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Model reference robust adaptive H ∞ controller design

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  • Control Theory and Applications
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Abstract

In this paper, a novel model reference robust adaptive H ∞ controller is designed, which not only guarantees asymptotically stability, but also optimizes adaptive H ∞ performance by estimating the optimal unknown control parameters. Furthermore, a novel state feedback framework is introduced, which depends on the optimal unknown parameter estimations, to guarantee that the defined cost function is minimized. At the same time, the minimal adaptive H ∞ performance index is obtained.

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References

  1. G. Tao, Adaptive Control Design and Analysis, Wiley, New York, 2003.

    Book  MATH  Google Scholar 

  2. P. A. Ioannou and J. Sun, Robust Adaptive Control, Prentice-Hall, London, 1996.

    MATH  Google Scholar 

  3. I. D. Landau and H. M. Silveira, “A stability theorem with applications to adaptive control,” IEEE Trans. on Automatic Control, vol. 24, no. 2, pp. 205–312, 1979.

    Article  MathSciNet  MATH  Google Scholar 

  4. I. D. Landau, “An extension of a stability theorem applicable to adaptive control,” IEEE Trans. on Automatic Control, vol. 25, no. 4, pp. 814–817, 1980. [click]

    Article  MathSciNet  MATH  Google Scholar 

  5. H. J. Fan and C.Y. Wen, “Adaptive control of a class of 2-D discrete systems,” IEEE Trans. on Automatic Control, vol. 50, no. 1, pp. 166–172, 2003.

    MathSciNet  Google Scholar 

  6. C. Y. Wen and J. Zhou, “Robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance,” IEEE Trans. on Automatic Control, vol. 56, no. 7, pp. 1672–1678, 2011. [click]

    Article  MathSciNet  Google Scholar 

  7. B. Benjamin and K. S. Narendra, “Bounded error adaptive control,” IEEE Trans. on Automatic Control, vol. 27, no. 6, pp. 1161–1168, 1982. [click]

    Article  MATH  Google Scholar 

  8. E. Lavretsky,and K.A. Wise, Robust and Adaptive Control with Aerospace Applications, Springer-Verlag, 2012.

    MATH  Google Scholar 

  9. G. Kreisselmeier and B. D. Anderson, “Robust model reference adaptive control,” IEEE Trans. on Automatic Control, vol. 31, no. 2, pp. 127–133, 1986. [click]

    Article  MathSciNet  MATH  Google Scholar 

  10. Z. T. Ding and X. D. Ye, “A flat-zone modification for robust adaptive control of nonlinear output feedback systems with unknown high-frequency gains,” IEEE Trans. on Automatic Control, vol. 47, no. 2, pp. 358–363, 2002. [click]

    Article  MathSciNet  MATH  Google Scholar 

  11. E. Kharisov and N. Hovakimyan, “L1 adaptive output feedback controller for minimum phase systems” Proc. of the 30th American Control Conf., pp. 1182–1187 2011.

    Google Scholar 

  12. G. Tao, “Inherent robustness of MRAC schemes,” Systems and Control Letters. vol. 29, no. 3, pp. 165–173, 1996.

    Article  MathSciNet  MATH  Google Scholar 

  13. G. Fen, “New robust model reference adaptive control algorithm,” IEE Proc.-Control Theory and Applications, vol. 41, no. 3, pp. 177–180, 1994.

    Google Scholar 

  14. G. Tao, “A robust adaptive law for l1+a modeling errors,” IEEE Trans. on Automatic Control, vol. 44, no. 1, pp. 186–190, 1999. [click]

    Article  MathSciNet  MATH  Google Scholar 

  15. J. Sun and P. Ioannou, “Robust adaptive LQ control schemes,” IEEE Trans. on Automatic Control, vol. 37, no. 1, pp. 100–106, 1992. [click]

    Article  MathSciNet  MATH  Google Scholar 

  16. X. Su, L.Wu, P. Shi, et al. “H ∞ model reduction of Takagi-Sugeno fuzzy stochastic systems,” IEEE Trans. Syst. Man Cybern. B, Cybern., vol. 42, no. 6, pp. 1574–1585, 2012. [click]

  17. X. Su, P. Shi, L. Wu, and M. V. Basin, “Reliable filtering with strict dissipativity for T-S fuzzy time-delay systems,” IEEE Transactions on Cybernetics, vol. 44, no. 12, pp. 2470–2483, 2014. [click]

    Article  Google Scholar 

  18. D. Ye and G.H. Yang, “Adaptive fault-tolerant tracking control against actuator faults with application to flight control,” IEEE Trans. on Control System Technology, vol. 14, no. 6, pp. 1088–1096, 2006. [click]

    Article  Google Scholar 

  19. P. P. Khargonekar, I. R. Petersen, and K. Zhou, “Robust stabilization of uncertain linear systems: quadratic stabilizability and H ∞ control theory,” IEEE Trans. on Automatic Control, vol. 35, no. 3, pp. 356–361, 1990. [click]

    Article  MathSciNet  MATH  Google Scholar 

  20. C. Tan, G. Tao, and R. Y. Qi, “An adaptive control scheme using multiple reference models,” International Journal of Adaptive Control & Signal Processing, vol. 28, no. 11,pp. 1290–1298, 2014. [click]

    Article  MathSciNet  MATH  Google Scholar 

  21. A. H. Sayed and P. V. Kokotovic, “A note on a Lyapunov argument for stochastic gradient methods in the presence of nose” proc. of the 1995 American control conf., pp. 587–588 1995.

    Chapter  Google Scholar 

  22. G. H. Yang and D. Ye, “Reliable control of linear systems with adaptive mechanism,” IEEE Trans. on Automatic Control, vol. 55, no. 1, pp. 242–247, 2010.

    Article  MathSciNet  Google Scholar 

  23. B. Jiang, M. Staroswiecki, and V. Cocquempot, “Fault accommodation for nonlinear dynamic systems,” IEEE Trans. on Automatic Control, vol. 51, no. 9, pp. 1578–1583, 2006. [click]

    Article  MathSciNet  MATH  Google Scholar 

  24. X. D. Zhang and F. Yu, “Active self-adaptive control of high-speed train pantograph” Proc. of Power Engineering and Automation Conf. (PEAM), pp. 152–156 2011.

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Electrical Engineering, University of Jinan, 250022, Jinan, China

    Qiang Zhang

  2. Institute of Electrical Engineering and Intelligent Equipment, School of Internet of Things Engineering, Jiangnan University, 214122, Wuxi, China

    De-Zhi Xu

  3. College of Automation Engineering, University of Aeronautics and Astronautics, 210016, Nanjing, China

    Kang-Kang Zhan

Authors
  1. Qiang Zhang
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  2. De-Zhi Xu
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  3. Kang-Kang Zhan
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Corresponding author

Correspondence to De-Zhi Xu.

Additional information

Recommended by Associate Editor Yingmin Jia under the direction of Editor PooGyeon Park. This work was partially supported by National Natural Science Foundation of China (61503156, 61403161), the Fundamental Research Funds for the Central Universities (JUSRP11562, JUSRP51406A, NJ20150011) and National Key Research and Development Program (2016YFD0400301).

Qiang Zhang received his M.Sc. degree in Electrical Engineering from University of Jinan, Jinan, China in 2005 and his Ph.D. degree in the College of Automation Engineering from Nanjing University of Aeronautics and Astronautics, China in 2013. He has been an Associate Professor in Electrical Engineering, University of Jinan. His research interests include robotics and automation, robust control, adaptive control and flight control.

Dezhi Xu received his M.Sc. degree in automatic control from Lanzhou University of Technology, Lanzhou, China in 2010 and his Ph.D. degree in the College of Automation Engineering from Nanjing University of Aeronautics and Astronautics, China in 2013. He has been an Associate Professor in Electrical Engineering, Jiangnan University. His research interests include fault diagnosis and fault-tolerant control, data-driven control. He is an IEEE Member.

Kangkang Zhang received his B.S. degree in automatic control from Henan University of Technology Henan, China in 2008, M.Sc. degree in control theory and control engineering from Northeastern University, Shenyang, China in 2014. He is now a Ph.D. student at the College of Automation Engineering, Nanjing University of Aeronautics and Astronautics. His research interest covers sliding mode control, fault diagnosis, fault-tolerant control.

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Zhang, Q., Xu, DZ. & Zhan, KK. Model reference robust adaptive H ∞ controller design. Int. J. Control Autom. Syst. 15, 1507–1514 (2017). https://doi.org/10.1007/s12555-016-0149-9

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  • DOI: https://doi.org/10.1007/s12555-016-0149-9

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