Skip to main content
SpringerLink
Log in

Fast adaptive regression-based model predictive control

  • Research Article
  • Published:
Control Theory and Technology Aims and scope Submit manuscript

Abstract

Model predictive control (MPC) is an optimal control method that predicts the future states of the system being controlled and estimates the optimal control inputs that drive the predicted states to the required reference. The computations of the MPC are performed at pre-determined sample instances over a finite time horizon. The number of sample instances and the horizon length determine the performance of the MPC and its computational cost. A long horizon with a large sample count allows the MPC to better estimate the inputs when the states have rapid changes over time, which results in better performance but at the expense of high computational cost. However, this long horizon is not always necessary, especially for slowly-varying states. In this case, a short horizon with less sample count is preferable as the same MPC performance can be obtained but at a fraction of the computational cost. In this paper, we propose an adaptive regression-based MPC that predicts the best minimum horizon length and the sample count from several features extracted from the time-varying changes of the states. The proposed technique builds a synthetic dataset using the system model and utilizes the dataset to train a support vector regressor that performs the prediction. The proposed technique is experimentally compared with several state-of-the-art techniques on both linear and non-linear models. The proposed technique shows a superior reduction in computational time with a reduction of about 35–65% compared with the other techniques without introducing a noticeable loss in performance.

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
Fig. 6
Algorithm 1
Fig. 7
Algorithm 2
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Code Availability

The code is available here https://github.com/ahmed-elliethy/fast-regression-mpc

Notes

  1. https://github.com/ahmed-elliethy/fast-regression-mpc.

  2. We used the same H for all experiments.

  3. A video that shows simulation for the vehicle controlled by the proposed ARMPC is shown in Sect. S.IV in the supplementary material.

References

  1. Garcia, C. E., Prett, D. M., & Morari, M. (1989). Model predictive control: Theory and practice—A survey. Automatica, 25(3), 335–348.

    Article  MATH  Google Scholar 

  2. Hrovat, D., Di Cairano, S., Tseng, H. E., & Kolmanovsky, I. V. (2012). The development of model predictive control in automotive industry: A survey. In 2012 IEEE international conference on control applications (pp. 295–302). IEEE.

  3. Bakošová, M., & Oravec, J. (2014). Robust MPC of an unstable chemical reactor using the nominal system optimization. Acta Chimica Slovaca, 7(2), 87–93.

    Article  Google Scholar 

  4. Wang, C., & Song, Z. (2018). Convex model predictive control for rocket vertical landing. In: 2018 37th Chinese control conference (CCC) (pp. 9837–9842). IEEE. https://doi.org/10.23919/ChiCC.2018.8483147

  5. Song, D., Chang, Q., Zheng, S., Yang, S., Yang, J., & Joo, Y. H. (2020). Adaptive model predictive control for yaw system of variable-speed wind turbines. Journal of Modern Power Systems and Clean Energy, 9(1), 219–224.

    Article  Google Scholar 

  6. Mostafa, E., Elliethy, A., & Aly, H. A. (2022). Response-time enhancement of a hybrid controller of unmanned aerial vehicles using parametrization. In: 2022 13th International conference on electrical engineering (ICEENG) (pp. 150–153). IEEE.

  7. Maciejowski, J. M. (2002). Predictive control: With constraints. London: Pearson Education.

    MATH  Google Scholar 

  8. Khan, B., & Rossiter, J. A. (2013). Alternative parameterisation within predictive control: a systematic selection. International Journal of Control, 86(8), 1397–1409.

    Article  MathSciNet  MATH  Google Scholar 

  9. Muehlebach, M., & D’Andrea, R. (2019). A method for reducing the complexity of model predictive control in robotics applications. IEEE Robotics and Automation Letters, 4(3), 2516–2523.

    Article  Google Scholar 

  10. Hyatt, P., Williams, C. S. & Killpack, M. D. (2020). Parameterized and GPU-parallelized real-time model predictive control for high degree of freedom robots. arXiv preprint arXiv:2001.04931

  11. Funke, J., Brown, M., Erlien, S. M., & Gerdes, J. C. (2016). Collision avoidance and stabilization for autonomous vehicles in emergency scenarios. IEEE Transactions on Control Systems Technology, 25(4), 1204–1216.

    Article  Google Scholar 

  12. Ogren, P., & Robinson, J. (2010). Receding horizon control of UAVs using gradual dense-sparse discretizations. In: AIAA guidance, navigation, and control conference (pp. 8084), Toronto, Ontario, Canada.

  13. Kim, B.-A., Son, Y. S., Lee, S.-H., & Chung, C. C. (2013). Model predictive control using dual prediction horizons for lateral control. IFAC Proceedings Volumes, 46(10), 280–285.

    Article  Google Scholar 

  14. Rezaei, A., & Burl, J. B. (2015). Effects of time horizon on model predictive control for hybrid electric vehicles. IFAC-PapersOnLine, 48(15), 252–256.

    Article  Google Scholar 

  15. Kim, M., Lee, D., Ahn, J., Kim, M., & Park, J. (2021). Model predictive control method for autonomous vehicles using time-varying and non-uniformly spaced horizon. IEEE Access, 9, 86475–86487.

    Article  Google Scholar 

  16. Shekhar, R. C., & Maciejowski, J. M. (2012). Robust variable horizon MPC with move blocking. Systems and Control Letters, 61(4), 587–594. https://doi.org/10.1016/j.sysconle.2012.02.004

    Article  MathSciNet  MATH  Google Scholar 

  17. Cagienard, R., Grieder, P., Kerrigan, E. C., & Morari, M. (2004). Move blocking strategies in receding horizon control. In: IEEE conference on decision and control (vol. 2, pp. 2023–20282). https://doi.org/10.1109/CDC.2004.1430345

  18. Scokaert, P. O., & Mayne, D. Q. (1998). Min-max feedback model predictive control for constrained linear systems. IEEE Transactions on Automatic control, 43(8), 1136–1142.

    Article  MathSciNet  MATH  Google Scholar 

  19. Krener, A. J. (2018). Adaptive horizon model predictive control. IFAC-PapersOnLine, 51(13), 31–36.

    Article  Google Scholar 

  20. Bemporad, A., Borrelli, F., & Morari, M. (2000). Piecewise linear optimal controllers for hybrid systems. In: American control conference (vol. 2, pp. 1190–1194). IEEE.

  21. Bemporad, A., Morari, M., Dua, V., & Pistikopoulos, E. N. (2002). The explicit linear quadratic regulator for constrained systems. Automatica, 38(1), 3–20.

    Article  MathSciNet  MATH  Google Scholar 

  22. Alessio, A., & Bemporad, A. (2009). A survey on explicit model predictive control. Nonlinear Model Predictive Control (pp. 345–369). New York: Springer.

    Chapter  MATH  Google Scholar 

  23. Pannocchia, G., Rawlings, J. B., & Wright, S. J. (2007). Fast, large-scale model predictive control by partial enumeration. Automatica, 43(5), 852–860.

    Article  MathSciNet  MATH  Google Scholar 

  24. Bøhn, E., Gros, S., Moe, S., & Johansen, T. A. (2021). Reinforcement learning of the prediction horizon in model predictive control. IFAC-PapersOnLine, 54(6), 314–320.

    Article  Google Scholar 

  25. Bøhn, E., Gros, S., Moe, S., & Johansen, T.A. (2021). Optimization of the model predictive control meta-parameters through reinforcement learning. arXiv preprint arXiv:2111.04146

  26. Sutton, R. S., & Barto, A. G. (2018). Reinforcement learning: An introduction. MIT Press.

  27. Suzuki, K. (2013). Artificial neural networks: Architectures and applications. BoD-Books on Demand.

    Book  MATH  Google Scholar 

  28. Gardezi, M. S. M., & Hasan, A. (2018). Machine learning based adaptive prediction horizon in finite control set model predictive control. IEEE Access, 6, 32392–32400.

    Article  Google Scholar 

  29. Misin, M. (2020). Model predictive controller of a UAV using the LPV approach. Master’s thesis, Universitat Politècnica de Catalunya.

  30. Najman, L., & Romon, P. (2017). Modern approaches to discrete curvature (Vol. 2184). New York: Springer.

    Book  MATH  Google Scholar 

  31. Mallat, S. G. (1989). A theory for multiresolution signal decomposition: the wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(7), 674–693. https://doi.org/10.1109/34.192463

    Article  MATH  Google Scholar 

  32. Gunn, S. R., et al. (1998). Support vector machines for classification and regression. ISIS Technical Report, 14(1), 5–16.

    Google Scholar 

  33. Vapnik, V. (1999). The nature of statistical learning theory. Springer.

    MATH  Google Scholar 

  34. Chorowski, J., Wang, J., & Zurada, J. M. (2014). Review and performance comparison of SVM-and ELM-based classifiers. Neurocomputing, 128, 507–516.

    Article  Google Scholar 

  35. Daubechies, I. (1992). Ten lectures on wavelets. Philadelphia: SIAM.

    Book  MATH  Google Scholar 

  36. Kim, Y., & Bang, H. (2018). Introduction to Kalman filter and its applications. In F. Govaers (Ed.), Introduction and implementations of the Kalman filter. Chap. 2. IntechOpen. https://doi.org/10.5772/intechopen.80600

    Chapter  Google Scholar 

  37. Geletu, A. (2007). Solving optimization problems using the matlab optimization toolbox-a tutorial. TU-Ilmenau, Fakultät für Mathematik und Naturwissenschaften

Download references

Author information

Authors and Affiliations

  1. Electrical and Computer Engineering, Military Technical College, Cairo, 14627, Egypt

    Eslam Mostafa, Hussein A. Aly & Ahmed Elliethy

Authors
  1. Eslam Mostafa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hussein A. Aly
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ahmed Elliethy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ahmed Elliethy.

Ethics declarations

Conflict of interest

The author declares no competing interests.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file 1 (pdf 1767 KB)

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mostafa, E., Aly, H.A. & Elliethy, A. Fast adaptive regression-based model predictive control. Control Theory Technol. 21, 555–570 (2023). https://doi.org/10.1007/s11768-023-00153-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11768-023-00153-y

Keywords

Search

Navigation