Skip to main content
SpringerLink
Log in

Adaptive sliding mode control of switched systems with different input matrix

  • Regular Papers
  • Control Theory and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This paper investigates the sliding mode control (SMC) problem for switched systems. The parameter uncertainties are norm-bounded, and the upper bound of the nonlinear term and the loss of effectiveness of actuator faults are unknown. A novel adaptive sliding mode controller is constructed such that the influences of actuator faults and unknown nonlinearity can be effectively attenuated and the state variables can reach the predefined common sliding surface. Based on average dwell time strategy, the exponential stability condition of the switched systems is obtained. Finally, simulation results are presented to show the effectiveness of the proposed techniques.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. C. K. Ahn, “Switched exponential state estimation of neural networks based on passivity theory,” Nonlinear Dynamics, vol. 67, no. 67, pp. 573–586, 2012.

    Article  MathSciNet  MATH  Google Scholar 

  2. C. K. Ahn, “Receding horizon disturbance attenuation for Takagi-Sugeno fuzzy switched dynamic neural networks,” Information Sciences, vol. 280, pp. 53–63, 2014. [click]

    Article  MathSciNet  MATH  Google Scholar 

  3. Y. J. Wang and F. Ding, “Novel data filtering based parameter identification for multiple-input multiple-output systems using the auxiliary model,” Automatica, vol. 71, pp. 308–313, 2016. [click]

    Article  MathSciNet  MATH  Google Scholar 

  4. Y. J. Wang and F. Ding, “The filtering based iterative identification for multivariable systems,” IET Control Theory & Applications vol. 10, no, 8, pp. 894–902, 2016. [click]

    Article  MathSciNet  Google Scholar 

  5. D. Liberzon and A. S. Morse, “Basic problems in stability and design of switched systems,” IEEE Control Systems, vol. 19, no. 5, pp. 59–70, 1999. [click]

    Article  Google Scholar 

  6. H. Y. Li, P. Shi, D. Y. Yao, and L. G. Wu, “Observerbased adaptive sliding mode control for nonlinear Markovian jump systems,” Automatica, vol. 64, pp. 133–142, 2016. [click]

    Article  MathSciNet  MATH  Google Scholar 

  7. H. Lin and P. J. Antsaklis, “Stability and stabilizability of switched linear systems: a survey of recent results,” IEEE Transactions on Automatic control, vol. 54, no. 2, pp. 308–322, 2009. [click]

    Article  MathSciNet  MATH  Google Scholar 

  8. J. Tao, R. Q. Lu, P. Shi, H. Y. Su, and Z.-G. Wu, “Dissipativity-based reliable control for fuzzy Markov jump systems with actuator faults,” IEEE Transactions on Cybernetics, vol. 47, no. 9, pp. 2377–2388, 2017.

    Article  Google Scholar 

  9. Y. Xu, R. Q. Lu, H. Peng, K. Xie, and A. K. Xue, “Asynchronous dissipative state estimation for stochastic complex networks with quantized jumping coupling and uncertain measurements,” IEEE Transactions on Neural Networks & Learning Systems, vol. 28, no. 2, pp. 268–277, 2017.

    Article  MathSciNet  Google Scholar 

  10. Y. Xu, R. Q. Lu, P. Shi, J. Tao, and S. L. Xie, “Robust estimation for neural networks with randomly occurring distributed delays and Markovian jump coupling,” IEEE Transactions on Neural Networks & Learning Systems, DOI: 10.1109/TNNLS.2016.2636325.

  11. L. X. Zhang, S. L. Zhuang, and P. Shi, “Non-weighted quasi-time-dependent H¥ filtering for switched linear systems with persistent dwell-time,” Automatica, vol. 54, pp. 201–209, 2015. [click]

    Article  MathSciNet  MATH  Google Scholar 

  12. M. S. Branicky, “Multiple Lyapunov functions and other analysis tools for switched and hybrid systems,” IEEE Transactions on Automatic Control, vol. 43, no. 4, pp. 475–482, 1998. [click]

    Article  MathSciNet  MATH  Google Scholar 

  13. L. X. Zhang and H. J. Gao, “Asynchronously switched control of switched linear systems with average dwell time,” Automatica, vol. 46, no. 5, pp. 953–958, 2010. [click]

    Article  MathSciNet  MATH  Google Scholar 

  14. L. Bai, Q. Zhou, L. J. Wang, Z. D. Yu, and H. Y. Li, “Observer-based adaptive control for stochastic nonstrictfeedback systems with unknown backlash-like hysteresis,” International Journal of Adaptive Control and Signal Processing, DOI:10.1002/acs.2780.

  15. T. T. Han, S. S. Ge, and T. H. Lee, “Persistent dwell-time switched nonlinear systems: Variation paradigm and gauge design,” IEEE Transactions on Automatic Control, vol. 55, no. 2, pp. 321–337, 2010. [click]

    Article  MathSciNet  MATH  Google Scholar 

  16. L. X. Zhang, Y. Z. Zhu, Z. P. Ning, and X. Y. Yin, “Resilient estimation for networked systems with variable communication capability,” IEEE Transactions on Automatic Control, vol. 61, no. 12, pp. 4150–4156, 2016. [click]

    Article  MathSciNet  MATH  Google Scholar 

  17. R. Wang, M. Liu, and J. Zhao, “Reliable H ∞ control for a class of switched nonlinear systems with actuator failures,” Nonlinear Analysis: Hybrid Systems, vol. 1, no. 3, pp. 317–325, 2007. [click]

    MathSciNet  MATH  Google Scholar 

  18. J. Zhao and D. J. Hill, “On stability, L2-gain and H¥ control for switched systems,” Automatica, vol. 44, no. 5, pp. 1220–1232, 2008. [click]

    Article  MathSciNet  MATH  Google Scholar 

  19. Z.W. Gao and S. X. Ding, “Actuator fault robust estimation and fault-tolerant control for a class of nonlinear descriptor systems,” Automatica, vol. 43, no. 5, pp. 912–920, 2007. [click]

    Article  MathSciNet  MATH  Google Scholar 

  20. H. Y. Li, P. Shi, and D. Y. Yao, “Adaptive sliding mode control of Markov jump nonlinear systems with actuator faults,” IEEE Transactions on Automatic Control, vol. 62, no. 4, 1933–1939. 2017.

    Article  MathSciNet  MATH  Google Scholar 

  21. R. Q. Lu, Y. Xu, and R. D. Zhang, “A new design of model predictive tracking control for networked control system under random packet loss and uncertainties,” IEEE Transactions on Industrial Electronics, vol. 63, no. 11, pp. 6999–7007, 2016. [click]

    Article  Google Scholar 

  22. Y. Q. Wu, X. Y. Meng, L. H. Xie, R. Q. Lu, H. Y. Su, and Z.-G. Wu, “An input-based triggering approach to leaderfollowing problems,” Automatica, vol. 75, pp. 221–228, 2017. [click]

    Article  MathSciNet  MATH  Google Scholar 

  23. Y. Xu, R. Q. Lu, P. Shi, H. Y. Li, and S. L. Xie, “Finitetime distributed state estimation over sensor networks with round-robin protocol and fading channels,” IEEE Transactions on Cybernetics, DOI: 10.1109/TCYB.2016.2635122.

  24. Q. Zhou, C. W. Wu, and P. Shi, “Observer-based adaptive fuzzy tracking control of nonlinear systems with time delay and input saturation,” Fuzzy Sets and Systems, vol. 316, pp. 49–68, 2017.

    Article  MathSciNet  Google Scholar 

  25. H. Y. Li, J. H. Wang, H. P. Du, and H. R. Karimi, “Adaptive sliding mode control for Takagi-Sugeno fuzzy systems and its applications,” IEEE Transactions on Fuzzy Systems, DOI: 10.1109/TFUZZ.2017.2686357, 2017.

    Google Scholar 

  26. H. Y. Li, J. H. Wang, L. G. Wu, H. K. Lam, and Y. B. Gao, “Optimal guaranteed cost sliding mode control of interval type-2 fuzzy time-delay systems,” IEEE Transactions on Fuzzy Systems, DOI: 10.1109/TFUZZ.2017.2648855.

  27. M. Liu, L. X. Zhang, P. Shi, and Y. X. Zhao, “Sliding mode control of continuous-time Markovian jump systems with digital data transmission,” Automatica, vol. 80, pp. 200–209, 2017.

    Article  MathSciNet  MATH  Google Scholar 

  28. Y. G. Niu and X. Y. 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. [click]

    Article  MathSciNet  MATH  Google Scholar 

  29. Q. Zhou, D. Y. Yao, J. H. Wang, and C. W. Wu, “Robust control of uncertain semi-Markovian jump systems using sliding mode control method,” Applied Mathematics and Computation, vol. 286, pp. 72–87, 2016.

    Article  MathSciNet  Google Scholar 

  30. A. Rosales and I. Boiko, “Disturbance attenuation for systems with second-order sliding modes via linear compensators,” IET Control Theory & Applications, vol. 9, no. 4, pp. 526–537, 2015. [click]

    Article  MathSciNet  Google Scholar 

  31. Y. H. Liu, Y. G. Niu, J. Lam, and B. Y. Zhang, “Sliding mode control for uncertain switched systems with partial actuator faults,” Asian Journal of Control, vol. 16, no. 6, pp. 1779–1788, 2014. [click]

    Article  MathSciNet  MATH  Google Scholar 

  32. X. D. Zhao, H. Liu, Z. H. Wang, “Weighted H¥ performance analysis of switched linear systems with modedependent average dwell time,” International Journal of Systems Science, vol. 44, no. 11, pp. 1–10, 2012.

    Google Scholar 

  33. H. Shen, Z. G. Wu, and H. P. Ju, “Reliable mixed passive and H¥ filtering for semi-Markov jump systems with randomly occurring uncertainties and sensor failures,” International Journal of Robust & Nonlinear Control, vol. 25, no. 17, pp. 3231–3251, 2014. [click]

    Article  MathSciNet  MATH  Google Scholar 

  34. L. X. Zhang, T. Yang, and P. Colaneri, “Stability and stabilization of semi-Markov jump linear systems with exponentially modulated periodic distributions of sojourn time,” IEEE Transactions on Automatic Control, vol. 62, no. 6, pp. 2870–2885, 2017.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Automation, Guangdong University of Technology, Guangzhou, 510006, Guangdong, China

    Deyin Yao, Renquan Lu & Yong Xu

  2. School of Automation, Guangdong University of Technology, Guangzhou, 510006, China

    Hongyi Li

  3. College of Engineering, Bohai University, Jinzhou, 121013, China

    Hongyi Li

Authors
  1. Deyin Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Renquan Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yong Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hongyi Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Renquan Lu.

Additional information

Recommended by Associate Editor Jun Yoneyama under the direction of Editor Myo Taeg Lim. This work is supported by the Funds for China National Funds for Distinguished Young Scientists (61425009), the National Natural Science Foundation of China under Grants (U1611262, 61622302, 61573070, 61503106), Guangdong Province Higher Vocational Colleges & Schools Pearl River Scholar approved in 2015 and the China National 863 Technology Projects under Grant (2015BAF32B03-05).

Deyin Yao received the M.S. in Control Theory from Bohai University, Research Institute of Automation, Jinzhou, China in 2016, and he is currently pursuing the Ph.D. degree in School of Automation, Guangdong University of Technology, Guangzhou, China. His research interests include robust control, sliding mode control and neural control.

Renquan Lu received the Ph.D. degree in control science and engineering from Zhejiang University, Hangzhou, China, in 2004. He was a research fellow with School of Electrical Engineering and Computer Science, University of Newcastle. He was a recipient of the National Science Fund for Distinguished Young Scientists of China in 2014, and New Century Excellent Talents in University of Ministry of Education of China in 2010. Currently, he is a full Professor in School of Automation, at Guangdong University of Technology, Guangzhou, China. His research interests include robust control, Networked Control Systems, and complex systems.

Yong Xu received the Ph.D. degree from Zhejiang University, Hangzhou, China, in 2014. He was a Visiting Internship Student with the Department of Electronic and Computer Engineering, The Hong Kong University of Science and Technology, from June 2013 to November 2013. He is currently a Lecturer with the School of Automation, Guangdong University of Technology, Guangzhou, China. His current research interests include networked control systems, state estimation, and Markov jump systems.

Hongyi Li received his Ph.D. degree in Intelligent Control from the University of Portsmouth, Portsmouth, UK, in 2012. His coauthored paper received the 2016 Andrew P. Sage Best Transactions Paper Award from IEEE System, Man, Cybernetics (SMC) Society. His research interests include fuzzy control, robust control and their applications.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yao, D., Lu, R., Xu, Y. et al. Adaptive sliding mode control of switched systems with different input matrix. Int. J. Control Autom. Syst. 15, 2500–2506 (2017). https://doi.org/10.1007/s12555-016-0570-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-016-0570-0

Keywords

Search

Navigation