Distributed Observers for LTI Systems

TL;DR

This paper introduces a novel distributed observer framework for LTI systems that enables asymptotic state estimation across sensor networks with various topologies, including extensions for time-varying networks and fault scenarios.

Contribution

It presents a new class of distributed observers that combine local Luenberger observers with consensus dynamics, offering a fully distributed design and robustness to network changes.

Findings

Guarantees asymptotic state reconstruction for general LTI systems

Allows fully distributed observer design under certain constraints

Extends to time-varying networks and fault scenarios

Abstract

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.