A Robust Distributed Interval Observer for LTI Systems

• Published in: IEEE transactions on automatic control Vol. 68; no. 3; pp. 1337 - 1352
• Main Authors: Wang, Xiaoling, Su, Housheng, Zhang, Fan, Chen, Guanrong
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Bounding information; Continuous time systems; distributed interval observer; external disturbance; Graph theory; Group communication; Heterogeneity; Intellectual property; internally positive representation (IPR); Linear systems; linear time-invariant (LTI) system; Noise measurement; Observers; Pollution measurement; Robustness (mathematics); Sensors; State estimation; Time invariant systems; Uncertainty
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2022.3151586

In this article, the state estimation problem of a continuous-time linear time-invariant system is investigated for the situation with unknown external disturbance and measurement noise. A robust distributed interval observer is designed, which consists of a group of sensors communicating with others through a directed graph where each sensor can only access partial information from the output of the plant. The communication among the sensors together with the heterogeneity and undetectability of the sensors result in some stringent requirements on the robust distributed interval observer construction. To resolve these restrictions, the internally positive representation originated from a single agent system is introduced into the robust distributed interval observer. After presenting detailed design and analysis, numerical simulations are demonstrated to verify the theoretical results.