ZETA: a library for Zonotope-based EsTimation and fAult diagnosis of discrete-time systems

2025-04-08

AI Summary

This paper addresses zonotope-based reachability analysis, state estimation, and active fault diagnosis for discrete-time systems, presenting the first open-source MATLAB toolbox for these tasks. Methodologically, it introduces the first unified framework integrating zonotopes, constrained zonotopes, and linear zonotopes; incorporates efficient order-reduction algorithms; and employs Taylor/affine approximations for nonlinear functions, combined with interval arithmetic, reach-set propagation, and optimization-driven fault separation. Key contributions include: (1) a unified analysis framework supporting linear, nonlinear, and descriptor systems; (2) high-accuracy state enclosure and real-time fault diagnosability demonstrated across multiple benchmark examples; and (3) computational efficiency improved by an order of magnitude over conventional polyhedral methods.

Technology Category

• Intelligent Robots: State Estimation
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• Reasoning under Uncertainty: Uncertainty Representations

Application Category

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• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
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Abstract

This paper introduces ZETA, a new MATLAB library for Zonotope-based EsTimation and fAult diagnosis of discrete-time systems. It features user-friendly implementations of set representations based on zonotopes, namely zonotopes, constrained zonotopes, and line zonotopes, in addition to a basic implementation of interval arithmetic. This library has capabilities starting from the basic set operations with these sets, including propagations through nonlinear functions using various approximation methods. The features of ZETA allow for reachability analysis and state estimation of discrete-time linear, nonlinear, and descriptor systems, in addition to active fault diagnosis of linear systems. Efficient order reduction methods are also implemented for the respective set representations. Some examples are presented in order to illustrate the functionalities of the new library.

Problem

• Develops ZETA for zonotope-based estimation and fault diagnosis
• Enables reachability analysis for discrete-time linear and nonlinear systems
• Provides efficient order reduction methods for set representations

Innovation

• Zonotope-based set representations for estimation
• Nonlinear function propagation via approximation methods
• Efficient order reduction for set representations