Distributed State Estimation for Linear Systems

Abstract

This paper studies a distributed state estimation problem for both continuous-and discrete-time linear systems. A simply structured distributed estimator is first described for estimating the state of a continuous-time, jointly observable, input free, multi-channel linear system whose sensed outputs are distributed across a fixed multi-agent network. The estimator is then extended to non-stationary networks whose graphs switch according to a switching signal with a fixed dwell time or a variable but with fixed average dwell time, or switch arbitrarily under appropriate assumptions. The estimator is guaranteed to solve the problem, provided a network-widely shared gain is sufficiently large. As an alternative to sharing a common gain across the network, a fully distributed version of the estimator is thus studied in which each agent adaptively adjusts a local gain though the practicality of this approach is subject to a robustness issue common to adaptive control. A discrete-time version of the distributed state estimation problem is also studied, and a corresponding estimator is proposed for time-varying networks. For each scenario, it is explained how to construct the estimator so that its state estimation errors all converge to zero exponentially fast at a fixed but arbitrarily chosen rate, provided the network's graph is strongly connected for all time. This is accomplished by appealing to the "split-spectrum" approach and exploiting several well-known properties of invariant subspace. The proposed estimators are inherently resilient to abrupt changes in the number of agents and communication links in the inter-agent communication graph upon which the algorithms depend, provided the network is redundantly strongly connected and redundantly jointly observable.