Behaviors, trajectories and data: A novel perspective on the design of unknown-input observers

TL;DR

This paper introduces a new approach for designing unknown-input observers for linear systems using behavior theory, applicable when models are known or only data is available, providing necessary conditions and design algorithms.

Contribution

It applies Willems' behavior theory to the unknown-input observer design problem, offering a unified framework for known and data-driven scenarios.

Findings

Derived necessary and sufficient conditions for UIO existence

Developed algorithms for UIO design based on behavior projections

Extended the approach to systems with unknown models using data

Abstract

The purpose of this paper is to propose a novel perspective, based on Willems' "behavior theory", on the design of an unknown-input observer for a given linear time-invariant discrete-time state-space model, with unknown disturbances affecting both the state and the output equations. The problem is first addressed assuming that the original system model is known, and later assuming that the model is unknown but historical data satisfying a certain assumption are available. In both cases, fundamental concepts in behavior theory, as the projection of a behavior, the inclusion of a behavior in another one, and the use of kernel and image representations, provide quite powerful tools to determine necessary and sufficient conditions for the existence of an unknown-input observer (UIO), as well as algorithms to design one of them, if it exists.