Set-based state estimation and fault diagnosis of linear discrete-time descriptor systems using constrained zonotopes

TL;DR

This paper introduces set-valued state estimation and fault diagnosis methods for linear descriptor systems using constrained zonotopes, which improve accuracy and efficiency by directly incorporating system constraints.

Contribution

The paper develops novel algorithms based on constrained zonotopes for set-valued state estimation and fault diagnosis in descriptor systems, allowing direct inclusion of linear constraints.

Findings

Constrained zonotopes enable more accurate state estimation.

The methods do not require rank assumptions on system structure.

Numerical examples demonstrate improved performance.

Abstract

This paper presents new methods for set-valued state estimation and active fault diagnosis of linear descriptor systems. The algorithms are based on constrained zonotopes, a generalization of zonotopes capable of describing strongly asymmetric convex sets, while retaining the computational advantages of zonotopes. Additionally, unlike other set representations like intervals, zonotopes, ellipsoids, paralletopes, among others, linear static constraints on the state variables, typical of descriptor systems, can be directly incorporated in the mathematical description of constrained zonotopes. Therefore, the proposed methods lead to more accurate results in state estimation in comparison to existing methods based on the previous sets without requiring rank assumptions on the structure of the descriptor system and with a fair trade-off between accuracy and efficiency. These advantages are highlighted in two numerical examples.