2000 character limit reached
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.
- 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.
- D. A. Allan and J. B. Rawlings, “A Lyapunov-like Function for Full Information Estimation,” American Control Conference (ACC), pp. 4497-4502, 2019.
- 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.
- 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.
- D. Angeli, “A Lyapunov approach to incremental stability properties,” IEEE Transactions on Automatic Control, vol. 47, no. 3, pp. 410-421, 2002.
- 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.
- M. Miskowicz, “Reducing Communication by Event-Triggered Sampling,” Event-Based Control and Signal Processing, pp. 37-58, 2015.
- 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.
- 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.
- W. Hu, “Robust stability of optimization-based state estimation,” arXiv:1702.01903v3 [math.OC], 2017.
- 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.
- C. Kellett, “A compendium of comparison function results,” Mathematics of Control Signals and Systems, vol. 26, 2014.
- 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.
- 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.
- S. Knüfer and M. A. Müller, “Nonlinear full information and moving horizon estimation: Robust global asymptotic stability,” Automatica, 150:110603, 2023.
- 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.
- M. A. Müller, “Nonlinear moving horizon estimation in the presence of bounded disturbances,” Automatica, vol. 79, pp. 306-314, 2017.
- C. Peng, F. Li, “A survey on recent advances in event-triggered communication and control,” Information Sciences, vol. 457–458, pp. 113-125, 2018.
- 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.
- 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.
- E. D. Sontag and Y. Wang, “Output-to-state stability and detectability of nonlinear systems,” Systems Control Lett., vol. 29, 1995.
- E. D. Sontag, “Comments on integral variants of ISS,” Systems Control Lett., vol. 34, 1998.
- 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.
- 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.
- 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.
- 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.