Abstract
The problem of constructing interval observers for discrete-time linear systems under external disturbances, measurement noise, and parametric uncertainties is studied. The relations allowing designing the interval observer of the minimal dimension that estimates the set of admissible values of the specified linear vector function of the system state are derived. The theoretical results are illustrated by an example.
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REFERENCES
A. N. Zhirabok, A. V. Zuev, and Kim Chkhun Ir, “Method to design interval observers for linear time-invariant systems,” J. Comput. Syst. Sci. Int. 61 (4), 485–495 (2022).
D. V. Efimov and T. Raïssi, “Design of interval observers for uncertain dynamical systems,” Autom. Remote Control 77 (2), 191–225 (2016).
A. Khan, W. Xie, L. Zhang, and L. Liu, “Design and applications of interval observers for uncertain dynamical systems,” IET Circuits Devices Syst. 14, 721–740 (2020).
N. Kolesov, A. Gruzlikov, and E. Lukoyanov, “Using fuzzy interacting observers for fault diagnosis in systems with parametric uncertainty,” in Proceedings of the XII International Symposium “Intelligent Systems,” INTELS’16 (Moscow, 2016), pp. 499–504.
A. S. Kremlev and S. G. Chebotarev, “Synthesis of interval observer for a linear system with variable parameters,” Izv. Vyssh. Uchebn. Zaved., Priborostr. 56 (4), 42–46 (2013).
D. Efimov, T. Raissi, S. Chebotarev, and A. Zolghadri, “Interval state observer for nonlinear time varying systems,” Automatica 49, 200–206 (2013).
S. Chebotarev, D. Efimov, T. Raissi, and A. Zolghadri, “Interval observers for continuous-time LPV systems with L1/L2 performance,” Automatica 51, 82–89 (2015).
F. Mazenc and O. Bernard, “Asymptotically stable interval observers for planar systems with complex poles,” IEEE Trans. Autom. Control 55 (2), 523–527 (2010).
J. Blesa, V. Puig, and Y. Bolea, “Fault detection using interval LPV models in an open-flow canal,” Control Eng. Pract. 18, 460–470 (2010).
G. Zheng, D. Efimov, and W. Perruquetti, “Interval state estimation for uncertain nonlinear systems,” in IFAC Nolcos 2013 (Toulouse, France, 2013).
K. Zhang, B. Jiang, X. Yan, and C. Edwards, “Interval sliding mode based fault accommodation for non-minimal phase LPV systems with online control application,” Int. J. Control 93 (11), 2675–2689 (2019). https://doi.org/10.1080/00207179.2019.1687932
A. N. Zhirabok, A. V. Zuev, and A. E. Shumsky, “Diagnosis of linear systems based on sliding mode observers,” J. Comput. Syst. Sci. Int. 58 (6), 898–914 (2019).
A. N. Zhirabok, A. V. Zuev, and A. E. Shumsky, “Diagnosis of linear dynamic systems: An approach based on sliding mode observers,” Autom. Remote Control 81 (2), 221–225 (2020).
X. Low, A. Willsky, and G. Verghese, “Optimally robust redundancy relations for failure detection in uncertain systems,” Automatica 22, 333–344 (1996).
V. F. Filaretov, A. V. Zuev, and A. S. Gubankov, Control of Manipulators in Various Technological Operations (Nauka, Moscow, 2018) [in Russian].
Funding
This study was supported by the Russian Science Foundation, project no. 23-29-000191, https://rscf.ru/project/23-29-00191/
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Zhirabok, A.N., Zuev, A.V. & Kim, C. Interval Estimation in Discrete-Time Linear Systems with Parametric Uncertainties. J. Comput. Syst. Sci. Int. 62, 1037–1047 (2023). https://doi.org/10.1134/S1064230723060138
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DOI: https://doi.org/10.1134/S1064230723060138