Distributed Observers for LTI Systems with Finite Convergence Time: A Parameter Estimation-based Approach

TL;DR

This paper introduces a new distributed observer method for linear time-invariant systems that guarantees finite-time convergence using parameter estimation, with minimal communication assumptions and robustness to disturbances.

Contribution

It presents a finite-time convergent distributed observer based on parameter estimation, requiring only a Hamiltonian walk in the communication graph, unlike previous high-gain methods.

Findings

Achieves finite-time convergence without high gain.

Requires only a Hamiltonian walk in the communication graph.

Demonstrates robustness to disturbances and delays.

Abstract

A novel approach to solve the problem of distributed state estimation of linear time-invariant systems is proposed in this paper. It relies on the application of parameter estimation-based observers, where the state observation task is reformulated as a parameter estimation problem. In contrast with existing results our solution achieves convergence in finite-time, without injection of high gain, and imposes very weak assumptions on the communication graph---namely the existence of a Hamiltonian walk. The scheme is shown to be robust vis-\'a-vis external disturbances and communication delays.