Distributed Observers for LTI Systems

• Published in: IEEE transactions on automatic control Vol. 63; no. 11; pp. 3689 - 3704
• Main Authors: Mitra, Aritra, Sundaram, Shreyas
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.11.2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Distributed estimation; distributed observers; Eigenvalues and eigenfunctions; Heuristic algorithms; large-scale networks; linear system theory; Linear systems; Network topologies; Observers; sensor networks; Sensor systems; State estimation; System dynamics
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2018.2798998

We consider the problem of distributed state estimation of a linear time-invariant (LTI) system by a network of sensors. We develop a distributed observer that guarantees asymptotic reconstruction of the state for the most general class of LTI systems, sensor network topologies, and sensor measurement structures. Our analysis builds upon the following key observation-a given node can reconstruct a portion of the state solely by using its own measurements and constructing appropriate Luenberger observers; hence, it only needs to exchange information with neighbors (via consensus dynamics) for estimating the portion of the state that is not locally detectable. This intuitive approach leads to a new class of distributed observers with several appealing features. Furthermore, by imposing additional constraints on the system dynamics and network topology, we show that it is possible to construct a simpler version of the proposed distributed observer that achieves the same objective while admitting a fully distributed design phase. Our general framework allows extensions to time-varying networks that result from communication losses, and scenarios including faults or attacks at the nodes.