Event-based fault detection for interval type-2 fuzzy systems with measurement outliers

Qi Li; Hong Xue; Changxin Lu

doi:10.3934/dcdss.2020412

Article Contents

2021, Volume 14, Issue 4: 1301-1328. Doi: 10.3934/dcdss.2020412

This issue Previous Article Complex systems with impulsive effects and logical dynamics: A brief overview Next Article $ \mathcal{H}_{\infty} $ control for fuzzy markovian jump systems based on sampled-data control method

Event-based fault detection for interval type-2 fuzzy systems with measurement outliers

1.
College of Engineering, Bohai University, Jinzhou 121013, Liaoning, China
2.
School of Mathematics and Physics, Bohai University, Jinzhou 121013, Liaoning, China

^* Corresponding author: Hong Xue
^* Corresponding author: Hong Xue

Received: December 31, 2019

Revised: March 31, 2020

Early access: July 2020

Published: April 2021

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Abstract

This paper investigates the event-based fault detection (FD) problem for a category of discrete-time interval type-2 fuzzy systems with measurement outliers. For the sake of decreasing the utilization of limited communication bandwidth, an event-based mechanism is introduced. Based on the saturation function technique, a novel event-based FD observer is first designed to reduce the influence of outliers in the dynamic systems. Then, on the basis of Lyapunov stability theory, sufficient conditions are provided to ensure that the error system satisfies the $ \mathcal{H}_{\infty} $ performance and the $ \mathcal{H}_{\infty} $ fault performance in different cases, respectively. In contrast to the existing event-based FD results, the false alarm, which is induced by measurement outliers, can be effectively avoided by the designed FD observer with saturation function. Lastly, some simulation results are given to verify the effectiveness of the method presented in this paper.

Keywords:

Mathematics Subject Classification: 93D09, 93B53.

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Figure 1. Estimation errors of the system

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Figure 2. Trajectory of $ \bar{\sigma}(k) $

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Figure 3. Event-based release instants and release interval

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Figure 4. Evaluation function $ J(k) $ and threshold $ \mathcal{J}_{th} $

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Figure 5. Evaluation function $ J(k) $ and threshold $ \mathcal{J}_{th} $

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Figure 6. Evaluation function $ J(k) $ and threshold $ \mathcal{J}_{th} $

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Figure 7. Tunnel diode circuit

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Figure 8. Estimation errors of the system

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Figure 9. Trajectory of $ \bar{\sigma}(k) $

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Figure 10. Event-based release instants and release interval

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Figure 11. Evaluation function $ J(k) $ and threshold $ \mathcal{J}_{th} $

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Figure 12. Evaluation function $ J(k) $ and threshold $ \mathcal{J}_{th} $

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Figure 13. Evaluation function $ J(k) $ and threshold $ \mathcal{J}_{th} $

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Table 1. Lower and upper membership functions of the system

$ {\underline{u}}_{\mathcal{L}11}(x_{1})=1-e^{-\frac{x_{1}^{2}}{1.5}} $	$ { \bar{u}}_{\mathcal{L}11}(x_{1})=1-e^{-\frac{x_{1}^{2}}{1.2}} $
$ {\underline{u}}_{\mathcal{L}21}(x_{1})=1-{\bar{u}}_{\mathcal{L}11}(x_{1}) $	$ {\bar{u}}_{\mathcal{L}21}(x_{1})=1-{\underline{u}}_{\mathcal{L}11}(x_{1}) $

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Table 2. Lower and upper membership functions of the observer

$ {\underline{u}}_{\mathcal{V}11}(x_{1})=e^{-\frac{x_{1}^{2}}{0.4}} $	$ {\bar{ u}}_{\mathcal{V}11}(x_{1})=e^{-\frac{x_{1}^{2}}{0.4}} $
$ {\underline{u}}_{\mathcal{V}21}(x_{1})=1-{\underline{u}}_{\mathcal{V} 11}(x_{1}) $	$ {\bar{u}}_{\mathcal{V}21}(x_{1})=1-{\underline{u}}_{\mathcal{V }11}(x_{1}) $

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Table 3. Lower and upper membership functions of the system

$ {\underline{u}}_{\mathcal{L}11}(x_{1})=\frac{\bar{e}_{\max }-\bar{e}}{\bar{e }_{\max }-\bar{e}_{\min }},\partial=0.03 $	$ {\bar{u}}_{\mathcal{L} 11}(x_{1})=\frac{\bar{e}_{\max }-\bar{e}}{\bar{e}_{\max }-\bar{e}_{\min }} ,\partial=0.01 $
$ {\underline{u}}_{\mathcal{L}21}(x_{1})=\frac{\bar{e}-\bar{e}_{\min}}{\bar{e} _{\max }-\bar{e}_{\min }},\partial=0.01 $	$ {\bar{u}}_{\mathcal{L}21}(x_{1})= \frac{\bar{e}-\bar{e}_{\min}}{\bar{e}_{\max }-\bar{e}_{\min }},\partial=0.03 $

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Table 4. Lower and upper membership functions of the observer

$ {\underline{u}}_{\mathcal{V}11}(x_{1})=0.4e^{-\frac{x_{1}^{2}}{1.2}} $	$ { \bar{u}}_{\mathcal{V}11}(x_{1})=0.4e^{-\frac{x_{1}^{2}}{1.2}} $
$ {\underline{u}}_{\mathcal{V}21}(x_{1})=1-{\underline{u}}_{\mathcal{V} 11}(x_{1}) $	$ {\bar{u}}_{\mathcal{V}21}(x_{1})=1-{\underline{u}}_{\mathcal{V }11}(x_{1}) $

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