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Prescribed performance adaptive neural tracking control for strict-feedback Markovian jump nonlinear systems with time-varying delay

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  • Control Theory and Applications
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Abstract

A prescribed performance adaptive neural tracking control problem is investigated for strict-feedback Markovian jump nonlinear systems with time-varying delay. First, a new prescribed performance constraint variable is proposed to generate the virtual control that forces the tracking error to fall within prescribed boundaries. Combining with the approximation capability of neural networks and backstepping design, the adaptive tracking controller is designed. The designed controller is independent on time delay by constructing appropriate Lyapunov functions to offset the unknown time-varying delays. It is proved that the closed-loop system is uniformly ultimately bounded in probability, and that both steady-state and transient-state performances are guaranteed. Finally, simulation results are given to illustrate the effectiveness of the proposed approach.

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References

  1. M. Wang, B. Chen, X. P. Liu, and P. Shi, “Adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear time-delay systems,” Fuzzy Sets and Systems, vol. 159, no. 8, pp. 949–967, April 2008. [click]

    Article  MathSciNet  MATH  Google Scholar 

  2. X. J. Su, P. Shi, L. G. 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, November 2014. [click]

    Article  Google Scholar 

  3. X. J. Su, L. G. Wu, P. Shi, and Y. D. Song, “A novel approach to output feedback control of fuzzy stochastic systems,” Automatica, vol. 50, no. 12, pp. 3268–3275, December 2014. [click]

    Article  MathSciNet  MATH  Google Scholar 

  4. X. J. Su, P. Shi, L. G. Wu, and Y. D. Song, “Fault detection filtering for nonlinear switched stochastic systems,” IEEE Transactions on Automatic Control, vol. 61, no. 5, pp. 1310–1315, May 2016. [click]

    Article  MathSciNet  MATH  Google Scholar 

  5. B. Chen, X. P. Liu, K. F Liu, P. Shi, and C. Lin, “Direct adaptive fuzzy control for nonlinear systems with timevarying delays,” Information Sciences, vol. 180, no. 5, pp. 776–792, March 2010. [click]

    Article  MathSciNet  MATH  Google Scholar 

  6. H. T. Gao, T. P. Zhang, and X. N. Xia, “Adaptive neural control of stochastic nonlinear systems with unmodeled dynamics and time-varying state delays,” Journal of the Franklin Institute, vol. 351, no. 6, pp. 3182–3199, June 2014. [click]

    Article  MathSciNet  MATH  Google Scholar 

  7. W. C. Meng, Q. M. Yang, and Y. X. Sun, “Adaptive neural control of nonlinear MIMO systems with time-varying output constraints,” IEEE Trans. on Neural Networks & Learning Systems, vol. 26, no. 5, pp. 1074–1085, May 2015. [click]

    Article  MathSciNet  Google Scholar 

  8. B. S. Kim and S. J. Yoo, “Approximation-based adaptive tracking control of nonlinear pure-feedback systems with time-varying output constraints,” International Journal of Control, Automation, and Systems, vol. 13, no. 2, pp. 257–265, April 2015. [click]

    Article  Google Scholar 

  9. C. L. Hwang and C. Jan, “Recurrent-neural-network-based multivariable adaptive control for a class of nonlinear dynamic systems with time-varying delay,” IEEE Trans. on Neural Networks & Learning Systems, vol. 27, no. 2, pp. 388–401, February 2016. [click]

    Article  MathSciNet  Google Scholar 

  10. Z. X. Yu, S. G. Li, and Z. S. Yu, “Adaptive neural control for a class of pure-feedback nonlinear time-delay systems with asymmetric saturation actuators,” Neurocomputing, vol. 173, pp. 1461–1470, January 2016. [click]

    Article  Google Scholar 

  11. P. Shi and F. Li, “A survey on Markovian jump systems: modeling and design,” International Journal of Control, Automation, and Systems, vol. 13, no. 1, pp. 1–16, February 2015. [click]

    Article  MathSciNet  Google Scholar 

  12. S. H. Kim, “Delay-dependent stability analysis for singular Markovian jump systems with incomplete transition probabilities,” Fuzzy Sets and Systems, vol. 352, no. 1, pp. 236–247, January 2015.

    MathSciNet  MATH  Google Scholar 

  13. C. Liu and L. J. Xu, “PI tracking control for nonlinear timevarying delay Markov jump systems,” International Journal of Control, Automation, and Systems, vol. 13, no. 2, pp. 319–326, April 2015. [click]

    Article  MathSciNet  Google Scholar 

  14. J. B. Qiu, Y. L. Wei, and H. R. Karimi, “New approach to delay-dependent H ∞ control for continuous-time Markovian jump systems with time-varying delay and deficient transition descriptions,” Journal of the Franklin Institute, vol. 352, no. 1, pp. 189–215, January 2015. [click]

    Article  MathSciNet  MATH  Google Scholar 

  15. W. H. Qi and X. W. Gao, “Finite-time H ∞ control for stochastic time-delayed Markovian switching systems with partly known transition rates and nonlinearity,” International Journal of Systems Science, vol. 47, no. 2, pp. 500–508, April 2015. [click]

    Article  MathSciNet  MATH  Google Scholar 

  16. M. K. Song, J. B. Park, and Y. H. Joo, “Robust stabilization for uncertain Markovian jump fuzzy systems based on free weighting matrix method,” Fuzzy Sets and Systems, vol. 277, pp. 81–96, October 2015. [click]

    Article  MathSciNet  Google Scholar 

  17. J. W. Zhu and G. H. Yang, “Adaptive sliding-mode control for stochastic Markovian jumping systems with actuator faults,” IET Control Theory & Applications, vol. 10, no. 6, pp. 664–673, April 2016. [click]

    Article  MathSciNet  Google Scholar 

  18. J. Zhu, H. Xi, H Ji, and B. Wang, “A robust adaptive controller for Markovian jump uncertain nonlinear systems with wiener noises of unknown covariance,” International Journal of Control, Automation, and Systems, vol. 5, no. 2, pp. 128–137, April 2007.

    Google Scholar 

  19. Z. J. Wu, X. J. Xie, P. Shi, and Y. Q. Xia, “Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching,” Automatica, vol. 45, no. 4, pp. 997–1004, April 2009. [click]

    Article  MathSciNet  MATH  Google Scholar 

  20. Z. J. Wu, J. Yang, and P. Shi, “Adaptive tracking for stochastic nonlinear systems with Markovian switching,” IEEE Trans. Autom. Control, vol. 55, no. 9, pp. 2135–2141, September 2010. [click]

    Article  MathSciNet  Google Scholar 

  21. R. Chang, Y. M. Fang, J. X. Li, and L. Liu, “Neuralnetwork-based adaptive tracking control for Markovian jump nonlinear systems with unmodeled dynamics,” Neurocomputing, vol. 179, pp. 44–53, February 2016. [click]

    Article  Google Scholar 

  22. C. C. Hua, L. L. Zhang, and X. P. Guan, “Output feedback control for interconnected time-delay systems with prescribed performance,” Neurocomputing, vol. 129, pp. 208–215, April 2014. [click]

    Article  Google Scholar 

  23. C. C. Hua and Y. F. Li, “Output feedback prescribed performance control for interconnected time-delay systems with unknown Prandtl-Ishlinskii hysteresis,” Journal of the Franklin Institute, vol. 352, no. 7, pp. 2750–2764, July 2015.

    Article  MathSciNet  Google Scholar 

  24. C. C. Hua, L. L. Zhang, and X. P. Guan, “Decentralized output feedback adaptive NN tracking control for timedelay stochastic nonlinear systems with prescribed performance,” IEEE Trans. Neural Networks and Learning Systems, vol. 26, no. 11, pp. 2749–2759, November 2015. [click]

    Article  MathSciNet  Google Scholar 

  25. S. Sui, S. C. Tong, and Y. M. Li, “Observer-based fuzzy adaptive prescribed performance tracking control for nonlinear stochastic systems with input saturation,” Neurocomputing, vol. 158, pp. 100–108, June 2015. [click]

    Article  Google Scholar 

  26. L. L. Zhang, S. Sui, Y. M. Li, and S. C. Tong, “Adaptive fuzzy output feedback tracking control with prescribed performance for chemical reactor of MIMO nonlinear systems,” Nonlinear Dyn., vol. 80, no. 1, pp. 945–957, April 2015.

    Article  MATH  Google Scholar 

  27. S. I. Han and J. M. Lee, “Improved prescribed performance constraint control for a strict feedback non-linear dynamic system,” IET Control Theory Appl., vol. 7, no. 14, pp. 1818–1827, September 2013.

    Article  MathSciNet  Google Scholar 

  28. M. B. Yazdi and M. R. Jahed-Motlagh, “Stabiliza-tion of a CSTR with two arbitrarily switching modes using modal state feedback linearization,” Chemical Engineering Journal, vol. 155, no. 3, pp. 838–843, December 2009. [click]

    Article  Google Scholar 

  29. C. Y. Wang and X. H. Jiao, “Observer-based adaptive arbitrary switching fuzzy tracking control for a class of switched nonlinear systems,” International Journal of Control, Automation, and Systems, vol. 13, no. 4, pp. 823–830, August 2015. [click]

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Key Lab of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao, 066004, P. R. China

    Ru Chang, Yi-ming Fang, Le Liu & Ke-song Kang

  2. Department of Automation, Shanxi University, Taiyuan, 030006, P. R. China

    Ru Chang

  3. National Engineering Research Center for Equipment and Technology of Cold Strip Rolling, Qinhuangdao, 066004, P. R. China

    Yi-ming Fang

  4. HBIS Group tang steel corp, Tangshan, 063000, P.R. China

    Ke-song Kang

Authors
  1. Ru Chang
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  2. Yi-ming Fang
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  3. Le Liu
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  4. Ke-song Kang
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Corresponding author

Correspondence to Yi-ming Fang.

Additional information

Recommended by Associate Editor Xiaojie Su under the direction of Editor PooGyeon Park. This work is partially supported by the National Natural Science Foundation of China and Baosteel Group Co. Ltd. (U1260203), Natural Science Foundation of Hebei Province (F2015203400, F2016203263), Science and Technology Research Youth Foundation Project in Colleges and Universities of Hebei Province (QN2016122) and Higher education innovation team of Hebei Province Leading Talent Cultivation Project (LJRC013).

Ru Chang received her B.S. degree in applied mathematics from the Taiyuan Normal University in 2007, her M.S. degree in operation science and control theory from the Yanshan University in 2010, and her Ph.D. degree in control science and engineering from the Yanshan University in 2016. She is currently an instructor with the Department of Automation, Shanxi University, Taiyuan, China. Her research interests include adaptive neural control, robust control, and complex nonlinear systems.

Yi-ming Fang received his B.E. and M.E. degrees in automation from the Northeast Heavy Machinery Institute (which was renamed Yanshan University in 1997), Qiqihar, China, in 1985 and 1988, respectively, and his Ph.D. degree in mechanical and electronic engineering from the Yanshan University in 2003. He is currently a Professor with the Department of Automation, Yanshan University, Qinhuangdao. His research interests include modeling & simulation and control of complex system, adaptive control and robust control of metallurgical automation system.

Le Liu received his B.E. degree in automation from the Hebei University of Science & Technology in 2008, his M.E. and Ph.D. degrees in control science and engineering from the Yanshan University, in 2011 and 2015, respectively. He is currently an instructor with the Department of Automation, Yanshan University, Qinhuangdao. His research interests include decoupling control and coordination control of the multivariable systems.

Ke-song Kang received his B.E. degree in automation and his M.E. degree in control science and control engineering, from the Yanshan University, in 2013 and 2016, respectively. He is currently an Assistant Engineer with the HBIS Group Tang Steel Corp, Tangshan, China. His research interests include industrial automation, adaptive control and robust control theory, control of hydraulic servo system.

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Chang, R., Fang, Ym., Liu, L. et al. Prescribed performance adaptive neural tracking control for strict-feedback Markovian jump nonlinear systems with time-varying delay. Int. J. Control Autom. Syst. 15, 1020–1031 (2017). https://doi.org/10.1007/s12555-015-0295-5

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  • DOI: https://doi.org/10.1007/s12555-015-0295-5

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