Data-Driven Observers Design for Descriptor Systems

TL;DR

This paper introduces a data-driven approach for designing state observers for descriptor systems, deriving conditions directly from data and extending to unknown input observers, validated through simulations.

Contribution

It provides necessary and sufficient data-driven conditions for observer existence and extends the framework to unknown input and extended state observers.

Findings

Derived data-driven existence conditions match classical model-based ones.

Extended the framework to unknown input observers for systems with unknown disturbances.

Validated methods through numerical simulations demonstrating effectiveness.

Abstract

State estimation constitutes a core task in monitoring, supervision, and control of dynamic systems. This paper proposes a data-driven framework for the design of state observers for descriptor systems. Necessary and sufficient conditions for the existence of a standard state observer are derived purely from data under mild assumptions. When the system is subject to unknown inputs, we further extend the framework to the data-driven design method for full-order unknown input observer (UIO). Notably, for both the standard state observer and the UIO, we establish the mathematical equivalence between the proposed data-driven existence conditions and classical model-based ones. Moreover, the data-driven approach is applied to the design of extended state observers, enabling simultaneous estimation of system states and disturbances via system augmentation. Numerical simulations validate the effectiveness of the proposed methods.