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Data-Driven Control of Linear Systems via Quantized Feedback

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Abstract

Quantized feedback control is fundamental to system synthesis with limited communication capacity. In sharp contrast to the existing literature on quantized control which requires an explicit dynamical model, the authors study the quadratic stabilization and performance control problems with logarithmically quantized feedback in a direct data-driven framework, where the system state matrix is not exactly known and instead, belongs to an ambiguity set that is directly constructed from a finite number of noisy system data. To this end, the authors firstly establish sufficient and necessary conditions via linear matrix inequalities for the existence of a common quantized controller that achieves our control objectives over the ambiguity set. Then, the authors provide necessary conditions on the data for the solvability of the LMIs, and determine the coarsest quantization density via semi-definite programming. The theoretical results are validated through numerical examples.

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References

  1. Elia N and Mitter S K, Stabilization of linear systems with limited information, IEEE Trans. On Automatic Control, 2001, 46(9): 1384–1400.

    Article  MathSciNet  Google Scholar 

  2. Fu M and Xie L, The sector bound approach to quantized feedback control, IEEE Trans. on Automatic Control, 2005, 50(11): 1698–1711.

    Article  MathSciNet  Google Scholar 

  3. You K, Su W, Fu M, et al., Attainability of the minimum data rate for stabilization of linear systems via logarithmic quantization, Automatica, 2011, 47(1): 170–176.

    Article  MathSciNet  Google Scholar 

  4. Kang X and Ishii H, Coarsest quantization for networked control of uncertain linear systems, Automatica, 2015, 51: 1–8.

    Article  MathSciNet  Google Scholar 

  5. Zhou J, Wen C, Wang W, et al., Adaptive backstepping control of nonlinear uncertain systems with quantized states, IEEE Trans. on Automatic Control, 2019, 64(11): 4756–4763.

    Article  MathSciNet  Google Scholar 

  6. Kalman R E, Nonlinear aspects of sampled-data control systems, Proc. Symp. Nonlinear Circuit Analysis VI, 1956, 273–313.

  7. De Persis C and Tesi P, Formulas for data-driven control: Stabilization, optimality, and robustness, IEEE Trans. on Automatic Control, 2019, 65(3): 909–924.

    Article  MathSciNet  Google Scholar 

  8. De Persis C and Tesi P, Low-complexity learning of linear quadratic regulators from noisy data, Automatica, 2021, 128: 109548.

    Article  MathSciNet  Google Scholar 

  9. Van Waarde H J, Eising J, Trentelman H L, et al., Data informativity: A new perspective on data-driven analysis and control, IEEE Trans. on Automatic Control, 2020, 65(11): 4753–4768.

    Article  MathSciNet  Google Scholar 

  10. van Waarde H J, Camlibel M K, and Mesbahi M, From noisy data to feedback controllers: Non-conservative design via a matrix S-lemma, IEEE Trans. on Automatic Control, 2020, 67(1): 162–175.

    Article  Google Scholar 

  11. Kang S and You K, Minimum input design for direct data-driven property identification of unknown linear systems, Automatica, 2023, 156: 111130.

    Article  MathSciNet  Google Scholar 

  12. Zhao F, Fu X, and You K, On the sample complexity of stabilizing linear systems via policy gradient methods, 2022, arXiv: 2205.14335.

  13. Werner S W and Peherstorfer B, On the sample complexity of stabilizing linear dynamical systems from data, Foundations of Computational Mathematics, 2023, DOI: https://doi.org/10.1007/s10208-023-09605-y.

  14. Hu Y, Wierman A, and Qu G, On the sample complexity of stabilizing lti systems on a single trajectory, Advances in Neural Information Processing Systems, 2022, 35: 16989–17002.

    Google Scholar 

  15. Zhao F, Li X, and You K, Data-driven control of unknown linear systems via quantized feedback, Proceedings of the Learning for Dynamics and Control Conference (PMLR), Philadelphia, 2022, 467–479.

  16. Willems J C, Rapisarda P, Markovsky I, et al., A note on persistency of excitation, Systems & Control Letters, 2005, 54(4): 325–329.

    Article  MathSciNet  Google Scholar 

  17. Dörfler F, Coulson J, and Markovsky I, Bridging direct and indirect data-driven control formulations via regularizations and relaxations, IEEE Trans. on Automatic Control, 2022, 68(2): 883–897.

    Article  MathSciNet  Google Scholar 

  18. Coulson J, Lygeros J, and Dörfler F, Data-enabled predictive control: In the shallows of the DeePC, 18th European Control Conference, Napoli, 2019, 307–312.

  19. Berberich J, Köhler J, Müller M A, et al., Data-driven model predictive control with stability and robustness guarantees, IEEE Trans. on Automatic Control, 2020, 66(4): 1702–1717.

    Article  MathSciNet  Google Scholar 

  20. Bisoffi A, De Persis C, and Tesi P, Trade-offs in learning controllers from noisy data, Systems & Control Letters, 2021, 154: 104985.

    Article  MathSciNet  Google Scholar 

  21. Guo M, De Persis C, and Tesi P, Data-driven stabilization of nonlinear polynomial systems with noisy data, IEEE Trans. on Automatic Control, 2021, 67(8): 4210–4217.

    Article  MathSciNet  Google Scholar 

  22. Xu L, Turan M S, Guo B, et al., A data-driven convex programming approach to worst-case robust tracking controller design, 2021, arXiv: 2102.11918.

  23. Rotulo M, De Persis C, and Tesi P, Online learning of data-driven controllers for unknown switched linear systems, 2021, arXiv: 2105.11523.

  24. Berberich J, Scherer C W, and Allgöwer F, Combining prior knowledge and data for robust controller design, 2020, arXiv: 2009.05253.

  25. Hayakawa T, Ishii H, and Tsumura K, Adaptive quantized control for linear uncertain discrete-time systems, Automatica, 2009, 45(3): 692–700.

    Article  MathSciNet  Google Scholar 

  26. Gao H and Chen T, A new approach to quantized feedback control systems, Automatica, 2008, 44(2): 534–542.

    Article  MathSciNet  Google Scholar 

  27. Fu M and Xie L, Finite-level quantized feedback control for linear systems, IEEE Trans. on Automatic Control, 2009, 54(5): 1165–1170.

    Article  MathSciNet  Google Scholar 

  28. Coutinho D F, Fu M, and de Souza C E, Input and output quantized feedback linear systems, IEEE Trans. on Automatic Control, 2010, 55(3): 761–766.

    Article  MathSciNet  Google Scholar 

  29. Shen B, Tan H, Wang Z, et al., Quantized/saturated control for sampled-data systems under noisy sampling intervals: A confluent vandermonde matrix approach, IEEE Trans. on Automatic Control, 2017, 62(9): 4753–4759.

    Article  MathSciNet  Google Scholar 

  30. Corradini M L and Orlando G, Robust quantized feedback stabilization of linear systems, Automatica, 2008, 44(9): 2458–2462.

    Article  MathSciNet  Google Scholar 

  31. Liu T, Jiang Z P, and Hill D J, A sector bound approach to feedback control of nonlinear systems with state quantization, Automatica, 2012, 48(1): 145–152.

    Article  MathSciNet  Google Scholar 

  32. Yu X and Lin Y, Adaptive backstepping quantized control for a class of nonlinear systems, IEEE Trans. on Automatic Control, 2016, 62(2): 981–985.

    Article  MathSciNet  Google Scholar 

  33. Zhou K and Doyle J C, Essentials of Robust Control, Volume 104, Prentice Hall Upper Saddle River, Hoboken, 1998.

    Google Scholar 

  34. Zhou K, Doyle J C, and Glover K, Robust and Optimal Control, Springer-Verlag, London, 1996.

    Google Scholar 

  35. Boyd S and Vandenberghe L, Convex Optimization, Cambridge University Press, Cambridge, 2004.

    Book  Google Scholar 

  36. Grant M and Boyd S, CVX: Matlab software for disciplined convex programming, version 2.1, 2014, http://cvxr.com/cvx.

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Authors and Affiliations

  1. Department of Automation and BNRist, Tsinghua University, Beijing, 100084, China

    Xingchen Li, Feiran Zhao & Keyou You

Authors
  1. Xingchen Li
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  2. Feiran Zhao
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  3. Keyou You
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Corresponding author

Correspondence to Keyou You.

Ethics declarations

YOU Keyou is an editorial board member for Journal of Systems Science & Complexity and was not involved in the editorial review or the decision to publish this article. All authors declare that there are no competing interests.

Additional information

This research was supported by The research was supported by National Key R&D Program of China under Grant No. 2022ZD0116700, National Natural Science Foundation of China under Grant Nos. 62033006 and 62325305.

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Li, X., Zhao, F. & You, K. Data-Driven Control of Linear Systems via Quantized Feedback. J Syst Sci Complex 37, 152–168 (2024). https://doi.org/10.1007/s11424-024-3452-1

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  • DOI: https://doi.org/10.1007/s11424-024-3452-1

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