Skip to main content
SpringerLink
Log in

A Model Predictive Approach to Dynamic Control Law Design in Discrete-Time Uncertain Systems

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

A model predictive control (MPC) scheme is mainly developed in discrete-time uncertain systems. The control law contains a dynamic property in the proposed MPC. Hence, the MPC with a dynamic control policy is simply known as model predictive dynamic control (MPDC). To this end, a suitable matrix transformation is suggested to convert the MPDC problem into another optimization issue. Then, a systematic procedure based on linear matrix inequality (LMI) is addressed to the MDPC design. Hence, the MPDC synthesis is translated into an LMI minimization problem, which handles both constraints on the control inputs and plant outputs. The optimization problem can be numerically solved at each sample time through the well-known LMI solver. Then, the parameters of the dynamic controller would be automatically updated at each sample time. The method is applied in a discrete-time example to verify the effectiveness of the presented approach versus similar results.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. F. Allgöwer, A. Zheng, Nonlinear Model Predictive Control (Springer, Basel, 2012)

    Google Scholar 

  2. S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory (SIAM, Pennsylvania, 1994)

    MATH  Google Scholar 

  3. E.F. Camacho, C.B. Alba, Model predictive control, 2nd edn. (Springer Science & Business Media, London, 2013)

    Google Scholar 

  4. M. Cannon, B. Kouvaritakis, Infinite horizon predictive control of constrained continuous-time linear systems. Automatica 36(7), 943–955 (2000)

    MathSciNet  MATH  Google Scholar 

  5. P. Chalupa, J. Novák, P. Januška, State space MPC using state observers. Int. J. Circuits Syst. Signal Process. 8, 9–14 (2014)

    MATH  Google Scholar 

  6. Q.-X. Chen, L. Yu, Robust model predictive control for uncertain discrete time-delay systems via dynamic output feedback. Kongzhi Lilun Yu Yinyong/Control Theory Appl. 23(3), 401–406 (2007)

    MATH  Google Scholar 

  7. F.A. Cuzzola, J.C. Geromel, M. Morari, An improved approach for constrained robust model predictive control. Automatica 38(7), 1183–1189 (2002)

    MathSciNet  MATH  Google Scholar 

  8. D.M. De la Pena, D.R. Ramírez, E.F. Camacho, T. Alamo, Explicit solution of min–max MPC with additive uncertainties and quadratic criterion. Syst. Control Lett. 55(4), 266–274 (2006)

    MathSciNet  MATH  Google Scholar 

  9. B. De Schutter, T.J. van den Boom, MPC for continuous piecewise-affine systems. Syst. Control Lett. 52(3–4), 179–192 (2004)

    MathSciNet  MATH  Google Scholar 

  10. M. Elloumi, M. Ghamgui, D. Mehdi, F. Tadeo, M. Chaabane, Stability and Stabilization of 2D Singular Systems: A Strict LMI Approach. Circuits Syst. Signal Process. 38(7), 3041–3057 (2019)

    Google Scholar 

  11. R.M. Esfanjani, S. Nikravesh, Stabilizing model predictive control for constrained nonlinear distributed delay systems. ISA Trans. 50(2), 201–206 (2011)

    MATH  Google Scholar 

  12. V. Ghaffari, A robust control system scheme based on model predictive controller (MPC) for continuous-time systems. Optim. Control Appl. Methods 38(6), 1032–1041 (2017)

    MathSciNet  MATH  Google Scholar 

  13. V. Ghaffari, S.V. Naghavi, A. Safavi, Robust model predictive control of a class of uncertain nonlinear systems with application to typical CSTR problems. J. Process Control 23(4), 493–499 (2013)

    Google Scholar 

  14. H. Khalil, Nonlinear Systems, 3rd edn. (Upper Saddle River, New Jersey, 2002)

    MATH  Google Scholar 

  15. D.J. Kim, C.M. Kang, S.-H. Lee, C.C. Chung, Discrete-time integral sliding model predictive control for dynamic lateral motion of autonomous driving vehicles. in Annual American Control Conference (ACC) 2018, pp. 4757–4763

  16. M.V. Kothare, V. Balakrishnan, M. Morari, Robust constrained model predictive control using linear matrix inequalities. Automatica 32(10), 1361–1379 (1996)

    MathSciNet  MATH  Google Scholar 

  17. Z. Longge, L. Xiangjie, The synchronization between two discrete-time chaotic systems using active robust model predictive control. Nonlinear Dyn. 74(4), 905–910 (2013)

    MathSciNet  MATH  Google Scholar 

  18. L. Lu, Y. Zou, Y. Niu, Event-driven robust output feedback control for constrained linear systems via model predictive control method. Circuits Syst. Signal Process. 36(2), 543–558 (2017)

    MATH  Google Scholar 

  19. Y. Lu, Y. Arkun, Quasi-min-max MPC algorithms for LPV systems. Automatica 36(4), 527–540 (2000)

    MathSciNet  MATH  Google Scholar 

  20. M. Morari, J.H. Lee, Model predictive control: past, present and future. Comput. Chem. Eng. 23(4), 667–682 (1999)

    Google Scholar 

  21. G. Pannocchia, J.B. Rawlings, S.J. Wright, Conditions under which suboptimal nonlinear MPC is inherently robust. Syst. Control Lett. 60(9), 747–755 (2011)

    MathSciNet  MATH  Google Scholar 

  22. N. Poursafar, H.D. Taghirad, M. Haeri, Model predictive control of non-linear discrete time systems: a linear matrix inequality approach. IET Control Theory Appl. 4(10), 1922–1932 (2010)

    MathSciNet  Google Scholar 

  23. S.J. Qin, T.A. Badgwell, A survey of industrial model predictive control technology. Control Eng. Pract. 11(7), 733–764 (2003)

    Google Scholar 

  24. J.B. Rawlings, Tutorial overview of model predictive control. IEEE Control Syst. 20(3), 38–52 (2000)

    Google Scholar 

  25. M. Razi, M. Haeri, Efficient algorithms for online tracking of set points in robust model predictive control. Int. J. Syst. Sci. 48(8), 1635–1645 (2017)

    MathSciNet  MATH  Google Scholar 

  26. M. Reble, F. Allgöwer, Unconstrained model predictive control and suboptimality estimates for nonlinear continuous-time systems. Automatica 48(8), 1812–1817 (2012)

    MathSciNet  MATH  Google Scholar 

  27. J. Richalet, Industrial applications of model based predictive control. Automatica 29(5), 1251–1274 (1993)

    MathSciNet  Google Scholar 

  28. C. Scherer, S. Weiland, Linear matrix inequalities in control (Dutch Institute for Systems and Control, Delft, 2000)

    Google Scholar 

  29. S. Shamaghdari, S. Nikravesh, M. Haeri, Integrated guidance and control of elastic flight vehicle based on robust MPC. Int. J. Robust Nonlinear Control 25(15), 2608–2630 (2015)

    MathSciNet  MATH  Google Scholar 

  30. T. Shi, R. Lu, Q. Lv, Robust static output feedback infinite horizon RMPC for linear uncertain systems. J. Franklin Inst. 353(4), 891–902 (2016)

    MathSciNet  MATH  Google Scholar 

  31. T. Shi, P. Shi, S. Wang, Robust sampled-data model predictive control for networked systems with time-varying delay. Int. J. Robust Nonlinear Control 29(6), 1758–1768 (2019)

    MathSciNet  MATH  Google Scholar 

  32. Y. Song, Z. Wang, D. Ding, G. Wei, Robust model predictive control under redundant channel transmission with applications in networked DC motor systems. Int. J. Robust Nonlinear Control 26(18), 3937–3957 (2016)

    MathSciNet  MATH  Google Scholar 

  33. Y. Song, G. Wei, S. Liu, Distributed output feedback MPC with randomly occurring actuator saturation and packet loss. Int. J. Robust Nonlinear Control 26(14), 3036–3057 (2016)

    MathSciNet  MATH  Google Scholar 

  34. G. Strang, Introduction to Linear Algebra, 4th edn. (Wellesley-Cambridge Press, Wellesley, 2009)

    MATH  Google Scholar 

  35. X. Tang, L. Deng, Model predictive control for uncertain discrete-time TS fuzzy systems via event-triggered dynamic output feedback scheme. in Annual International Conference on CYBER Technology in Automation, Control, and Intelligent Systems 2018, pp. 1427–1432

  36. A. Ulbig, S. Olaru, D. Dumur, P. Boucher, Explicit nonlinear predictive control for a magnetic levitation system. Asian J. Control 12(3), 434–442 (2010)

    MathSciNet  Google Scholar 

  37. Z. Wan, M.V. Kothare, An efficient off-line formulation of robust model predictive control using linear matrix inequalities. Automatica 39(5), 837–846 (2003)

    MathSciNet  MATH  Google Scholar 

  38. J. Wang, Y. Song, S. Zhang, S. Liu, A.M. Dobaie, Robust model predictive control for linear discrete-time system with saturated inputs and randomly occurring uncertainties. Asian J. Control 20(1), 425–436 (2018)

    MathSciNet  MATH  Google Scholar 

  39. R. Wu, D. Fan, H.H.-C. Iu, T. Fernando, Dynamic surface control for discrete-time strict-feedback systems with network-induced delays using predictive event-triggered strategy. Int. J. Syst. Sci. 50(2), 337–350 (2019)

    MathSciNet  Google Scholar 

  40. J. Zhang, H. Yang, M. Li, Q. Wang, Robust model predictive control for uncertain positive time-delay systems. Int. J. Control Autom. Syst. 17(2), 307–318 (2019)

    Google Scholar 

  41. K. Zhu, Y. Song, D. Ding, G. Wei, H. Liu, Robust MPC under event-triggered mechanism and Round-Robin protocol: an average dwell-time approach. Inf. Sci. 457, 126–140 (2018)

    MathSciNet  Google Scholar 

  42. Y. Zou, Q. Wang, T. Jia, Y. Niu, Multirate event-triggered MPC for NCSs with transmission delays. Circuits Syst. Signal Process. 35(12), 4249–4270 (2016)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, School of Engineering, Persian Gulf University, Bushehr, Iran

    Valiollah Ghaffari

Authors
  1. Valiollah Ghaffari
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Valiollah Ghaffari.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ghaffari, V. A Model Predictive Approach to Dynamic Control Law Design in Discrete-Time Uncertain Systems. Circuits Syst Signal Process 39, 4829–4848 (2020). https://doi.org/10.1007/s00034-020-01396-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-020-01396-9

Keywords

Search

Navigation