Towards a minimal order distributed observer for linear systems

TL;DR

This paper investigates the existence of minimal order distributed observers for continuous-time LTI systems, demonstrating conditions under which such observers can be constructed with reduced state dimension based on network and system properties.

Contribution

It establishes the existence of reduced order distributed observers for observable systems over strongly connected networks, generalizing classical minimal observers.

Findings

Distributed observer exists with dimension Nn - sum of p_i

Special case reduces to classical minimal observer

Conditions require system observability and strongly connected network

Abstract

In this paper we consider the distributed estimation problem for continuous-time linear time-invariant (LTI) systems. A single linear plant is observed by a network of local observers. Each local observer in the network has access to only part of the output of the observed system, but can also receive information on the state estimates of its neigbours. Each local observer should in this way generate an estimate of the plant state. In this paper we study the problem of existence of a reduced order distributed observer. We show that if the observed system is observable and the network graph is a strongly connected directed graph, then a distributed observer exists with state space dimension equal to $Nn - \sum_{i =1}^N p_i$, where $N$ is the number of network nodes, $n$ is the state space dimension of the observed plant, and $p_i$ is the rank of the output matrix of the observed output received by the $i$th local observer. In the case of a single observer, this result specializes to the well-known minimal order observer in classical observer design.