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A hybrid systems framework for data-based adaptive control of linear time-varying systems (2405.14426v2)

Published 23 May 2024 in eess.SY and cs.SY

Abstract: We consider the data-driven stabilization of discrete-time linear time-varying systems. The controller is defined as a linear state-feedback law whose gain is adapted to the plant changes through a data-based event-triggering rule. To do so, we monitor the evolution of a data-based Lyapunov function along the solution. When this Lyapunov function does not satisfy a designed desirable condition, an episode is triggered to update the controller gain and the corresponding Lyapunov function using the last collected data. The resulting closed-loop dynamics hence exhibits both physical jumps, due to the system dynamics, and episodic jumps, which naturally leads to a hybrid discrete-time system. We leverage the inherent robustness of the controller and provide general conditions under which various stability notions can be established for the system. Two notable cases where these conditions are satisfied are treated, and numerical results illustrating the relevance of the approach are discussed.

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References (25)
  1. R. Sanfelice and A. Teel, “Dynamical properties of hybrid systems simulators,” Automatica, vol. 46, no. 2, pp. 239–248, 2010.
  2. W. Heemels, K. Johansson, and P. Tabuada, “An introduction to event-triggered and self-triggered control,” in IEEE Conference on Decision and Control, pp. 3270–3285, 2012.
  3. C. De Persis and P. Tesi, “Formulas for data-driven control: Stabilization, optimality, and robustness,” IEEE Trans. on Automatic Control, vol. 65, no. 3, pp. 909–924, 2020.
  4. H. van Waarde, M. Camlibel, and M. Mesbahi, “From noisy data to feedback controllers: Nonconservative design via a matrix S-lemma,” IEEE Trans. on Automatic Control, vol. 67, no. 1, pp. 162–175, 2020.
  5. J. Berberich, C. Scherer, and F. Allgöwer, “Combining prior knowledge and data for robust controller design,” IEEE Trans. on Automatic Control, vol. 68, no. 8, pp. 4618–4633, 2023.
  6. M. Rotulo, C. De Persis, and P. Tesi, “Online learning of data-driven controllers for unknown switched linear systems,” Automatica, vol. 145, p. 110519, 2022.
  7. S. Liu, K. Chen, and J. Eising, “Online data-driven adaptive control for unknown linear time-varying systems,” in IEEE Conference on Decision and Control, pp. 8775–8780, 2023.
  8. B. Nortmann and T. Mylvaganam, “Direct data-driven control of linear time-varying systems,” IEEE Trans. on Automatic Control, vol. 68, no. 8, pp. 4888–4895, 2023.
  9. M. Mazo, A. Anta, and P. Tabuada, “An ISS self-triggered implementation of linear controllers,” Automatica, vol. 46, no. 8, pp. 1310–1314, 2010.
  10. X. Wang and M. Lemmon, “On event design in event-triggered feedback systems,” Automatica, vol. 47, no. 10, pp. 2319–2322, 2011.
  11. A. Maass, W. Wang, D. Nešić, R. Postoyan, and W. Heemels, “Event-triggered control through the eyes of a hybrid small-gain theorem,” IEEE Trans. on Automatic Control, vol. 68, no. 10, pp. 5906–5921, 2023.
  12. C. De Persis, R. Postoyan, and P. Tesi, “Event-triggered control from data,” IEEE Trans. on Automatic Control, vol. available on-line, 2023.
  13. W.-L. Qi, K.-Z. Liu, R. Wang, and X.-M. Sun, “Data-driven ℒ2subscriptℒ2\mathcal{L}_{2}caligraphic_L start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT-stability analysis for dynamic event-triggered networked control systems: A hybrid system approach,” IEEE Trans. on Industrial Electronics, vol. 70, no. 6, pp. 6151–6158, 2022.
  14. X. Wang, J. Berberich, J. Sun, G. Wang, F. Allgöwer, and J. Chen, “Model-based and data-driven control of event-and self-triggered discrete-time linear systems,” IEEE Trans. on Cyb., vol. 53, no. 9, pp. 6066 – 6079, 2023.
  15. Princeton University Press, Princeton, U.S.A., 2012.
  16. H. van Waarde, J. Eising, H. Trentelman, and M. Camlibel, “Data informativity: a new perspective on data-driven analysis and control,” IEEE Trans. on Automatic Control, vol. 65, no. 11, pp. 4753–4768, 2020.
  17. J. C. Willems, P. Rapisarda, I. Markovsky, and B. D. Moor, “A note on persistency of excitation,” Syst. & Contr. Lett., vol. 54, no. 4, pp. 325–329, 2005.
  18. A. Girard, “Dynamic triggering mechanisms for event-triggered control,” IEEE Trans. on Automatic Control, vol. 60, no. 7, pp. 1992–1997, 2015.
  19. S. Benahmed, R. Postoyan, M. Granzotto, L. Buşoniu, J. Daafouz, and D. Nešić, “Stability analysis of optimal control problems with time-dependent costs,” Automatica, vol. 157, p. 111272, 2023.
  20. A. Bisoffi, C. De Persis, and P. Tesi, “Trade-offs in learning controllers from noisy data,” Systems & Control Letters, vol. 154, 2021.
  21. A. Bisoffi, C. De Persis, and P. Tesi, “Data-driven control via Petersen’s lemma,” Automatica, vol. 145, p. 110537, 2022.
  22. D. Borgers, V. Dolk, G. Dullerud, A. Teel, and W. Heemels, “Time-regularized and periodic event-triggered control for linear systems,” in Control Subject to Computational and Communication Constraints, pp. 121–149, Springer, 2018.
  23. M. Abdelrahim, R. Postoyan, J. Daafouz, and D. Nešić, “Robust event-triggered output feedback controllers for nonlinear systems,” Automatica, vol. 75, pp. 96–108, 2017.
  24. P. Tallapragada and N. Chopra, “Event-triggered dynamic output feedback control for LTI systems,” in IEEE Conference on Decision and Control, Maui, U.S.A., pp. 6597–6602, 2012.
  25. W. Wang, D. Nešić, R. Postoyan, I. Shames, and W. Heemels, “State-feedback event-holding control for nonlinear systems,” in IEEE Conf. on Decision and Control, Nice, France, pp. 1650–1655, 2019.

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