Skip to main content
Log in

A model predictive control strategy with switching cost functions for cooperative operation of trains

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

The cooperative control of trains is proposed as an innovative method for further improving operation efficiency. Model predictive control (MPC) has been widely discussed for multiple trains because it can handle the challenges posed by the cooperative control problem, such as complex constraints. In real situations, multiple objectives, such as comfort and safety, must be considered when controlling multiple trains with MPC, and the total objective may change during operation, affecting control performance. In this paper, a distributed structure based on switching cost function model predictive control (ScMPC) for multiple trains in a switching situation is given, where the cost functions of the train control problem change with the variable demand of cooperative operation. Furthermore, the feasibility of the proposed method and stability of the closed-loop system are proved to guarantee the stable operation of the controlled trains. Finally, the control method’s effectiveness is verified. Three kinds of cost functions are given, and their control performance is compared to show the effect of different weights and the advantage of ScMPC.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Song H, Gao S, Li Y, et al. Train-centric communication based autonomous train control system. IEEE Trans Intell Veh, 2023, 8: 721–731

    Article  Google Scholar 

  2. Wu X, Yang M, Lian W, et al. Cascading delays for the high-speed rail network under different emergencies: a double layer network approach. IEEE CAA J Autom Sin, 2022. doi: https://doi.org/10.1109/JAS.2022.105530

  3. Dong H, Ning B, Cai B, et al. Automatic train control system development and simulation for high-speed railways. IEEE Circuits Syst Mag, 2010, 10: 6–18

    Article  Google Scholar 

  4. Tang H, Wang Q, Feng X. Robust stochastic control for high-speed trains with nonlinearity, parametric uncertainty, and multiple time-varying delays. IEEE Trans Intell Transp Syst, 2017, 19: 1027–1037

    Article  Google Scholar 

  5. Di Meo C, Di Vaio M, Flammini F, et al. ERTMS/ETCS virtual coupling: proof of concept and numerical analysis. IEEE Trans Intell Transp Syst, 2019, 21: 2545–2556

    Article  Google Scholar 

  6. Quaglietta E, Wang M, Goverde R M P. A multi-state train-following model for the analysis of virtual coupling railway operations. J Rail Transp Planning Manage, 2020, 15: 100195

    Article  Google Scholar 

  7. Yang K, Berbineau M, Ghys J P, et al. Propagation measurements with regional train at 60 GHz for virtual coupling application. In: Proceedings of 2017 11th European Conference on Antennas and Propagation (EUCAP), 2017. 126–130

  8. Zhang Z, Song H, Wang H, et al. Cooperative multi-scenario departure control for virtual coupling trains: a fixed-time approach. IEEE Trans Veh Technol, 2021, 70: 8545–8555

    Article  Google Scholar 

  9. Guo X, Wang J, Liao F. Adaptive fuzzy fault-tolerant control for multiple high-speed trains with proportional and integral-based sliding mode. IET Control Theory Appl, 2017, 11: 1234–1244

    Article  MathSciNet  Google Scholar 

  10. Li C, Wang J, Shan J, et al. Robust cooperative control of networked train platoons: a negative-imaginary systems’ perspective. IEEE Trans Control Netw Syst, 2021, 8: 1743–1753

    Article  MathSciNet  Google Scholar 

  11. Bai W, Lin Z, Dong H. Coordinated control in the presence of actuator saturation for multiple high-speed trains in the moving block signaling system mode. IEEE Trans Veh Technol, 2020, 69: 8054–8064

    Article  Google Scholar 

  12. Gao S, Hou Y, Dong H, et al. High-speed trains automatic operation with protection constraints: a resilient nonlinear gain-based feedback control approach. IEEE CAA J Autom Sin, 2019, 6: 992–999

    Article  MathSciNet  Google Scholar 

  13. Zhao H, Dai X, Zhang Q, et al. Robust event-triggered model predictive control for multiple high-speed trains with switching topologies. IEEE Trans Veh Technol, 2020, 69: 4700–4710

    Article  Google Scholar 

  14. Li S, Yang L, Gao Z. Distributed optimal control for multiple high-speed train movement: an alternating direction method of multipliers. Automatica, 2020, 112: 108646

    Article  MathSciNet  MATH  Google Scholar 

  15. Felez J, Kim Y, Borrelli F. A model predictive control approach for virtual coupling in railways. IEEE Trans Intell Transp Syst, 2019, 20: 2728–2739

    Article  Google Scholar 

  16. Farooqi H, Incremona G P, Colaneri P. Railway collaborative ecodrive via dissension based switching nonlinear model predictive control. Eur J Control, 2019, 50: 153–160

    Article  MathSciNet  MATH  Google Scholar 

  17. Zhong W, Li S, Xu H, et al. On-line train speed profile generation of high-speed railway with energy-saving: a model predictive control method. IEEE Trans Intell Transp Syst, 2022, 23: 4063–4074

    Article  Google Scholar 

  18. Müller M A, Allgöwer F. Improving performance in model predictive control: switching cost functionals under average dwell-time. Automatica, 2012, 48: 402–409

    Article  MathSciNet  MATH  Google Scholar 

  19. Bemporad A, de la Peña D M. Multiobjective model predictive control. Automatica, 2009, 45: 2823–2830

    Article  MathSciNet  MATH  Google Scholar 

  20. He D, Li H, Du H. Lexicographic multi-objective MPC for constrained nonlinear systems with changing objective prioritization. Automatica, 2021, 125: 109433

    Article  MathSciNet  MATH  Google Scholar 

  21. He D, Yu S, Yu L. Multi-objective nonlinear model predictive control through switching cost functions and its applications to chemical processes. Chin J Chem Eng, 2015, 23: 1662–1669

    Article  Google Scholar 

  22. Müller M A, Martius P, Allgöwer F. Model predictive control of switched nonlinear systems under average dwell-time. J Process Control, 2012, 22: 1702–1710

    Article  Google Scholar 

  23. Ticha M B, Sircoulomb V, Langlois N. Real-time implementation of switched multi-objective prioritizing MPC for a brandy distillation process. In: Proceedings of the 25th IEEE International Conference on Emerging Technologies and Factory Automation (ETFA), 2020. 468–475

  24. Iwnicki S. Handbook of Railway Vehicle Dynamics. Boca Raton: CRC Press, 2006

    Book  Google Scholar 

  25. Wu Q, Spiryagin M, Cole C. Longitudinal train dynamics: an overview. Vehicle Syst Dyn, 2016, 54: 1688–1714

    Article  Google Scholar 

  26. Scheepmaker G M, Goverde R M P, Kroon L G. Review of energy-efficient train control and timetabling. Eur J Operational Res, 2017, 257: 355–376

    Article  MathSciNet  MATH  Google Scholar 

  27. Zhao X, Zhang L, Shi P, et al. Stability and stabilization of switched linear systems with mode-dependent average dwell time. IEEE Trans Automat Contr, 2011, 57: 1809–1815

    Article  MathSciNet  MATH  Google Scholar 

  28. Zhang L, Gao H. Asynchronously switched control of switched linear systems with average dwell time. Automatica, 2010, 46: 953–958

    Article  MathSciNet  MATH  Google Scholar 

  29. Mayne D Q, Rawlings J B, Rao C V, et al. Constrained model predictive control: stability and optimality. Automatica, 2000, 36: 789–814

    Article  MathSciNet  MATH  Google Scholar 

  30. Blanchini F. Set invariance in control. Automatica, 1999, 35: 1747–1767

    Article  MathSciNet  MATH  Google Scholar 

  31. Chen H, Allgöwer F. A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability. Automatica, 1998, 34: 1205–1217

    Article  MathSciNet  MATH  Google Scholar 

  32. Grüne L, Pannek J. Nonlinear model predictive control. In: Proceedings of Nonlinear Model Predictive Control, 2017. 45–69

  33. Dunbar W B, Caveney D S. Distributed receding horizon control of vehicle platoons: stability and string stability. IEEE Trans Automat Contr, 2012, 57: 620–633

    Article  MathSciNet  MATH  Google Scholar 

  34. Yu S, Chen H, Böhm C, et al. Enlarging the terminal region of NMPC with parameter-dependent terminal control law. In: Proceedings of Nonlinear Model Predictive Control, 2009. 69–78

Download references

Acknowledgements

This work was jointly supported by National Natural Science Foundation of China (Grant Nos. 61925302, 61790573, 62273027) and Construction of China-ASEAN International Joint Laboratory for Comprehensive Transportation (Grant No. GUIKE AD20297125).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hairong Dong.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, Z., Song, H., Wang, H. et al. A model predictive control strategy with switching cost functions for cooperative operation of trains. Sci. China Inf. Sci. 66, 172206 (2023). https://doi.org/10.1007/s11432-022-3662-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11432-022-3662-x

Keywords

Navigation