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Sample-based nonlinear detectability for discrete-time systems (2312.13658v1)

Published 21 Dec 2023 in eess.SY and cs.SY

Abstract: This paper introduces two sample-based formulations of incremental input/output-to-state stability (i-IOSS), a suitable detectability notion for general nonlinear systems. In this work we consider the case of limited output information, i.e., measurements are only infrequently and/or irregularly available. The output-dependent term of the sample-based i-IOSS bound is properly modified to yield a characterization for detectability in presence of incomplete output sequences. We provide both a non-timediscounted and a time-discounted formulation of samplebased i-IOSS. Furthermore, conditions for an i-IOSS system to be also sample-based i-IOSS are given and the relation between the two formulations of sample-based i-IOSS is shown.

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References (26)
  1. D. A. Allan and J. B. Rawlings, “An input/output-to-state stability converse theorem for closed positive invariant sets,” TWCCC Technical Report 2018–01, 2018.
  2. D. A. Allan and J. B. Rawlings, “A Lyapunov-like Function for Full Information Estimation,” American Control Conference (ACC), pp. 4497-4502, 2019.
  3. D. A. Allan, J. B. Rawlings, and A. R. Teel, “Nonlinear detectability and incremental input/output-to-state stability,” TWCCC Technical Report 2020–01, 2020.
  4. D. A. Allan and J. B. Rawlings, “Robust Stability of Full Information Estimation,” SIAM Journal on Control and Optimization, vol. 59, no. 5, pp. 3472-3497, 2021.
  5. D. Angeli, “A Lyapunov approach to incremental stability properties,” IEEE Transactions on Automatic Control, vol. 47, no. 3, pp. 410-421, 2002.
  6. V. Brun, A. Eriksen, R. Selseth, K. Johanssson, R. Vik, Renate, B. Davidsen, M. Kaut, and L. Hellemo, “Patient-Tailored Levothyroxine Dosage with Pharmacokinetic/Pharmacodynamic Modeling: A Novel Approach After Total Thyroidectomy,” Thyroid, vol. 31, 2021.
  7. M. Miskowicz, “Reducing Communication by Event-Triggered Sampling,” Event-Based Control and Signal Processing, pp. 37-58, 2015.
  8. J. W. Dietrich, G. Landgrafe-Mende, E. Wiora, A. Chatzitomaris, H. H. Klein, J. E. M. Midgley, and R. Hoermann, “Calculated Parameters of Thyroid Homeostasis: Emerging Tools for Differential Diagnosis and Clinical Research,” Frontiers in Endocrinology, vol. 7, 2016.
  9. X. Ge, Q.-L. Han, X.-M. Zhang, L. Ding and F. Yang, “Distributed Event-Triggered Estimation Over Sensor Networks: A Survey,” IEEE Transactions on Cybernetics, vol. 50, no. 3, pp. 1306-1320, 2020.
  10. W. Hu, “Robust stability of optimization-based state estimation,” arXiv:1702.01903v3 [math.OC], 2017.
  11. L. Ji, J. B. Rawlings, W. Hu, A. Wynn and M. Diehl, “Robust Stability of Moving Horizon Estimation Under Bounded Disturbances,” IEEE Transactions on Automatic Control, vol. 61, no. 11, pp. 3509-3514, 2016.
  12. C. Kellett, “A compendium of comparison function results,” Mathematics of Control Signals and Systems, vol. 26, 2014.
  13. S. Knüfer and M. A. Müller, “Robust Global Exponential Stability for Moving Horizon Estimation,” 57th IEEE Conference on Decision and Control (CDC), pp. 3477-3482, 2018.
  14. S. Knüfer and M. A. Müller, “Time-Discounted Incremental Input/Output-to-State Stability,” 59th IEEE Conference on Decision and Control (CDC), pp. 5394-5400, 2020.
  15. S. Knüfer and M. A. Müller, “Nonlinear full information and moving horizon estimation: Robust global asymptotic stability,” Automatica, 150:110603, 2023.
  16. I. Krauss, V. G. Lopez and M. A. Müller, “Sample-based observability of linear discrete-time systems,” 61st IEEE Conference on Decision and Control (CDC), pp. 4199-4205, 2022.
  17. M. A. Müller, “Nonlinear moving horizon estimation in the presence of bounded disturbances,” Automatica, vol. 79, pp. 306-314, 2017.
  18. C. Peng, F. Li, “A survey on recent advances in event-triggered communication and control,” Information Sciences, vol. 457–458, pp. 113-125, 2018.
  19. J. B. Rawlings and L. Ji, “Optimization-based state estimation: Current status and some new results,” Journal of Process Control, vol. 22, pp. 1439–1444, 2012.
  20. J. B. Rawlings, D. Q. Mayne and M. M. Diehl, “Model Predictive Control: Theory Computation and Design,” vol. 2. Madison, WI, USA: Nob Hill Publishing, 2017.
  21. E. D. Sontag and Y. Wang, “Output-to-state stability and detectability of nonlinear systems,” Systems Control Lett., vol. 29, 1995.
  22. E. D. Sontag, “Comments on integral variants of ISS,” Systems Control Lett., vol. 34, 1998.
  23. J. D. Schiller, S. Muntwiler, J. Köhler, M. N. Zeilinger and M. A. Müller, “A Lyapunov function for robust stability of moving horizon estimation,” IEEE Transactions on Automatic Control, 2023, doi: 10.1109/TAC.2023.3280344.
  24. L. Y. Wang, C. Li, G. Yin, L. Guo, and C.-Z. Xu, “State observability and observers of linear-time-invariant systems under irregular sampling and sensor limitations,” IEEE Transactions on Automatic Control, vol. 56, no. 11, pp. 2639–2654, 2011.
  25. M. Wolff, J.W. Dietrich and M. A. Müller, “Optimal Hormone Replacement Therapy in Hypothyroidism - A Model Predictive Control Approach,” Frontiers in Endocrinology, vol. 13, 2022.
  26. S. Zeng and F. Allgöwer, “A general sampled observability result and its applications,” 55th IEEE Conference on Decision and Control (CDC), pp. 3997-4002, 2016.
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