Syst. 15, 1198–1206 (2017). https://doi.org/10.1007/s12555-015-0416-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-015-0416-1

Keywords

Search

Navigation