Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Switching control system based on robust model reference adaptive control

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

For conventional adaptive control, time-varying parametric uncertainty and unmodeled dynamics are ticklish problems, which will lead to undesirable performance or even instability and nonrobust behavior, respectively. In this study, a class of discrete-time switched systems with unmodeled dynamics is taken into consideration. Moreover, nonlinear systems are here supposed to be approximated with the class of switched systems considered in this paper, and thereby switching control design is investigated for both switched systems and nonlinear systems to assure stability and performance. For robustness against unmodeled dynamics and uncertainty, robust model reference adaptive control (RMRAC) law is developed as the basis of controller design for each individual subsystem in the switched systems or nonlinear systems. Meanwhile, two different switching laws are presented for switched systems and nonlinear systems, respectively. Thereby, the authors incorporate the corresponding switching law into the RMRAC law to construct two schemes of switching control respectively for the two kinds of controlled systems. Both closed-loop analyses and simulation examples are provided to illustrate the validity of the two proposed switching control schemes. Furthermore, as to the proposed scheme for nonlinear systems, its potential for practical application is demonstrated through simulations of longitudinal control for F-16 aircraft.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. Leith D J, Shorten R N, and Leithead W E, Issues in the design of switched linear control systems: A benchmark study, International Journal of Adaptive Control and Signal Processing, 2003, 17(2): 103–118.

    Article  MATH  Google Scholar 

  2. Ni W and Cheng D Z, Stabilization of switched linear systems with constrained inputs, Journal of Systems Science and Complexity, 2012, 25(1): 60–70.

    Article  MathSciNet  MATH  Google Scholar 

  3. Bao L P, Fei S M, and Yu L, Exponential stability of linear distributed parameter switched systems with time-delay, Journal of Systems Science and Complexity, 2014, 27(2): 263–275.

    Article  MathSciNet  MATH  Google Scholar 

  4. Ibanez C A, Suarez-Castanon M S, and Gutierrez-Frias O, A switching controller for the stabilization of the damping inverted pendulum cart system, International Journal of Innovative Computing, Information and Control, 2013, 9(9): 3585–3597.

    Google Scholar 

  5. Narendra K S and Balakrishnan J, Improving transient response of adaptive control systems using multiple models and switching, IEEE Transactions on Automatic Control, 1994, 39: 1861–1866.

    Article  MathSciNet  MATH  Google Scholar 

  6. Boskovic J D, Li S M, and Mehra R K, Research on system identification for reconfigurable flight control system, Technical Report, NASA Langley, 1999.

    Google Scholar 

  7. Boskovic J D and Mehra R K, Multi-mode switching in flight control, Proceedings of the 19th Digital Avionics Systems Conference, Volume 2, 6F2/1–6F2/8, 2000.

    Google Scholar 

  8. Boskovic J D and Mehra R K, Multiple-model adaptive flight control scheme for accommodation of actuator failures, Journal of Guidance, Control, and Dynamics, 2002, 25(4): 712–724.

    Google Scholar 

  9. Goodwin G C, Graebe S F, and Salgado M E, Control System Design, Prentice Hall, New Jersey, 2001.

    Google Scholar 

  10. Narendra K S and Balakrishnan J, Performance improvement in adaptive control systems using multiple models and switching, Proceeding of the Seventh Yale Workshop on Adaptive Learning System, Center for Systems Science, New Haven, 1992.

    Google Scholar 

  11. Narendra K S and Balakrishnan J, Adaptive control using multiple models, IEEE Transactions on Automatic Control, 1997, 42(2): 171–187.

    Article  MathSciNet  MATH  Google Scholar 

  12. Narendra K S and Xiang C, Adaptive control of discrete-time systems using multiple models, IEEE Transactions on Automatic Control, 2000, 45(9): 1669–1686.

    Article  MathSciNet  MATH  Google Scholar 

  13. Zhang Y X and Guo L, Stochastic adaptive switching control based on multiple models, Journal of Systems Science and Complexity, 2001, 15(1): 18–34.

    MathSciNet  MATH  Google Scholar 

  14. Zhuo H and Narendra K S, New concepts in adaptive control using multiple models, IEEE Transactions on Automatic Control, 2012, 57(1): 78–89.

    Article  MathSciNet  Google Scholar 

  15. Xu L, Wang Q, Li W, et al., Stability analysis and stabilisation of full-envelope networked flight control systems: Switched system approach, IET Control Theory & Applications, 2012, 6(2): 286–296.

    Article  MathSciNet  Google Scholar 

  16. Chen L, Nonlinear adaptive control using neural networks and multiple models, PhD thesis, National University of Singapore, 2011.

    Google Scholar 

  17. Egardt B, Stability of Adaptive Controllers, Lecture Notes in Control and Information Sciences, Volume 20, Springer-Verlag, Berlin, 1979.

    MATH  Google Scholar 

  18. Ioannou P A and Kokotovic P V, Adaptive Systems with Reduced Models, Lecture Notes in Control and Information Sciences, Volume 47, Springer-Verlag, New York, 1983.

    Book  Google Scholar 

  19. Rohrs C E, Valavani L, Athans M, et al., Robustness of continuous-time adaptive control algorithms in the presence of unmodeled dynamics, IEEE Transactions on Automatic Control, 1985, 30(9): 881–889.

    Article  MATH  Google Scholar 

  20. Ioannou P A and Sun J, Robust Adaptive Control, Number 1 in Control theory, PTR Prentice-Hall, 1996.

    MATH  Google Scholar 

  21. Giovanini L, Robust adaptive control using multiple models, switching and tuning, IET Control Theory & Applications, 2011, 5(18): 2168–2178.

    Article  MathSciNet  Google Scholar 

  22. Rifai E, Robust adaptive control of a class of switched systems, Proceedings of American Control Conference, 2008, 3695–3700.

    Google Scholar 

  23. Lavretsky E and Wise K, Robust and Adaptive Control: With Aerospace Applications, Springer, New York, 2012.

    MATH  Google Scholar 

  24. Tao G, Adaptive Control Design and Analysis, John Wiley and Sons, New York, 2003.

    Book  MATH  Google Scholar 

  25. Desoer C A and Vidyasagar M, Feedback Systems: Input-Output Properties, Academic Press, New York, 1975.

    MATH  Google Scholar 

  26. Morse A S, Parametrizations for multivariable adaptive control, Proceedings of the 20th IEEE Conference on Decision and Control, San Diego, 1981.

    Google Scholar 

  27. Singh R P and Narendra K S, Prior information in the design of multivariable adaptive controllers, IEEE Transactions on Automatic Control, 1984, 29(12): 1108–1111.

    Article  MathSciNet  MATH  Google Scholar 

  28. Elliott H and Wolovich W A, A parameter adaptive control structure for linear multivariable systems, IEEE Transactions on Automatic Control, 1982, 27(5): 340–352.

    Article  MATH  Google Scholar 

  29. Wolovich W A and Falb P L, Invariants and canonical forms under dynamic compensation, SIAM Journal on Control and Optimization, 1976, 14(6): 996–1008.

    Article  MathSciNet  MATH  Google Scholar 

  30. Tao G and Ioannou P A, Robust model reference adaptive control for multivariable plants, International Journal of Adaptive Control and Signal Processing, 1988, 2(3): 217–248.

    Article  MATH  Google Scholar 

  31. Tao G and Ioannou P A, Robust stability and performance improvement of multivariable adaptive control systems, International Journal of Control, 1989, 50(5): 1825–1855.

    Article  MathSciNet  MATH  Google Scholar 

  32. Wu Q, Wang S F, and Du J H, Principles of automatic control, 2nd Edition, Tsinghua University Press, Beijing, 2006.

    Google Scholar 

  33. Kailath T, Linear Systems, Wiley, Englewood Cliffs, 1980.

    MATH  Google Scholar 

  34. Lai C Y, Identification and control of nonlinear systems using multiple models, PhD thesis, National University of Singapore, 2011.

    Google Scholar 

  35. Liberzon D, Switching in Systems and Control, Birkhauser Boston, New York, 2003.

    Book  MATH  Google Scholar 

  36. Xiang W and Xiao J, Stabilization of switched continuous-time systems with all modes unstable via dwell time switching, Automatica, 2014, 50(3): 940–945.

    Article  MathSciNet  MATH  Google Scholar 

  37. Narendra K S, Driollet O A, Matthias F, et al., Adaptive control using multiple models, switching and tuning, International Journal of Adaptive Control and Signal Processing, 2003, 17(2): 87–102.

    Article  MATH  Google Scholar 

  38. Narendra K S and Parthasarathy K, Identification and control of dynamical systems using neural networks, IEEE Transactions on Neural Networks, 1990, 1(1): 4–27.

    Article  Google Scholar 

  39. Wang W and Li X, Multi-Model Adaptive Control, Science Press, Beijing, 2001.

    Google Scholar 

  40. Goodwin G C and Sin K S, Adaptive Filtering, Prediction and Control, Prentice Hail, Englewood Clifs, 1984.

    MATH  Google Scholar 

  41. Stevens B L, Lewis F L, and Du J H, Aircraft Control and Simulation, Wiley, New York, 2003.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Automation, Beijing Institute of Technology, Beijing, 100081, China

    Qiong Hu, Qing Fei, Hongbin Ma, Qinghe Wu & Qingbo Geng

  2. Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai, 201800, China

    Qiong Hu

  3. State Key Laboratory of Intelligent Control and Decision of Complex Systems, Beijing Institution of Technology, Beijing, 100081, China

    Qing Fei, Hongbin Ma & Qinghe Wu

Authors
  1. Qiong Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qing Fei
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hongbin Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Qinghe Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Qingbo Geng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qing Fei.

Additional information

This research was supported by Deep Exploration Technology and Experimentation Project under Grant No. 201311194-04, partially supported by the National Natural Science Foundation of China under Grant Nos. 61321002 and 61473038, Beijing Outstanding Talents Programme under Grant No. 2012D009011000003, and Graduate Teaching/Innovation Funding of Beijing Institute of Technology.

This paper was recommended for publication by Editor HUANG Jie.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hu, Q., Fei, Q., Ma, H. et al. Switching control system based on robust model reference adaptive control. J Syst Sci Complex 29, 897–932 (2016). https://doi.org/10.1007/s11424-016-4223-4

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-016-4223-4

Keywords

Search

Navigation