Expert Analysis: New Methods for Set-Based State Estimation and Active Fault Diagnosis of Linear Descriptor Systems


In this paper, the authors propose new methods for set-based state estimation and active fault diagnosis (AFD) of linear descriptor systems. The goal of these methods is to improve the accuracy and efficiency of fault diagnosis in these systems by incorporating linear static constraints on the state variables.

Previous Set Representations

The authors begin by contrasting the simple set representations, such as intervals, ellipsoids, and zonotopes, with the linear static constraints present in descriptor systems. While previous works have proposed set-based methods using constrained zonotopes, these methods have made the assumption that an enclosure on the states is known for all time steps. This assumption is not valid for unstable descriptor systems, where the enclosure may not be known.

New Representation for Unbounded Sets

To address this limitation, this paper proposes a new representation for unbounded sets that can be used for state estimation and AFD of both stable and unstable linear descriptor systems. This new representation retains many of the advantageous properties of constrained zonotopes, such as efficient complexity reduction methods, while allowing for the description of different classes of sets like strips, hyperplanes, and the entire $n$-dimensional Euclidean space.

Advantages and Numerical Examples

The authors highlight the advantages of their proposed approaches over constrained zonotope methods through numerical examples. These examples demonstrate how the proposed methods can provide less conservative enclosures and more accurate fault diagnosis compared to previous approaches.

Future Directions

This paper presents important advancements in set-based state estimation and AFD of linear descriptor systems. However, there are still opportunities for further research. One area of potential improvement is the development of more efficient complexity reduction methods for the new set representation. Additionally, exploring the application of these methods to real-world systems and expanding their capabilities to handle more complex fault scenarios would also be valuable directions for future research.

In conclusion, the methods proposed in this paper offer promising solutions for enhancing set-based state estimation and AFD of linear descriptor systems. Their ability to handle unstable systems and their improved accuracy make them valuable tools for fault diagnosis. Further research in this area will likely contribute to the development of even more effective techniques for real-world applications.
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