State estimation using a network of distributed observers with switching communication topology

State estimation of linear time-invariant (LTI) systems by using a network of distributed observers is studied in this paper. We assume that each observer has access to a local measurement which may be insufficient to provide the observability of the system, but the ensemble of all measurements in the network guarantees the observability. In this condition, the objective is to design a distributed state estimation approach such that, while the observers can exchange their estimated state vectors under a communication network, the estimated state vector of each observer converges to the state vector of the system. We consider a scenario when the communication links may fail and rebuild over time and the communication network does not stay connected constantly. Accordingly, the main contribution of the paper is to propose a distributed approach (with guarantees on the feasibility of the design) such that the state vector of the system is estimated by each observer if the union/joint of communication links in bounded intervals of time makes the network communication graph connected. Moreover, we also consider a scenario when the LTI system is subject to external disturbances and measurement noise. In this case, we derive sufficient conditions on the proposed approach such that if the communication topology stays connected during links failure, a desired H infinity performance to attenuate the effect of external disturbances and measurement noise on estimation errors is guaranteed. Simulation results show the effectiveness of the proposed estimation approach.(c) 2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

This paper focuses on the state estimation of linear time-invariant (LTI) systems using a network of distributed observers. The observability of the system is guaranteed by the ensemble of all measurements in the network, even though each observer has access to only a local measurement. The main contribution is the proposal of a distributed approach that ensures convergence of the estimated state vector of each observer to the state vector of the system, even when the communication links may fail and rebuild over time. The paper also considers the scenario of external disturbances and measurement noise, providing conditions for desired performance in attenuating their effects on estimation errors.