A Hybrid Observer for Estimating the State of a Distributed Linear System

TL;DR

This paper introduces a hybrid observer method for distributed linear systems where multiple agents estimate the system state through local observations and neighbor communications, ensuring convergence under certain connectivity and stability conditions.

Contribution

It presents a novel hybrid observer design that guarantees exponential convergence for distributed systems with time-varying communication graphs and asynchronous updates.

Findings

Convergence to the true state is achieved under strong connectivity and joint observability.

The method is robust to changes in communication topology and asynchronous updates.

Exponential convergence is guaranteed for exponentially stable systems.

Abstract

A hybrid observer is described for estimating the state of a system of the form dot x=Ax, y_i=C_ix, i=1,...,m. The system's state x is simultaneously estimated by m agents assuming agent i senses y_i and receives appropriately defined data from its neighbors. Neighbor relations are characterized by a time-varying directed graph N(t). Agent i updates its estimate x_i of x at event times t_{i1},t_{i2} ... using a local continuous-time linear observer and a local parameter estimator which iterates q times during each event time interval [t_{i(s-1)},t_{is}), s>=1, to obtain an estimate of x(t_{is}). Subject to the assumptions that N(t) is strongly connected, and the system is jointly observable, it is possible to design parameters so that x_i converges to x with a pre-assigned rate. This result holds when agents communicate asynchronously with the assumption that N(t) changes slowly. Exponential convergence is also assured if the event time sequence of the agents are slightly different, although only if the system being observed is exponentially stable; this limitation however, is a robustness issue shared by all open loop state estimators with small modeling errors. The result also holds facing abrupt changes in the number of vertices and arcs in the inter-agent communication graph upon which the algorithm depends.