Papers
Topics
Authors
Recent
Detailed Answer
Quick Answer
Concise responses based on abstracts only
Detailed Answer
Well-researched responses based on abstracts and relevant paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses
Gemini 2.5 Flash
Gemini 2.5 Flash 77 tok/s
Gemini 2.5 Pro 33 tok/s Pro
GPT-5 Medium 25 tok/s Pro
GPT-5 High 27 tok/s Pro
GPT-4o 75 tok/s Pro
Kimi K2 220 tok/s Pro
GPT OSS 120B 465 tok/s Pro
Claude Sonnet 4 36 tok/s Pro
2000 character limit reached

Data-Driven Min-Max MPC for Linear Systems: Robustness and Adaptation (2404.19096v2)

Published 29 Apr 2024 in eess.SY and cs.SY

Abstract: Data-driven controllers design is an important research problem, in particular when data is corrupted by the noise. In this paper, we propose a data-driven min-max model predictive control (MPC) scheme using noisy input-state data for unknown linear time-invariant (LTI) system. The unknown system matrices are characterized by a set-membership representation using the noisy input-state data. Leveraging this representation, we derive an upper bound on the worst-case cost and determine the corresponding optimal state-feedback control law through a semidefinite program (SDP). We prove that the resulting closed-loop system is robustly stabilized and satisfies the input and state constraints. Further, we propose an adaptive data-driven min-max MPC scheme which exploits additional online input-state data to improve closed-loop performance. Numerical examples show the effectiveness of the proposed methods.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (49)
  1. L. Ljung. System Identification: Theory for the user. Prentice Hall PTR, 1999.
  2. From noisy data to feedback controllers: non-conservative design via a matrix S-lemma. IEEE Transactions on Automatic Control, 2020.
  3. Data informativity: a new perspective on data-driven analysis and control. IEEE Transactions on Automatic Control, 65(11):4753–4768, 2020.
  4. Combining prior knowledge and data for robust controller design. IEEE Transactions on Automatic Control, 68(8):4618–4633, 2023.
  5. C. De Persis and P. Tesi. Formulas for data-driven control: Stabilization, optimality, and robustness. IEEE Transactions on Automatic Control, 65(3):909–924, 2020.
  6. Robust data-driven state-feedback design. In 2020 American Control Conference (ACC), pages 1532–1538, 2020.
  7. Trade-offs in learning controllers from noisy data. Systems & Control Letters, 154:104985, 2021.
  8. Quadratic matrix inequalities with applications to data-based control. SIAM Journal on Control and Optimization, 61(4):2251–2281, 2023.
  9. The informativity approach: To data-driven analysis and control. IEEE Control Systems Magazine, 43(6):32–66, 2023.
  10. Model predictive control: theory, computation, and design, volume 2. Nob Hill Publishing Madison, 2017.
  11. H. Yang and S. Li. A data-driven predictive controller design based on reduced hankel matrix. In 2015 10th Asian Control Conference (ASCC), pages 1–7. IEEE, 2015.
  12. Data-enabled predictive control: In the shallows of the DeePC. In Proc. European Control Conference (ECC), pages 307–312, 2019.
  13. Data-driven model predictive control with stability and robustness guarantees. IEEE Transactions on Automatic Control, 66(4):1702–1717, 2021.
  14. Robust stability analysis of a simple data-driven model predictive control approach. IEEE Transactions on Automatic Control, 68(5):2625–2637, 2022.
  15. I. Markovsky and F. Dörfler. Behavioral systems theory in data-driven analysis, signal processing, and control. Annual Reviews in Control, 52:42–64, 2021.
  16. Behavioral theory for stochastic systems? A data-driven journey from Willems to Wiener and back again. Annual Reviews in Control, 55:92–117, 2023.
  17. Data-driven control based on the behavioral approach: From theory to applications in power systems. IEEE Control Systems Magazine, 43(5):28–68, 2023.
  18. Handbook of linear data-driven predictive control: Theory, implementation and design. Annual Reviews in Control, 56:100914, 2023.
  19. A note on persistency of excitation. Systems Control Letters, 54(4):325–329, 2005.
  20. I. Markovsky and P. Rapisarda. Data-driven simulation and control. International Journal of Control, 81(12):1946–1959, 2008.
  21. A novel constraint-tightening approach for robust data-driven predictive control. International Journal of Robust and Nonlinear Control, 2022.
  22. Robust constraint satisfaction in data-driven MPC. In 59th IEEE Conference on Decision and Control (CDC), pages 1260–1267, 2020.
  23. Robust constrained model predictive control using linear matrix inequalities. Automatica, 32(10):1361–1379, 1996.
  24. Min-max control of constrained uncertain discrete-time linear systems. IEEE Transactions on Automatic Control, 48(9):1600–1606, 2003.
  25. M. Diehl. Formulation of closed-loop min–max MPC as a quadratically constrained quadratic program. IEEE transactions on automatic control, 52(2):339–343, 2007.
  26. Y. Lu and Y. Arkun. Quasi-min-max MPC algorithms for LPV systems. Automatica, 36(4):527–540, 2000.
  27. Input to state stability of min–max MPC controllers for nonlinear systems with bounded uncertainties. Automatica, 42(5):797–803, 2006.
  28. On input-to-state stability of min–max nonlinear model predictive control. Systems & Control Letters, 57(1):39–48, 2008.
  29. Further results on “robust MPC using linear matrix inequalities”. In Nonlinear Model Predictive Control: Towards New Challenging Applications, pages 89–98. Springer, 2009.
  30. C. Scherer and S. Weiland. Linear matrix inequalities in control. New York : Spring-Verlag, 3 edition, 2000.
  31. Linear matrix inequalities in system and control theory. SIAM, 1994.
  32. K. Hu and T. Liu. Robust data-driven predictive control for unknown linear time-invariant systems. arXiv preprint arXiv:2401.07222, 2024.
  33. LMI-based data-driven robust model predictive control. IFAC-PapersOnLine, 56(2):4783–4788, 2023.
  34. Data-driven predictive control with adaptive disturbance attenuation for constrained systems. arXiv preprint arXiv:2403.14935, 2024.
  35. Online learning of data-driven controllers for unknown switched linear systems. Automatica, 145:110519, 2022.
  36. Robust MPC with recursive model update. Automatica, 103:461–471, 2019.
  37. Adaptive model predictive control with robust constraint satisfaction. IFAC-PapersOnLine, 50(1):3313–3318, 2017.
  38. Linear robust adaptive model predictive control: Computational complexity and conservatism. In 58th Conference on Decision and Control (CDC), pages 1383–1388, 2019.
  39. A robust adaptive model predictive control framework for nonlinear uncertain systems. International Journal of Robust and Nonlinear Control, 31(18):8725–8749, 2021.
  40. Robust adaptive MPC using control contraction metrics. Automatica, 155:111169, 2023.
  41. K. Zhang and Y. Shi. Adaptive model predictive control for a class of constrained linear systems with parametric uncertainties. Automatica, 117:108974, 2020.
  42. Adaptive model predictive control for constrained linear systems. In 2013 European Control Conference (ECC), pages 382–387. IEEE, 2013.
  43. Dual adaptive model predictive control. Automatica, 80:340–348, 2017.
  44. Constrained adaptive model-predictive control for a class of discrete-time linear systems with parametric uncertainties. IEEE Transactions on Automatic Control, 65(5):2223–2229, 2019.
  45. Adaptive MPC for constrained systems with parameter uncertainty and additive disturbance. IET Control Theory & Applications, 13(15):2500–2506, 2019.
  46. Data-driven min-max MPC for linear systems. arXiv:2309.17307, 2023.
  47. M. A. Woodbury. Inverting modified matrices. Princeton University, Princeton, NJ, 1950. Statistical Research Group, Memo. Rep. no. 42,.
  48. T. Martin and F. Allgöwer. Data-driven inference on optimal input-output properties of polynomial systems with focus on nonlinearity measures. IEEE Transactions on Automatic Control, pages 1–16, 2022.
  49. Tube-based robust nonlinear model predictive control. International journal of robust and nonlinear control, 21(11):1341–1353, 2011.
Citations (2)
View on Semantic Scholar
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up

Summary

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

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

Follow-Up Questions

We haven't generated follow-up questions for this paper yet.

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