Distributed state estimation by a network of observers under communication and measurement delays

Abstract

In this paper we study the distributed state estimation of autonomous dynamic systems, under arbitrarily large communication and measurement delays. In the distributed estimation problem, we consider a network of observer agents that cannot independently determine all the states of the observed plant from their own collected measurements, but they must collaborate with neighboring agents to agree on the correct state estimation. Our current work considers the presence of arbitrarily large time delays in the communication and measurements of the observer agents, and we propose a framework for distributed observers following the low gain methodology. Sufficient conditions for the stability of the corresponding observation error dynamics are derived, including an upper bound for the low gain parameter of the observer equations. In the presence of bounded noisy measurements from the plant, we derive the upper-bound on the local estimation errors. The results of the distributed state estimation is then applied to propose a solution to the leader–follower synchronization problem for multi-agent systems under leader-agent and inter-agent communication delays. An illustrative example is also presented to verify the effectiveness of the theoretical analysis.