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Finite-time Sliding Mode Control of Markovian Jump Systems Subject to Actuator Faults

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  • Control Theory and Applications
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Abstract

This paper addresses the problem of finite-time boundedness (FTB) for a class of Markovian jump systems (MJSs) via sliding mode control (SMC) technique, in which there may happen actuator faults in all of control channels and mismatched external disturbance. By means of the available boundary information of actuator faults, a suitable sliding mode controller is designed such that state trajectories are driven to sliding surface before a specified finite (possibly short) time interval. Furthermore, a partitioning strategy is introduced to derive the sufficient conditions for ensuring the FTB of the closed-loop systems over the whole specified finite-time interval including the reaching phase and the sliding motion phase. Finally, a practical example are provided from an F-404 aircraft engine system to illustrate the proposed method.

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References

  1. A. Fekih, “Fault-tolerant flight control design for effective and reliable aircraft systems,” Journal of Control and Decision, vol. 1, no. 4, pp. 299–316, 2014.

    Article  Google Scholar 

  2. G. Tao, “Direct adaptive actuator failure compensation control: a tutorial,” Journal of Control and Decision, vol. 1, no. 1, pp. 75–101, 2014.

    Article  Google Scholar 

  3. M. Yadegar, A. Afshar, and N. Meskin, “Fault-tolerant control of non-linear systems based on adaptive virtual actuator,” IET Control Theory & Applications, vol. 11, no. 9, pp. 1371–1379, 2017.

    Article  MathSciNet  Google Scholar 

  4. Y. Niu and X. Wang, “Sliding mode control design for uncertain delay systems with partial actuator degradation,” International Journal of Systems Science, vol. 40, no. 4, pp. 403–409, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  5. D. Ye, L. Su, J. Wang, and Y. Pan, “Adaptive reliable H¥ optimization control for linear systems with time-varying actuator fault and delays,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 47, no. 7, pp. 1635–1643, 2017.

    Article  Google Scholar 

  6. M. Liu, L. Zhang, and W. Zheng, “Fault reconstruction for stochastic hybrid systems with adaptive discontinuous observer and non-homogeneous differentiator,” Automatica, vol. 85, pp. 339–348, 2017.

    Article  MathSciNet  MATH  Google Scholar 

  7. S. Mobayen and F. Tchier, “A novel robust adaptive second-order sliding mode tracking control technique for uncertain dynamical systems with matched and unmatched disturbances,” International Journal of Control, Automation and Systems, vol. 15, no. 3, pp. 1097–1106, 2017.

    Article  Google Scholar 

  8. O. L. V. Costa, M. D. Fragoso, and M. G. Todorov, Continuous-time Markov Jump Linear Systems, Springer, London, 2012.

    MATH  Google Scholar 

  9. 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, 2015.

    Article  MathSciNet  Google Scholar 

  10. Y. Niu, D. W. C. Ho, and X. Wang, “Sliding mode control for Itô stochastic jump systems with Markovian switching,” Automatica, vol. 43, no. 10, pp. 1784–1790, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  11. B. Chen, Y. Niu, and Y. Zou, “Adaptive sliding mode control for stochastic Markovian jumping systems with actuator degradation,” Automatica, vol. 49, no. 6, pp. 1748–1754, 2013.

    Article  MathSciNet  MATH  Google Scholar 

  12. L. Chen, M. Liu, and S. Fu, “Adaptive sliding mode control for stochastic jump systems against sensor and actuator failures,” IET Control Theory & Applications, vol. 10, no. 16, pp. 2000–2009, 2016.

    Article  MathSciNet  Google Scholar 

  13. J. Zhu and G. Yang, “Adaptive sliding-mode control for stochastic Markovian jumping systems with actuator faults,” IET Control Theory & Applications, vol. 10, no. 6, pp. 664–674, 2016.

    Article  MathSciNet  Google Scholar 

  14. H. Li, P. Shi, and D. Yao, “Adaptive sliding-mode control of Markov jump nonlinear systems with actuator faults,” IEEE Transactions on Automatic Control, vol. 82, no. 4, pp. 1933–1939, 2017.

    Article  MathSciNet  MATH  Google Scholar 

  15. S. Yin, H. Yang, and O. Kaynak, “Sliding mode observerbased FTC for Markovian jump systems with actuator and sensor faults,” IEEE Transactions on Automatic Control, vol. 82, no. 4, pp. 1933–1939, 2017.

    MATH  Google Scholar 

  16. P. Dorato, “Short time stability in linear time-varying systems,” Proceedings of the IRE International Convention Record, vol. 4, pp. 83–87, 1961.

    Google Scholar 

  17. F. Amato, M. Ariola, and P. Dorato, “Finite-time control of linear systems subject to parametric uncertainties and disturbances,” Automatica, vol. 37, no. 9, pp. 1459–1463, 2001.

    Article  MATH  Google Scholar 

  18. M. Shen, S. Yan, G. Zhang and J. H. Park, “Finite-time H¥ static output control of Markov jump systems with an auxiliary approach,” Applied Mathematics and Computation, vol. 273, pp. 553–561, 2016.

    Article  MathSciNet  Google Scholar 

  19. M. Shen, S. Yan, Z. Tang, and Z. Gu, “Finite-time H¥ filtering of Markov jump systems with incomplete transition probabilities: a probability approach,” IET Signal Processing, vol. 9, no. 7, pp. 572–578, 2015.

    Article  Google Scholar 

  20. J. Song, Y. Niu, and Y. Zou, “Finite-time stabilization via sliding mode control,” IEEE Transactions on Automatic Control, vol. 62, no. 3, pp. 1478–1483, 2017.

    Article  MathSciNet  MATH  Google Scholar 

  21. G. Garcia, S. Tarbouriech, and J. Bernussou, “Finite-time stabilization of linear time-varying continuous systems,” IEEE Transactions on Automatic Control, vol. 54, no. 2, pp. 364–369, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  22. F. Amato, C. Cosentino, G. de Tommasi, and A. Pironti, “New conditions for the finite-time stability of stochastic linear time-varying systems,” Proceedings of European Control Conference, pp. 1219–1224, 2015.

    Google Scholar 

  23. J. Song, Y. Niu, and Y. Zou, “Asynchronous output feedback control of time-varying Markovian jump systems within a finite-time interval,” Journal of the Franklin Institute, vol. 354, no. 15, pp. 6747–6765, 2017.

    Article  MathSciNet  MATH  Google Scholar 

  24. J. Song, Y. Niu, and Y. Zou, “Robust finite-time bounded control for discrete-time stochastic systems with communication constraint,” IET Control Theory & Applications, vol. 9, no. 13, pp. 2015–2021, 2015.

    Article  MathSciNet  Google Scholar 

  25. C. Deng and G.-H. Yang, “Decentralized fault-tolerant control for a class of nonlinear large-scale systems with actuator faults,” Information Sciences, vol. 382–383, pp. 334–349, 2017.

    Article  Google Scholar 

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Authors and Affiliations

  1. Key Laboratory of Advanced Control and Optimization for Chemical Process East China University of Science and Technology, Ministry of Education, Shanghai, 200237, China

    Zhiru Cao, Yugang Niu & Haijuan Zhao

Authors
  1. Zhiru Cao
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  2. Yugang Niu
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  3. Haijuan Zhao
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Corresponding author

Correspondence to Yugang Niu.

Additional information

Recommended by Associate Editor Jiuxiang Dong under the direction of Editor Guanh-Hong Yang. This work was supported in part by the NNSF (61673174, 61773162) and the 111 Project (B17017) from China.

Zhiru Cao received her B.S. degree from Nanjing Tech University, China, in 2016. She is now pursuing a Ph.D. degree in Control Science & Engineering at East China University of Science and Technology, China. Her current research areas are Markovian jump systems, sliding mode control, and finite-time control.

Yugang Niu is a professor with the East China University of Science & Technology. His research Areas includes sliding mode control, stochastic systems, wireless sensor networks, microgrid.

Haijuan Zhao received her B.S. and M.S. degrees from Qufu Normal University, China, in 2013 and 2016, respectively. She is now pursuing a Ph.D. degree in Control Science & Engineering at East China University of Science and Technology, China. Her current research interests include switched systems, finite-time stability, and sliding mode control.

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Cao, Z., Niu, Y. & Zhao, H. Finite-time Sliding Mode Control of Markovian Jump Systems Subject to Actuator Faults. Int. J. Control Autom. Syst. 16, 2282–2289 (2018). https://doi.org/10.1007/s12555-017-0501-8

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  • DOI: https://doi.org/10.1007/s12555-017-0501-8

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