Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
125 tokens/sec
GPT-4o
53 tokens/sec
Gemini 2.5 Pro Pro
42 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
47 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

On the equivalence of direct and indirect data-driven predictive control approaches (2403.05860v2)

Published 9 Mar 2024 in eess.SY and cs.SY

Abstract: Recently, several direct Data-Driven Predictive Control (DDPC) methods have been proposed, advocating the possibility of designing predictive controllers from historical input-output trajectories without the need to identify a model. In this work, we show that these approaches are equivalent to an indirect approach. Reformulating the direct methods in terms of estimated parameters and covariance matrices allows us to give new insights into how they work in comparison with, for example, Subspace Predictive Control (SPC). In particular, we show that for unconstrained problems the direct methods are equivalent to SPC with a reduced weight on the tracking cost. Via a numerical experiment, motivated by the reformulation, we also illustrate why the performance of direct DDPC methods with fixed regularization tends to degrade as the number of training samples increases.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (24)
  1. F. Dörfler, “Data-driven control: Part one of two: A special issue sampling from a vast and dynamic landscape,” IEEE Control Systems Magazine, vol. 43, no. 5, pp. 24–27, 2023.
  2. W. Favoreel, B. De Moor, and M. Gevers, “SPC: Subspace predictive control,” IFAC Proceedings Volumes, vol. 32, no. 2, pp. 4004–4009, 1999.
  3. J. Coulson, J. Lygeros, and F. Dörfler, “Data-enabled predictive control: In the shallows of the deepc,” in The 18th European Control Conference (ECC), 2019, pp. 307–312.
  4. J. Berberich, J. Köhler, M. A. Müller, and F. Allgöwer, “Data-driven model predictive control with stability and robustness guarantees,” IEEE Transactions on Automatic Control, vol. 66, no. 4, pp. 1702–1717, 2020.
  5. J. Berberich and F. Allgöwer, “A trajectory-based framework for data-driven system analysis and control,” in European Control Conference (ECC), 2020, pp. 1365–1370.
  6. M. Ferizbegovic, H. Hjalmarsson, P. Mattsson, and T. B. Schön, “Willems’ fundamental lemma based on second-order moments,” in 60th IEEE Conference on Decision and Control (CDC), 2021, pp. 396–401.
  7. V. Breschi, A. Chiuso, and S. Formentin, “Data-driven predictive control in a stochastic setting: A unified framework,” Automatica, vol. 152, p. 110961, 2023.
  8. M. Sader, Y. Wang, D. Huang, C. Shang, and B. Huang, “Causality-informed data-driven predictive control,” arXiv preprint arXiv:2311.09545, 2023.
  9. F. Dörfler, “Data-driven control: Part two of two: Hot take: Why not go with models?” IEEE Control Systems Magazine, vol. 43, no. 6, pp. 27–31, 2023.
  10. V. Krishnan and F. Pasqualetti, “On direct vs indirect data-driven predictive control,” in The 60th IEEE Conference on Decision and Control (CDC), 2021, pp. 736–741.
  11. F. Dörfler, J. Coulson, and I. Markovsky, “Bridging direct and indirect data-driven control formulations via regularizations and relaxations,” IEEE Transactions on Automatic Control, vol. 68, no. 2, pp. 883–897, 2022.
  12. Z.-S. Hou and Z. Wang, “From model-based control to data-driven control: Survey, classification and perspective,” Information Sciences, vol. 235, pp. 3–35, 2013.
  13. P. Verheijen, V. Breschi, and M. Lazar, “Handbook of linear data-driven predictive control: Theory, implementation and design,” Annual Reviews in Control, vol. 56, p. 100914, 2023.
  14. F. Fiedler and S. Lucia, “On the relationship between data-enabled predictive control and subspace predictive control,” in European Control Conference (ECC), 2021, pp. 222–229.
  15. P. Mattsson and T. B. Schön, “On the regularization in deepc,” IFAC-PapersOnLine, vol. 56, no. 2, pp. 625–631, 2023.
  16. M. Klädtke and M. S. Darup, “Implicit predictors in regularized data-driven predictive control,” IEEE Control Systems Letters, 2023.
  17. J.-W. van Wingerden, S. P. Mulders, R. Dinkla, T. Oomen, and M. Verhaegen, “Data-enabled predictive control with instrumental variables: the direct equivalence with subspace predictive control,” in 61st IEEE Conference on Decision and Control (CDC), 2022, pp. 2111–2116.
  18. Y. Wang, Y. Qiu, M. Sader, D. Huang, and C. Shang, “Data-driven predictive control using closed-loop data: An instrumental variable approach,” IEEE Control Systems Letters, 2023.
  19. S. J. Qin, W. Lin, and L. Ljung, “A novel subspace identification approach with enforced causal models,” Automatica, vol. 41, no. 12, pp. 2043–2053, 2005.
  20. Y. Lian, R. Wang, and C. N. Jones, “Koopman based data-driven predictive control,” arXiv preprint arXiv:2102.05122, 2021.
  21. M. Lazar, “Basis functions nonlinear data-enabled predictive control: Consistent and computationally efficient formulations,” arXiv preprint arXiv:2311.05360, 2023.
  22. V. Breschi, A. Chiuso, M. Fabris, and S. Formentin, “On the impact of regularization in data-driven predictive control,” in 62nd IEEE Conference on Decision and Control (CDC).   IEEE, 2023, pp. 3061–3066.
  23. V. Breschi, T. B. Hamdan, G. Mercère, and S. Formentin, “Tuning of subspace predictive controls,” IFAC-PapersOnLine, vol. 56, no. 3, pp. 103–108, 2023, 3rd Modeling, Estimation and Control Conference.
  24. V. Breschi, M. Fabris, S. Formentin, and A. Chiuso, “Uncertainty-aware data-driven predictive control in a stochastic setting,” IFAC-PapersOnLine, vol. 56, no. 2, pp. 10 083–10 088, 2023, 22nd IFAC World Congress.
Citations (2)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now