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Actuator Failure Compensation Control Scheme of the Nonlinear Triangular Systems by Static Gain Technique

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  • Control Theory and Applications
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Abstract

In this paper, the technique of static gain as a new research approach is applied in the nonlinear triangular systems to investigate the issue of actuator fault. By employing the static gain technique, the nonlinear lower-triangular systems are converted into the form which is easy to find its Lyapunov function. The fault parameters of the actuator are subsequently processed by the efficient adaptive estimation tactic, after that, the goal of guaranteeing the global boundness of all closed-loop signals can be achieved by utilizing a state controller with the hyperbolic functions. Moreover, by adopting the same strategy, the actuator failure compensation problem is also solved for the nonlinear upper-triangular systems. Last but not least, the effectiveness of the design scheme is verified by two numerical simulation examples.

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References

  1. B. Wang, H. B. Ji, and J. J. Zhu, “Robust control design of a class of nonlinear systems in polynomial lower-triangular form,” Int. J. Control Autom. Syst., vol. 7, no. 1, pp. 41–48, February 2009.

    Article  Google Scholar 

  2. X. Zhang and Y. Lin, “A new approach to global asymptotic tracking for a class of low-triangular nonlinear systems via output feedback,” IEEE Trans. Autom. Control, vol. 57, no. 12, pp. 3192–3196, December 2012.

    Article  MathSciNet  MATH  Google Scholar 

  3. X. Zhang and Y. Lin, “Adaptive output feedback tracking for a class of nonlinear systems,” Automatica, vol. 48, no. 9, pp. 2372–2376, September, 2012.

    Article  MathSciNet  MATH  Google Scholar 

  4. C. J. Qian and W. Lin, “Almost disturbance decoupling for a class of high-order nonlinear systems,” IEEE Trans. Autom. Control, vol. 45, no. 6, pp. 1208–1214, June 2000.

    Article  MathSciNet  MATH  Google Scholar 

  5. T. T. Gao, Y. J. Liu, L. Liu, and D. P. Li, “Adaptive neural network-Based control for a class of nonlinear pure-feedback systems with time-varying full state constraints,” IEEE/CAA Journal of Automatica Sinica, vol. 5, no. 5, pp. 923–933, September 2018.

    Article  MathSciNet  Google Scholar 

  6. L. Tang and D. J. Li, “Time-varying barrier lyapunov function based adaptive neural controller design for nonlinear pure-feedback systems with unknown hysteresis,” Int. J. Control Autom. Syst., vol. 17, no. 7, pp. 1642–1654, March 2019.

    Article  Google Scholar 

  7. X. F. Zhang and Z. L. Cheng, “Global stabilization of a class of time-delay nonlinear systems,” Int. J. Syst. Sci., vol. 36, no. 8, pp. 461–468, June 2005.

    Article  MathSciNet  MATH  Google Scholar 

  8. X. F. Zhang, L. Baron, Q. R. Liu, and E.-K. Boukas, “Design of stabilizing controllers with a dynamic gain for feedforward nonlinear time-delay systems,” IEEE Trans. Autom. Control, vol. 56, no. 3, pp. 692–697, March 2011.

    Article  MathSciNet  MATH  Google Scholar 

  9. X. F. Zhang, L. Liu, G. Feng, and C. H. Zhang, “Output feedback control of large-scale nonlinear time-delay systems in lower triangular form,” Automatica, vol. 49, no. 11, pp. 3476–3483, November 2013.

    Article  MathSciNet  MATH  Google Scholar 

  10. X. D. Chen and X. Zhang, “Output-feedback control strategies of lower-triangular nonlinear nonholonomic systems in any prescribed finite time,” Int. J. Robust Nonlinear Control, vol. 29, no. 4, pp. 904–918, March 2019.

    Article  MathSciNet  MATH  Google Scholar 

  11. H. F. Li, X. F. Zhang, and Q. R. Liu, “Adaptive output feedback control for a class of large-scale output-constrained non-linear time-delay systems,” IET Control Theory Appl., vol. 12, no. 1, pp. 174–181, January 2018.

    Article  MathSciNet  Google Scholar 

  12. H. F. Li, Q. R. Liu, X. F. Zhang, and X. D. Cheng, “Quantized control for the class of feedforward nonlinear systems,” Sci. China Inform Sci., vol. 62, no. 8, August 2019.

  13. J. Y. Zhai and H. R. Karimi, “Global output feedback control for a class of nonlinear systems with unknown homogenous growth condition,” Int. J. Robust Nonlin., vol. 29, no. 7, pp. 2082–2095, January 2019.

    Article  MathSciNet  MATH  Google Scholar 

  14. G. Tao, S. M. Joshi, and X. L. Ma, “Adaptive state feedback and tracking control of systems with actuator failures,” IEEE Trans. Autom. Control, vol. 46, no. 1, pp. 78–95, January 2001.

    Article  MathSciNet  MATH  Google Scholar 

  15. S. H. Chen, G. Tao, and S. M. Joshi, “Adaptive actuator failure compensation designs for linear systems,” Int. J. Control Autom. Syst., vol. 2, no. 1, pp. 1–14, March 2004.

    Article  Google Scholar 

  16. M. Staroswiecki, K. Zhang, D. Berdjag, and M. Abbas-Turki, “Reducing the reliability over-cost in reconfiguration-based fault tolerant control under actuator faults,” IEEE T. on Automat. Contr., vol. 57, no. 12, pp. 3181–3186, December 2012.

    Article  MathSciNet  MATH  Google Scholar 

  17. Y. Liu, G. H. Yang, and X. J. Li, “Fault-tolerant control for uncertain linear systems via adaptive and LMI approaches,” Int. J. Syst. Sci., vol. 48, no. 2, pp. 347–356, May 2016.

    Article  MathSciNet  MATH  Google Scholar 

  18. J. Y. Gong, B. Jiang, and Q. K. Shen, “Adaptive fault-tolerant neural control for large-scale systems with actuator faults,” Int. J. Control Autom. Syst., vol. 17, no. 6, pp. 1421–1431, January 2019.

    Article  Google Scholar 

  19. D. Kharrat, H. Gassara, A. E. Hajjaji, and M. Chaabane, “Adaptive observer and fault tolerant control for takagisugeno descriptor nonlinear systems with sensor and actuator faults,” Int. J. Control Autom. Syst., vol. 16, no. 3, pp. 972–982, December 2018.

    Article  MATH  Google Scholar 

  20. H. M. Tran and H. Trinh, “Distributed functional observer based fault detection for interconnected time-delay systems,” IEEE Syst. J., vol. 13, no. 1, pp. 940–951, March 2019.

    Article  Google Scholar 

  21. Y. Xi and Y. Meng, “Adaptive actuator failure compensation control for hypersonic vehicle with full state constraints,” Aerosp Sci. Technol., vol. 85, pp. 464–473, February 2019.

    Article  Google Scholar 

  22. L. T. Xing, C. Y. Wen, Z. T. Liu, H. Y. Su, and J. P. Cai, “Adaptive compensation for actuator failures with event-triggered input,” Automatica, vol. 85, pp. 129–136, November 2017.

    Article  MathSciNet  MATH  Google Scholar 

  23. X. Tang, G. Tao, and S. M. Joshi, “Adaptive output feed-back actuator failure compensation for a class of non-linear systems,” Int. J. of Adapt. Control Signal Process., vol. 19, no. 6, pp. 419–444, August 2005.

    Article  MATH  Google Scholar 

  24. L. Liu, Z. S. Wang, and H. G. Zhang, “Adaptive NN fault-tolerant control for discrete-time systems in triangular forms with actuator fault,” Neurocomputing, vol. 152, no. 25, pp. 209–221, March 2015.

    Article  Google Scholar 

  25. H. Q. Wang, X. P. Liu, P. X. Liu, and S. Li, “Robust adaptive fuzzy fault-tolerant control for a class of non-lower-triangular nonlinear systems with actuator failures,” Inform. Sciences, vol. 336, no. 1, pp. 60–74, April 2016.

    Article  MATH  Google Scholar 

  26. L. Liu, Y. J. Liu, and S. C. Tong, “Neural networks-based adaptive finite-time fault-tolerant control for a class of strict-feedback switched nonlinear systems,” IEEE T. Cybernetics, vol. 49, no. 7, pp. 2536–2545, July, 2019.

    Article  Google Scholar 

  27. J. P. Cai, C. Y. Wen, H. Y. Su, and Z. T. Liu, “Robust adaptive failure compensation of hysteretic actuators for a class of uncertain nonlinear systems,” IEEE Trans. Autom. Control, vol. 58, no. 9, pp. 2388–2394, September 2013.

    Article  MathSciNet  MATH  Google Scholar 

  28. Z. Q. Zhang, S. Y. Xu, Y. Guo, and Y. M. Chu, “Robust adaptive output-feedback control for a class of nonlinear systems with time-varying actuator faults,” Int. J. of Adapt. Control Signal Process., vol. 24, no. 9, pp. 743–759, September, 2010.

    Article  MathSciNet  MATH  Google Scholar 

  29. P. Krishnamurthy and F. Khorrami, “Feedforward systems with ISS appended dynamics: Adaptive output-feedback stabilization and disturbance attenuation,” IEEE Trans. Autom. Control, vol. 53, no. 1, pp. 405–412, February, 2008.

    Article  MathSciNet  MATH  Google Scholar 

  30. C. X. Wang, Y. Q. Wu, and J. B. Yu, “Barrier Lyapunov functions-based dynamic surface control for pure-feedback systems with full state constraints,” IET Control Theory Appl., vol. 11, no. 4, pp. 524–530, February, 2017.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, Jinan, 250061, P. R. China

    Fei Zhu, Xianfu Zhang & Hanfeng Li

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  1. Fei Zhu
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  2. Xianfu Zhang
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  3. Hanfeng Li
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Correspondence to Xianfu Zhang.

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Recommended by Associate Editor Yan-Jun Liu under the direction of Editor Guang-Hong Yang. The work was supported by the National Natural Science Foundation of China (61973189 and 61503214), the Research Fund for the Taishan Scholar Project of Shandong Province of China (ts20190905), and the Foundation for Innovative Research Groups of National Natural Science Foundation of China (61821004).

Fei Zhu is presently a master’s student with the School of Control Science and Engineering, Shandong University, China. Her current research interests include nonlinear systems, and fault-tolerant control.

Xianfu Zhang received his M.S. degree in Fundamental Mathematics from the School of Mathematics Sciences, Shandong Normal University, China, in 1999, and a Ph.D. degree in operational research and control from the School of Mathematics, Shandong University, China, in 2005. From 1999 to 2011, he worked in the School of Science, Shandong Jianzhu University, China. From September 2008 to February 2009, he was a visiting scholar in the Department of Mechanical Engineering, Ecole Polytechnique de Montreal, Canada. From November 2009 to February 2010, and from July 2012 to October 2012, he was a research assistant in City University of Hong Kong, Hong Kong. He joined the School of Control Science and Engineering, Shandong University, China, in 2012, where he is currently a professor. His main research interests include nonlinear systems, fractional-order systems, and time-delay systems.

Hanfeng Li received his B.S. degree from the School of Mathematics and Statistics, Shandong Normal University, China, in 2016. Currently, he is a doctor at the School of Control Science and Engineering, Shandong University, China. His main research interests include nonlinear systems, time-delay systems, and large-scale systems.

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Zhu, F., Zhang, X. & Li, H. Actuator Failure Compensation Control Scheme of the Nonlinear Triangular Systems by Static Gain Technique. Int. J. Control Autom. Syst. 18, 2297–2305 (2020). https://doi.org/10.1007/s12555-019-0406-9

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  • DOI: https://doi.org/10.1007/s12555-019-0406-9

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