Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
126 tokens/sec
GPT-4o
47 tokens/sec
Gemini 2.5 Pro Pro
43 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

Data-Driven Min-Max MPC for Linear Systems: Robustness and Adaptation (2404.19096v1)

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

Summary

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

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