Skip to main content
SpringerLink
Log in

A Multi-step Output Feedback Robust MPC Approach for LPV Systems with Bounded Parameter Changes and Disturbance

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

Abstract

This paper considers a multi-step output feedback robust model predictive control (OFRMPC) approach for the linear parameter varying (LPV) systems with bounded changes of scheduling parameters and bounded disturbance. Less conservative bounds of future estimation error sets and system parametric uncertain sets are predicted by considering bounded changes of scheduling parameters in LPV systems. In the multi-step OFRMPC approach, an optimization problem is solved to obtain a sequence of controller gains, which considers predictions of future bounds of estimation error sets and system parametric uncertain sets. The optimized sequence of controller gains corresponding to a sequence of Lyaponov matrices have less constraint conditions and also introduce more degree of freedom for the optimization. The proposed multi-step OFRMPC guarantees robust uniform ultimately bounded of the estimation error and robust stability of the observer system. A numerical example is given to demonstrate the effectiveness of the approach.

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. M. L. Darby and M. Nikolaou, “MPC: Current practice and challenges,” Control Engineering Practice, vol. 20, no. (4), pp. 328–342, April 2012.

    Article  Google Scholar 

  2. S. J. Qin and T. A. Badgwell, “A survey of industrial model predictive control technology,” Control Engineering Practice, vol. 7, no. (11), pp.733–764, July 2003.

    Google Scholar 

  3. A. Kumara and Z. Ahmada, “Model predictive control (MPC) and its current issues in Chemical Engineering,” Chemical Engineering Communications, vol. 199, no. (4), pp. 472–511, 2012.

    Article  Google Scholar 

  4. P. Bumroongsri and S. Kheawhom, “Robust model predictive control with time–varying tubes,” International Journal of Control, Automation and Systems, vol. 15, no. (4), pp. 1479–1484, August 2017.

    Article  MATH  Google Scholar 

  5. D. Q. Mayne, “Model predictive control: recent developments and future promise,” Automatica, vol. 50, no. (12), pp. 2967–2986, December 2014.

    Article  MathSciNet  MATH  Google Scholar 

  6. R. Zhang, D. Chen, and X. Ma, “Nonlinear predictive control of a hydropower system model,” Entropy, vol. 17, no. (9), pp. 6129–6149, September 2015.

    Article  Google Scholar 

  7. M. V. Kothare, V. Balakrishnan, and M. Morari, “Robust constrained model predictive control using linear matrix inequalities,” Automatica, vol. 32, no. (10), pp. 1361–1379, October 1996.

    Article  MathSciNet  MATH  Google Scholar 

  8. H. S. Abbas, N. Meskin, J. Mohammadpour, and J. Hanema, “An MPC approach for LPV systems in inputoutput form,” Proceedings of the 54th IEEE Conference on Decision and Control, pp. 91–96, Osaka, Japan, December 2015.

    Google Scholar 

  9. W. Yang, J. Gao, G. Feng, and T. Zhang, “An optimal approach to output–feedback robust model predictive control of LPV systems with disturbances,” International Journal of Robust and Nonlinear Control, vol. 26, no. (15), pp. 3253–3273, October 2016.

    Article  MathSciNet  MATH  Google Scholar 

  10. D. He, H. Huang, and Q. Chen, “Quasi–min–max MPC for constrained nonlinear systems with guaranteed input–tostate stability,” Journal of the Franklin Institute, vol. 351, no. (6), pp. 3405–3423, June 2014.

    Article  MathSciNet  MATH  Google Scholar 

  11. Y. Lu and Y. Arkun, “Quasi–min–max MPC algorithms for LPV systems,” Automatica, vol. 36, no. (4), pp. 527–540, April 2000.

    Article  MathSciNet  MATH  Google Scholar 

  12. Y. I. Lee and B. Kouvaritakis, “Constrained robust model predictive control based on periodic invariance,” Automatica, vol. 42, no. (12), pp. 2175–2181, December 2006.

    Article  MathSciNet  MATH  Google Scholar 

  13. D. Li and Y. Xi, “The Feedback Robust MPC for LPV Systems with bounded rates of parameter changes,” IEEE Transactions on Automatic Control, vol. 55, no. (2), pp. 503–507, February 2010.

    Article  MathSciNet  MATH  Google Scholar 

  14. P. Zheng, D. Li, Y. Xi, and J. Zhang, “Improved model prediction and RMPC design for LPV systems with bounded parameter changes,” Automatica, vol. 49, no. (12), pp. 3695–3699, December 2013.

    Article  MathSciNet  MATH  Google Scholar 

  15. P. Zheng, D. Li, Y. Xi, and X. Li, “A sophisticated RMPC design for LPV systems based on the mixed multi–step feedback control,” Proceedings of the 34th Chinese Control Conference, pp. 4119–4123, Hangzhou, China, July 2015.

    Google Scholar 

  16. X. Ping, Z. Li, and P. Wang, “Dynamic output feedback robust MPC for LPV systems subject to input saturation and bounded disturbance,” International Journal of Control, Automation and Systems, vol. 15, no. (3), pp. 976–985, June 2017.

    Article  Google Scholar 

  17. T. Besselmann, J. Lofberg, and M. Morari, “Explicit MPC for LPV systems: Stability and optimality,” International Journal of Control, vol. 57, no. (9), pp. 2322–2332, September 2012.

    MathSciNet  MATH  Google Scholar 

  18. X. Ping and B. Ding, “Off–line approach to dynamic output feedback robust model predictive control,” Systems & Control Letters, vol. 62, no. (11), pp. 1038–1048, November 2013.

    Article  MathSciNet  MATH  Google Scholar 

  19. D. Li and Y. Xi, “Design of robust model predictive Ccntrol based on multi–step control set,” Acta Automatica Sinica, vol. 35, no. (4), pp. 433–437, April 2009.

    Article  MathSciNet  Google Scholar 

  20. H. Li, D. Chen, H. Zhang, C. Wu, and X. Wang, “Hamiltonian analysis of a hydro–energy generation system in the transient of sudden load increasing,” Applied Energy, vol. 185, pp. 244–253, January 2017.

    Article  Google Scholar 

  21. H. Li, D. Chen, H. Zhang, F. Wang, and D. Ba, “Nonlinear modeling and dynamic analysis of a hydro–turbine governing system in the process of sudden load increase transient,” Mechanical Systems and Signal Processing, vol. 80, pp. 414–428, December 2016.

    Article  Google Scholar 

  22. Y. Su, K. K. Tan, and T. H. Lee, “Tube based quasi–minmax output feedback MPC for LPV systems,” IFAC Proceedings Volumes, vol. 45, no. (15), pp. 186–191, 2012.

    Article  Google Scholar 

  23. X. Ping, “Output feedback robust MPC based on off–line observer for LPV systems via quadratic boundedness,” Asian Journal of control, vol. 19, no. (4), pp. 1641–1653, July 2017.

    Article  MathSciNet  MATH  Google Scholar 

  24. B. Ding, “Dynamic output feedback predictive control for nonlinear systems represented by a Takagi–Sugeno model, IEEE Transactions on Fuzzy Systems, vol. 19, no. (5), pp. 831–843, October 2011.

    Article  Google Scholar 

  25. T. H. Kim and H. W. Lee, “Quasi–min–max outputfeedback model predictive control for LPV systems with input saturation,” International Journal of Control, Automation and Systems, vol. 15, no. (3), pp. 1069–1076, June 2017.

    Article  Google Scholar 

  26. S. V. Raković, E. C. Kerrigan, K. I. Kouramas, and D. Q. Mayne, “Invariant approximations of the minimal robust positively invariant set,” IEEE Transactions on Automatic Control, vol. 50, no. (3), pp. 406–410, February 2005.

    Article  MathSciNet  MATH  Google Scholar 

  27. J. J. Martínez, “Minimal RPI sets computation for polytopic systems using the Bounded–real lemma and a new shrinking procedure,” IFAC–PapersOnLine, vol. 48, no. (26), pp. 182–187, 2015.

    Google Scholar 

  28. A. Alessandri, M. Baglietto, and G. Battistelli, “On estimation error bounds for receding–horizon filters using quadratic boundedness,” IEEE Transactions on Automatic Control, vol. 49, no. (8), pp. 1350–1355, August 2004.

    Article  MathSciNet  MATH  Google Scholar 

  29. A. Alessandri, M. Baglietto and G. Battistelli, “Design of state estimators for uncertain linear systems using quadratic boundedness,” Automatic, vol. 42, no. (3), pp. 497–502, March 2006.

    Article  MathSciNet  MATH  Google Scholar 

  30. G. Bitsoris, M. Vassilaki, and N. Athanasopoulos, “Robust positive invariance and ultimate boundedness of nonlinear systems,” Proc. of 20th Mediterranean Conference on Control & Automation, pp. 598–603, Barcelona, Spain, July 2012.

    Google Scholar 

  31. K. Derinkuyu and M. C. Pinar, “On the S–procedure and some variants,” Mathematical Methods of Operations Research, vol. 64, no. (1), pp. 55–77, August 2006.

    Article  MathSciNet  MATH  Google Scholar 

  32. P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI control toolbox for use with matlab, User’s guide, The Math Works Inc., Natick, MA, USA, 1995.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electro-Mechanical Engineering, Xidian University, Xi’an, China

    Xu-Bin Ping & Jia-Feng Zhang

  2. Information and Navigation College, Air Force Engineering University, Xi’an, China

    Peng Wang

Authors
  1. Xu-Bin Ping
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jia-Feng Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xu-Bin Ping.

Additional information

Recommended by Associate Editor Andrea Cristofaro under the direction of Editor Myo Taeg Lim. This work was funded by the Natural Science Basic Research Plan in Shaanxi Province of China (2017JQ6043), the National Nature Science Foundation of China (61773396, 61603285, 61403297).

Xu-Bin Ping received the Bachelor’s degree from Northwest University, Xi’an, China in 2005, the Master’s degree from the East China University of Science and Technology, Shanghai, China in 2008, and the Ph.D degree from Xi’an Jiaotong University, Xi’an, China, in 2013. His research interests include robust control, model predictive control.

Peng Wang was born in Shanxi Province of China. He received his Bachelor’s and Master’s degrees from Chang’an University, Shaanxi Province of China, in 2006 and 2009, respectively; and his Ph.D. degree from Xi’an Jiaotong University, Shaanxi Province of China in 2013. He is currently an associate professor with the Information and Navigation College, Air Force Engineering University. His research interests include receding horizon control, robust control, distributed estimation and distributed cooperative control.

Jia-Feng Zhang received the B.S. degree in automation from Xidian University, Xi’an, China in 2008, and the joint Ph.D by thesis “Modeling and verification of reconfigurable discrete event control systems” from Xidian University, Xi’an, China and Saarland University, Saarbrücken, Germany in 2015. She joined Xidian University, in 2015, where she is a lecturer of the School of Mechano-Electronic Engineering and a researcher of Systems Control and Automation Group.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ping, XB., Wang, P. & Zhang, JF. A Multi-step Output Feedback Robust MPC Approach for LPV Systems with Bounded Parameter Changes and Disturbance. Int. J. Control Autom. Syst. 16, 2157–2168 (2018). https://doi.org/10.1007/s12555-017-0630-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-017-0630-0

Keywords

Search

Navigation