A Novel Approach to Set-Membership Observer for Systems with Unknown Exogenous Inputs

TL;DR

This paper introduces a new set-membership observer for systems with unknown exogenous inputs, decomposing the system into observable and unobservable parts to improve state estimation under uncertainties.

Contribution

It presents a novel decomposition-based set-membership observer design for systems with unknown inputs, enhancing estimation accuracy and robustness.

Findings

The observer ensures boundedness of state estimates.

Numerical examples validate the effectiveness of the approach.

The method improves state estimation in uncertain systems.

Abstract

Motivated by the increasing need to monitor safety-critical systems subject to uncertainties, a novel set-membership approach is proposed to estimate the state of a dynamical system with unknown-but-bounded exogenous inputs. The proposed method decomposes the system into the strongly observable and weakly unobservable subsystem in which an unknown input observer and an ellipsoidal set-membership observer are designed for each subsystem, respectively. The conditions for the boundedness of the proposed set estimate are discussed, and the proposed set-membership observer is also tested numerically using illustrative examples.