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Adaptive neural network tracking of a class of switched nonlinear systems with time-varying output constraints

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  • Intelligent Control and Applications
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Abstract

An approximation-based adaptive design problem for output-constrained tracking of a class of switched pure-feedback nonlinear systems is investigated under arbitrary switchings. All switched nonlinearities are assumed to be unknown. Contrary to the existing control results for uncertain switched pure-feedback nonlinear systems where the number of the used function approximators should be equal to the order of the systems, an adaptive control scheme based on only two neural networks is designed by using a system transformation and the common Lyapunov function method, regardless of the order of the system. In the proposed controller, the output constraints are used to establish designable time-varying bounds on the tracking performance. The stability and the constraint satisfaction of the resulting closed-loop system are shown in the sense of Lyapunov stability criterion. Finally, simulation examples are provided to illustrate the effectiveness of the proposed methodology.

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References

  1. C. Briat and A. Seuret, “Affine minimal and modedependent dwell-time characterization for uncertain switched linear systems,” IEEE Trans. Autom. Contr., vol. 58, no. 5, pp. 1304–1310, 2013.

    Article  Google Scholar 

  2. X. Xu and P. J. Antsaklis, “Optimal control of switched systems based on parameterization of the switching instants,” IEEE Trans. Autom. Contr., vol. 49, no. 1, pp. 2–16, 2004.

    Article  MathSciNet  Google Scholar 

  3. D. Liberzon, Switching in Systems and Control, Birkhauser, Boston, MA, 2003.

    Book  MATH  Google Scholar 

  4. W. Xiang and J. Xiao, “Stabilization of switched continuous-time systems with all modes unstable via dwell time switching,” Automatica, vol. 50, no. 3, pp. 940–945, 2014. [click]

    Article  MathSciNet  MATH  Google Scholar 

  5. L. J. Long and J. Zhao, “H∞ control of switched nonlinear systems in p-normal form using multiple Lyapunov functions,” IEEE Trans. Autom. Contr., vol. 57, no. 5, pp. 1285–1291, 2012.

    Article  MathSciNet  Google Scholar 

  6. R. C. Ma and J. Zhao, “Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings,” Automatica, vol. 46, no. 11, pp. 1819–1823, 2010. [click]

    Article  MathSciNet  MATH  Google Scholar 

  7. J. L. Wu, “Stabilizing controllers design for switched nonlinear systems in strict-feedback form,” Automatica, vol. 45, no. 4, pp. 1092–1096, 2009. [click]

    Article  MathSciNet  MATH  Google Scholar 

  8. B. Niu and J. Zhao, “Tracking control for outputconstrained nonlinear switched systems with a barrier Lyapunov function,” Int. J. Syst. Sci., vol. 44, no. 5, pp. 978–985, 2013. [click]

    Article  MATH  Google Scholar 

  9. B. Niu and J. Zhao, “Barrier Lyapunov functions for the output tracking control of constrained nonlinear switched systems,” Syst. Control Lett., vol. 62, no. 10, pp. 963–971, 2013. [click]

    Article  MathSciNet  MATH  Google Scholar 

  10. M. Krstic, I. Kanellakopoulos, and P. Kokotovic, Nonlinear and Adaptive Control Design, Wiley Interscience, NJ, 1995.

    MATH  Google Scholar 

  11. X. Zhao, X. Zheng, B. Niu, and L. Liu, “Adaptive tracking control for a class of uncertain switched nonlinear systems,” Automatica, vol. 52, pp. 185–191, 2015. [click]

    Article  MathSciNet  MATH  Google Scholar 

  12. B. Niu, L. N. Liu, and Y. Y. Liu, “Adaptive backstepping based fuzzy tracking control scheme for output-constrained nonlinear switched lower triangular systems with timedelays,” Neurocomputing, vol. 175, pp. 759–767, 2016. [click]

    Article  Google Scholar 

  13. B. Jiang, Q. Shen, and P. Shi, “Neural-networked adaptive tracking control for switched nonlinear pure-feedback systems under arbitrary switching,” Automatica, vol. 61, pp. 119–125, 2015. [click]

    Article  MathSciNet  MATH  Google Scholar 

  14. Y. Li, S. Tong, and T. Li, “Adaptive fuzzy backstepping control design for a class of pure-feedback switched nonlinear systems,” Nonlinear Anal. Hybrid Syst., vol. 16, pp. 72–80, 2015. [click]

    Article  MathSciNet  MATH  Google Scholar 

  15. K. B. Ngo, R. Mahony, and Z. P. Jiang, “Integrator backstepping using barrier functions for systems with multiple state constraints,” Proc. of the 44th Conf. Decision and Control, pp. 8306–8312, 2005. [click]

    Google Scholar 

  16. K. P. Tee, S. S. Ge, and E. H. Tay, “Barrier Lyapunov functions for the control of output-constrained nonlinear systems,” Automatica, vol. 45, no. 4, pp. 918–927, 2009. [click]

    Article  MathSciNet  MATH  Google Scholar 

  17. B. Ren, S. S. Ge, K. P. Tee, and T. H. Lee, “Adaptive neural control for output feedback nonlinear systems using a barrier Lyapunov function,” IEEE Trans. Neural Netw., vol. 21, no. 8, pp. 1339–1345, 2010.

    Article  Google Scholar 

  18. K. P. Tee and S. S. Ge, “Control of nonlinear systems with partial state constraints using a barrier Lyapunov function,” Int. J. Contr., vol. 84, no. 12, pp. 2008–2023, 2011. [click]

    Article  MathSciNet  MATH  Google Scholar 

  19. W. Meng, Q. Yang, D. Pan, H. Zheng, G. Wang, and Y. Sun, “NN-based asymptotic tracking control for a class of strict-feedback uncertain nonlinear systems with output constraints,” Proc. of the 51st Conf. Decision and Control, pp. 5410–5415, 2012.

    Google Scholar 

  20. Q. Zhou, L. Wang, C. Wu, H. Li, and H. Du, “Adaptive fuzzy control for non-strict feedback systems with input saturation and output constraint,” IEEE Trans. Syst., Man, Cybern., Syst., vol. 47, no. 1, pp. 1–12, 2017.

    Article  Google Scholar 

  21. K. P. Tee, B. Ren, and S. S. Ge, “Control of nonlinear systems with time-varying output contraints,” Automatica, vol. 47, no. 11, pp. 2511–2516, 2011. [click]

    Article  MathSciNet  MATH  Google Scholar 

  22. B. S. Kim and S. J. Yoo, “Approximation-based adaptive tracking control of nonlinear pure-feedback systems with time-varying output constraints,” Int. J. Contr. Autom. Syst., vol. 13, no. 2, pp. 257–265, 2015. [click]

    Article  Google Scholar 

  23. W. Meng, Q. Yang, J. Si, and Y. Sun, “Adaptive neural control of a class output-constrained nonaffine systems,” IEEE Trans. Cybern., vol. 46, no. 1, pp. 85–95, 2016.

    Article  Google Scholar 

  24. M. Ni and M. J. Er, “Stability of linear systems with delayed perturbations: An LMI approach,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 49, no. 1, pp. 108–112, 2002.

    Article  MathSciNet  Google Scholar 

  25. D. A. White and D. A. Sofge, Handbook of Intelligent Control: Neural, Fuzzy, and Adaptive Approaches, Van Nostrand, New York, USA, 1993.

    Google Scholar 

  26. A. M. Zou and Z. G. Hou, “Adaptive control of a class of nonlinear pure-feedback systems using fuzzy backstepping approach,” IEEE Trans. Fuzzy Syst., vol. 16, no. 4, pp. 886–897, 2008.

    Article  Google Scholar 

  27. D. M. Dawson, J. J. Carroll, and M. Schneider, “Integrator backstepping control of a brush DC motor turning a robotic load,” IEEE Trans. Contr. Syst. Technol., vol. 2, pp. 233–244, 1994.

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Electrical and Electronics Engineering, Chung-Ang University, 84 Heukseok-Ro, Dongjak-Gu, Seoul, 156-756, South Korea

    Seung Woo Lee, Hyoung Oh Kim & Sung Jin Yoo

Authors
  1. Seung Woo Lee
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  2. Hyoung Oh Kim
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  3. Sung Jin Yoo
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Corresponding author

Correspondence to Sung Jin Yoo.

Additional information

Recommended by Associate Editor Do Wan Kim under the direction of Editor Euntai Kim. This research was supported by the Chung-Ang University Excellent Student Scholarship in 2016 and by the MSIP (Ministry of Science, ICT and Future Planning), Korea, under the ITRC (Information Technology Research Center) support program (IITP-2016-H8501-16-1018) supervised by the IITP (Institute for Information & communications Technology Promotion).

Seung-Woo Lee received his B.S. degree from the School of Electrical and Electronics Engineering, Chung-Ang University, Seoul, Korea, in 2015, where he is currently pursuing the Master degree with the Department of Electrical and Electronic Engineering. His current research interests include nonlinear adaptive control, intelligent control using neural networks, and their applications to switched nonlinear systems.

Hyoung-Oh Kim received his B.S. degree from the School of Electrical and Electronics Engineering, Chung-Ang University, Seoul, Korea, in 2016, where he is currently pursuing the Master degree with the Department of Electrical and Electronic Engineering. His current research interests include nonlinear adaptive control, nonlinear disturbance observer, and intelligent control using neural networks.

Sung-Jin Yoo received the B.S., M.S., and Ph.D degrees from Yonsei University, Seoul, Korea, in 2003, 2005, and 2009, respectively, in electrical and electronic engineering. He has been a Post-doctoral researcher in the Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Illinois from 2009 to 2010. He is currently an Associate Professor in the School of Electrical and Electronics Engineering, Chung-Ang University, Seoul, Korea. His research interests include nonlinear adaptive control, decentralized control, distributed control, and neural networks theories, and their applications to robotic, flight, and time-delay systems.

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Lee, S.W., Kim, H.O. & Yoo, S.J. Adaptive neural network tracking of a class of switched nonlinear systems with time-varying output constraints. Int. J. Control Autom. Syst. 15, 1425–1433 (2017). https://doi.org/10.1007/s12555-016-0339-5

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  • DOI: https://doi.org/10.1007/s12555-016-0339-5

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