A novel design of unknown input observers using set-theoretic methods for robust fault detection

Xu, Feng; Tan, Jiyuan; Wang, Xueqian; Puig, Vicenç; Liang, Bin; Yuan, Bo

doi:10.1109/acc.2016.7526604

Cited by 26 publications

(23 citation statements)

References 16 publications

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“…According to , a UIO for the LPV system (1) can be designed as

z_{k + 1} = N (ρ_{k}) z_{k} + T (ρ_{k}) u_{k} + K (ρ_{k}) y_{k},

{\overset{x}{true}}_{k} = M z_{k} + H y_{k},

ŷ_{k} = C {\overset{x}{true}}_{k},

where N ( ρ k ), T ( ρ k ), K ( ρ k ), M , and H are the parametric matrices of the UIO, which have compatible dimensions; z k is the state vector of the UIO; and

{\overset{x}{true}}_{k}

and

ŷ_{k}

are the estimated state and output vectors, respectively. Based on (1) and (3), we can define the SE‐error vector

e_{k}^{x} = x_{k} - {\overset{x}{true}}_{k},

whose dynamics can be derived as

\begin{matrix} right e_{k + 1}^{x} & left = (A (ρ_{k}) - H C A (ρ_{k}) - M K_{1} (ρ_{k}) C) e_{k}^{x} & right \\ right & left + [(A (ρ_{k}) - H C A (ρ_{k}) - M K_{1} (ρ_{k}) C ... \end{matrix}

…”

Section: Problem Formulationmentioning

confidence: 99%

“…The current paper is based on preliminary results by authors recently presented in . In , a preliminary algorithm combining active and passive robust approaches was presented, and used the set‐membership‐estimation framework and the UIO for robust estimation of state sets. Based on these preliminary results, the current work aims to present deeper results on robust SE and FD applications of SUIO and the extension to the LPV systems.…”

Section: Introductionmentioning

confidence: 99%

“…In this way, we will be able to broaden the applicability and benefit from the advantages of SUIOs in SE and FD applications.The current paper is based on preliminary results by authors recently presented in [21,22]. In [22], a preliminary algorithm combining active and passive robust approaches was presented, and i;k 2 P i for i D 1; 2; : : : ; m:Remark 2.1 P is typically defined as an interval vector (i.e., a box) composed of the intervals of the components of k (P i is the interval for the i-th component of k , and i;k and i;k are the minimal and maximal bounds of i;k , respectively).According to [10,22], a UIO for the LPV system (1) can be designed aś Provided that the standard method of designing UIOs, such as the one proposed in [5], is followed to design the UIO for the LPV system based on (6), the following conditions: ƒ 1 . k / D 0;(7a) under the aforementioned rank-based design conditions of UIO is the key to guarantee the stability (or under Theorem 4.1 for stability) of the SUIO for robust SE and FD.Moreover, the sets of the unknown inputs and the measurement noises obtained according to Remark 5.1 are given as zonotopes:…”

mentioning

confidence: 99%

“…The current paper is based on preliminary results by authors recently presented in [21,22]. In [22], a preliminary algorithm combining active and passive robust approaches was presented, and i;k 2 P i for i D 1; 2; : : : ; m:…”

mentioning

confidence: 99%

“…According to [10,22], a UIO for the LPV system (1) can be designed aś Provided that the standard method of designing UIOs, such as the one proposed in [5], is followed to design the UIO for the LPV system based on (6), the following conditions: ƒ 1 . k / D 0;…”

mentioning

confidence: 99%

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Generalized set‐theoretic unknown input observer for LPV systems with application to state estimation and robust fault detection

Tan

Wang

et al. 2017

Intl J Robust & Nonlinear

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Summary This paper proposes to design an unknown input observer (UIO) for the linear‐parameter‐varying (LPV) system on the basis of the set theory, which is named as the set‐theoretic UIO (SUIO). The advantage of the SUIO consists in that it combines active and passive approaches to obtain robustness in state estimation (SE) and fault detection (FD). The active approach is based on the use of UIO to decouple unknown inputs, while the passive approach is based on the set theory to bound uncertain factors that cannot be actively decoupled. As a result, the effect of both unknown inputs (process disturbances, modeling errors, etc.) and measurement noises can be appropriately handled in the residual signals compared with the standard UIO‐based SE and FD approaches. The design of SUIO can overcome the limitations of the traditional UIO design conditions, which can significantly broaden the application of the UIO‐based SE and FD theory. Moreover, this paper proposes a generalized framework that can provide more flexibility in the design of SUIO guaranteeing their stability by means of a group of matrix inequalities. Because the LPV system uses a collection of online obtainable scheduling variables to embed nonlinearities, the design of SUIO for the LPV system can be used to address the SE and FD problems of nonlinear systems. At the end of this paper, two case studies are used to illustrate the effectiveness of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd.

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“…According to , a UIO for the LPV system (1) can be designed as

z_{k + 1} = N (ρ_{k}) z_{k} + T (ρ_{k}) u_{k} + K (ρ_{k}) y_{k},

{\overset{x}{true}}_{k} = M z_{k} + H y_{k},

ŷ_{k} = C {\overset{x}{true}}_{k},

where N ( ρ k ), T ( ρ k ), K ( ρ k ), M , and H are the parametric matrices of the UIO, which have compatible dimensions; z k is the state vector of the UIO; and

{\overset{x}{true}}_{k}

and

ŷ_{k}

are the estimated state and output vectors, respectively. Based on (1) and (3), we can define the SE‐error vector

e_{k}^{x} = x_{k} - {\overset{x}{true}}_{k},

whose dynamics can be derived as

\begin{matrix} right e_{k + 1}^{x} & left = (A (ρ_{k}) - H C A (ρ_{k}) - M K_{1} (ρ_{k}) C) e_{k}^{x} & right \\ right & left + [(A (ρ_{k}) - H C A (ρ_{k}) - M K_{1} (ρ_{k}) C ... \end{matrix}

…”

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Generalized set‐theoretic unknown input observer for LPV systems with application to state estimation and robust fault detection

Tan

Wang

et al. 2017

Intl J Robust & Nonlinear

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Advances in State Estimation, Diagnosis and Control of Complex Systems

Wang¹

2021

Springer Theses

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pressurizing me to carefully prepare any publication at a top level and sufficiently produce high-quality results. Fourth, I want to thank Prof. Florin Stoican from University Politehnica of Bucharest, in Romania and Prof. Cristina Nicoleta Maniu from CentraleSupélec, Université Paris Saclay, in France for having reviewed this thesis with providing valuable comments. Especially, Prof. Stoican did a fantastic review with very detailed comments for each chapter of this thesis. Besides, I would like to thank Prof. Ramon Costa-Castelló from Universitat Politècnica de Catalunya, in Spain for joining my Ph.D. thesis committee.

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Introduction

Wang¹

2020

Advances in State Estimation, Diagnosis and Control of Complex Systems

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A novel design of unknown input observers using set-theoretic methods for robust fault detection

Cited by 26 publications

References 16 publications

Generalized set‐theoretic unknown input observer for LPV systems with application to state estimation and robust fault detection

Generalized set‐theoretic unknown input observer for LPV systems with application to state estimation and robust fault detection

Advances in State Estimation, Diagnosis and Control of Complex Systems

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