Skip to main content
SpringerLink
Log in

Robust Approximation-Based Event-Triggered MPC for Constrained Sampled-Data Systems

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

In this paper, an approximation-based event-triggered model predictive control (AETMPC) strategy is proposed to implement event-triggered model predictive control for continuous-time constrained nonlinear systems under the digital platform. In the AETMPC strategy, both of the optimal control problem (OCP) and the triggering conditions are defined in a discrete-time manner based on approximate discrete-time models, while the plant under control is continuous time. In doing so, sensing load is alleviated because the triggering condition does not need to be checked continuously, and the computation of the OCP is simpler since which is calculated in the discrete-time framework. Meanwhile, robust constraints are satisfied in a continuous-time sense by taking inter-sampling behavior into consideration, and a novel constraint tightening approach is presented accordingly. Furthermore, the feasibility of the AETMPC strategy is analyzed and the associated stability of the overall system is established. Finally, this strategy is validated by a numerical example.

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. Zhao Y B, Liu G P, Kang Y, et al., Packet-Based Control for Networked Control Systems, University of Glamorgan, Pontypridd, 2008.

    Google Scholar 

  2. Liu C, Gao J, Li H, et al., Aperiodic robust model predictive control for constrained continuous-time nonlinear systems: An event-triggered approach, IEEE Transactions on Cybernetics, 2017, 48(5): 1397–1405.

    Article  Google Scholar 

  3. Li H and Shi Y, Event-triggered robust model predictive control of continuous-time nonlinear systems, Automatica, 2014, 50(5): 1507–1513.

    Article  MathSciNet  Google Scholar 

  4. Hashimoto K, Adachi S, and Dimarogonas D V, Event-triggered intermittent sampling for nonlinear model predictive control, Automatica, 2017, 81: 148–155.

    Article  MathSciNet  Google Scholar 

  5. Eqtami A, Dimarogonas D V, and Kyriakopoulos K J, Event-triggered control for discrete-time systems, IEEE Proceedings of the 2010 American Control Conference, 2010, 4719–4724.

  6. Sun Z, Dai L, Liu K, et al., Robust self-triggered MPC with adaptive prediction horizon for perturbed nonlinear systems, IEEE Transactions on Automatic Control, 2019, 64(11): 4780–4787.

    Article  MathSciNet  Google Scholar 

  7. Wang M, Sun J, and Chen J, Input-to-state stability of perturbed nonlinear systems with event-triggered receding horizon control scheme, IEEE Transactions on Industrial Electronics, 2018, 66(8): 6393–6403.

    Article  Google Scholar 

  8. Li P, Kang Y, Zhao Y B, et al., Networked dual-mode adaptive horizon MPC for constrained nonlinear systems, IEEE Transactions on Systems, Man, and Cybernetics: Systems, early access, DOI: https://doi.org/10.1109/TSMC.2020.2971241.

  9. Magni L and Scattolini R, Model predictive control of continuous-time nonlinear systems with piecewise constant control, IEEE Transactions on Automatic Control, 2004, 49(6): 900–906.

    Article  MathSciNet  Google Scholar 

  10. Sopasakis P, Patrinos P, and Sarimveis H, MPC for sampled-data linear systems: Guaranteeing constraint satisfaction in continuous-time, IEEE Transactions on Automatic Control, 2013, 59(4): 1088–1093.

    Article  MathSciNet  Google Scholar 

  11. Nei D, Teel A R, and Kokotovi P V, Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations, Systems & Control Letters, 1999, 38(4–5): 259–270.

    MathSciNet  Google Scholar 

  12. He N and Shi D, Event-based robust sampled-data model predictive control: A non-monotonic Lyapunov function approach, IEEE Transactions on Circuits and Systems I: Regular Papers, 2015, 62(10): 2555–2564.

    Article  MathSciNet  Google Scholar 

  13. Khalil H K and Grizzle J W, Nonlinear Systems, Upper Saddle River, NJ: Prentice hall, 2002.

    Google Scholar 

  14. Rubagotti M, Raimondo D M, Ferrara A, et al., Robust model predictive control with integral sliding mode in continuous-time sampled-data nonlinear systems, IEEE Transactions on Automatic Control, 2010, 56(3): 556–570.

    Article  MathSciNet  Google Scholar 

  15. Jiang Z P and Praly L, Design of robust adaptive controllers for nonlinear systems with dynamic uncertainties, Automatica, 1998, 34(7): 825–840.

    Article  MathSciNet  Google Scholar 

  16. Grne L and Nesic D, Optimization-based stabilization of sampled-data nonlinear systems via their approximate discrete-time models, SIAM Journal on Control and Optimization, 2003, 42(1): 98–122.

    Article  MathSciNet  Google Scholar 

  17. Chen H and Allgwer F, A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability, Automatica, 1998, 34(10): 1205–1217.

    Article  MathSciNet  Google Scholar 

  18. Rajhans C, Patwardhan S C, and Pillai H, Discrete time formulation of quasi infinite horizon nonlinear model predictive control scheme with guaranteed stability, IFAC-Papers OnLine, 2017, 50(1): 7181–7186.

    Article  Google Scholar 

  19. Grne L and Pannek J, Nonlinear model predictive control, Nonlinear Model Predictive Control, Springer, Cham, 2017, 45–69.

    Chapter  Google Scholar 

  20. Nei D, Teel A R, and Sontag E D, Formulas relating KL stability estimates of discrete-time and sampled-data nonlinear systems, Systems & Control Letters, 1999, 38(1): 49–60.

    Article  MathSciNet  Google Scholar 

  21. Limn D, Alamo T, Salas F, et al., Input to state stability of minmax MPC controllers for nonlinear systems with bounded uncertainties, Automatica, 2006, 42(5): 797–803.

    Article  MathSciNet  Google Scholar 

  22. Stuart A and Humphries A R, Dynamical Systems and Numerical Analysis, Cambridge University Press, Cambridge, 1998.

    MATH  Google Scholar 

  23. Wang T, Kang Y, Li P, et al., Robust model predictive control for constrained networked nonlinear systems: An approximation-based approach, Neurocomputing, 418: 56–65.

Download references

Author information

Authors and Affiliations

  1. Department of Automation, University of Science and Technology of China, Hefei, 230027, China

    Tao Wang, Yu Kang, Pengfei Li & Peilong Yu

  2. State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei, 230027, China

    Yu Kang

  3. Institute of Advanced Technology, University of Science and Technology of China, Hefei, 230027, China

    Yu Kang

  4. College of Information Engineering, Zhejiang University of Technology, Hangzhou, 310023, China

    Yun-Bo Zhao

Authors
  1. Tao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu Kang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pengfei Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yun-Bo Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Peilong Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu Kang.

Additional information

This paper was supported by the National Key Research and Development Program of China under Grant Nos. 20I8AAA0I00800 and 20I8YFE0I06800, the National Natural Science Foundation of China under Grant Nos. 61725304, 6I67336I, 61673350 and 61422307, the Science and Technology Major Project of Anhui Province under Grant No. 9I2I98698036, the Chinese Academy of Sciences, the Youth Top-notch Talent Support Program and the Youth Yangtze River Scholar, and the Project funded by China Postdoctoral Science Foundation under Grand No. 2020M682036.

This paper was recommended for publication by Editor GUO Jin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, T., Kang, Y., Li, P. et al. Robust Approximation-Based Event-Triggered MPC for Constrained Sampled-Data Systems. J Syst Sci Complex 34, 2109–2124 (2021). https://doi.org/10.1007/s11424-021-0073-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-021-0073-9

Key words

Search

Navigation