Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

A fast algorithm for nonlinear model predictive control applied to HEV energy management systems


This paper presents a fast algorithm for nonlinear model predictive control. In real-time implementation, a nonlinear optimal problem is often rewritten as a nonlinear programming (NLP) problem using the Euler method, which is based on dividing the prediction horizon into N steps in a given time interval. However, real-time optimization is usually limited to slow processes, since the sampling time must be sufficient to support the task’s computational needs. In this study, by combining the Gauss pseudospectral method and model predictive control, a fast algorithm is proposed using fewer discrete points to transcribe an optimal control problem into an NLP problem while ensuring the same computational accuracy as traditional discretization methods. The approach is applied to the torque split control for hybrid electric vehicles (HEV) with a predefined torque demand, and its computational time is at least half that of the Euler method with the same accuracy.

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


  1. 1

    Grancharova A, Johansen T A. Explicit nonlinear model predictive control: theory and applications. In: Theory and Applications. Berlin: Springer, 2012. 429: 39–69

  2. 2

    Kirches C. Fast Numerical Methods for Mixed-Integer Nonlinear Model-Predictive Control. Wiesbaden: Vieweg+ Teubner Verlag/Springer Fachmedien Wiesbaden, 2011

  3. 3

    De Haan D, Guay M. A real-time framework for model-predictive control of continuous-time nonlinear systems. IEEE Trans Autom Control, 2007, 52: 2047–2057

  4. 4

    Betts J T. Survey of numerical methods for trajectory optimization. J Guid Control Dyna, 1998, 21: 193–207

  5. 5

    Benson D A, Huntington G T, Thorvaldsen T P, et al. Direct trajectory optimization and costate estimation via an orthogonal collocation method. J Guid Control Dyna, 2006, 29: 1435–1440

  6. 6

    Garg D, Patterson M A, Hager W W, et al. An overview of three pseudospectral methods for the numerical solution of optimal control problems. Adv Astronaut Sci, 2009, 135: 475–487

  7. 7

    Benson D. A Gauss pseudospectral transcription for optimal control. Dissertation for Ph.D. Degree. Cambridge: Massachusetts Institute of Technology, 2005

  8. 8

    Huntington G T. Advancement and analysis of a Gauss pseudospectral transcription for optimal control problems. Dissertation for Ph.D. Degree. Cambridge: Massachusetts Institute of Technology, 2007

  9. 9

    Xu S, Li S E, Zhang X, et al. Fuel-optimal cruising strategy for road vehicles with step-gear mechanical transmission. IEEE Trans Intell Transport Syst, 2015, 16: 3496–3507

  10. 10

    Li S E, Xu S, Huang X, et al. Eco-departure of connected vehicles with V2X communication at signalized intersections. IEEE Trans Veh Tech, 2015, 64: 5439–5449

  11. 11

    Burden R L, Faires J D, Reynolds A C. Numerical Analysis. Boston: Wadsworth Publishing Company, 1978

  12. 12

    Sezer V, Gokasan M, Bogosyan S. A novel ECMS and combined cost map approach for high-efficiency series hybrid electric vehicles. IEEE Trans Veh Tech, 2011, 60: 3557–3570

  13. 13

    Panday A, Bansal H O. A review of optimal energy management strategies for hybrid electric vehicle. Int J Veh Tech, 2014

  14. 14

    Ambuhl D, Guzzella L. Predictive reference signal generator for hybrid electric vehicles. IEEE Trans Veh Tech, 2009, 58: 4730–4740

  15. 15

    Adhikari S. Real-time power management of parallel full hybrid electric vehicles. Dissertation for Ph.D. Degree. Melbourne: The University of Melbourne. 2010

  16. 16

    Borhan H, Vahidi A, Phillips A M, et al. MPC-based energy management of a power-split hybrid electric vehicle. IEEE Trans Control Syst Tech, 2012, 20: 593–603

  17. 17

    Guo L L, Gao B Z, Chen H. On-line shift schedule optimization of 2-speed electric vehicle using moving horizon strategy. IEEE/ASME Trans Mech, 2016, 21: 2858–2869

  18. 18

    Borhan H A, Vahidi A, Phillips A M, et al. Predictive energy management of a power-split hybrid electric vehicle. In: Proceedings of IEEE American Control Conference, St. Louis, 2009. 3970–3976

  19. 19

    Zeng X, Huang K, Meng F. Model predictive control for parallel hybrid electric vehicles with potential real-time capability. J Autom Safe Energy, 2012, 3: 165–172

  20. 20

    Sciarretta A, de Nunzio G, Ojeda L L. Optimal ecodriving control: energy-efficient driving of road vehicles as an optimal control problem. IEEE Control Syst, 2015, 35: 71–90

  21. 21

    Dib W, Chasse A, Moulin P, et al. Optimal energy management for an electric vehicle in eco-driving applications. Control Eng Pract, 2014, 29: 299–307

  22. 22

    Gill P E, Murray W, Saunders M A. SNOPT: an SQP algorithm for large-scale constrained optimization. SIAM Rev, 2005, 47: 99–131

Download references


This work was supported by National Natural Science Foundation of China (Grant Nos. 61520106008, 61522307, 61374046) and Graduate Innovation Fund of Jilin University (Grant No. 2016188).

Author information

Correspondence to Hong Chen.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Guo, L., Gao, B., Li, Y. et al. A fast algorithm for nonlinear model predictive control applied to HEV energy management systems. Sci. China Inf. Sci. 60, 092201 (2017).

Download citation


  • energy management
  • hybrid electric vehicles
  • nonlinear model predictive control
  • Gauss pseudospectral method
  • nonlinear programming