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Article

Adaptive Fault Estimation for Hyperbolic PDEs

1
School of Automatin, Central South University, Changsha 480013, China
2
Department of Chemical & Materials Engineering, University of Alberta, Edmonton, AB T6G 2V4, Canada
*
Author to whom correspondence should be addressed.
Academic Editor: Denis N. Sidorov
Mathematics 2021, 9(14), 1613; https://doi.org/10.3390/math9141613
Received: 28 June 2021 / Revised: 5 July 2021 / Accepted: 6 July 2021 / Published: 8 July 2021
(This article belongs to the Special Issue Model Predictive Control and Optimization for Cyber-Physical Systems)
The new adaptive fault estimation scheme is proposed for a class of hyperbolic partial differential equations in this paper. The multiplicative actuator and sensor faults are considered. There are two cases that require special consideration: (1). only one type of fault (actuator or sensor) occurs; (2). two types of faults occurred simultaneously. To solve the problem of fault estimation, three challenges need to be solved: (1). No prior information of fault type is known; (2). Unknown faults are always coupled with state and input; (3). Only one boundary measurement is available. The original plant is converted to Observer canonical form. Two filters are proposed and novel adaptive laws are developed to estimate unknown fault parameters. With the help of the proposed update laws, the true state of the faulty plant can be estimated by the proposed observers composed of two filters. By selecting a suitable Lyapunov function, it is proved that under unknown external disturbance, the estimation errors of state parameters and fault parameters decay to arbitrarily small value. Finally, the validity of the proposed observer and adaptive laws is verified by numerical simulation. View Full-Text
Keywords: observer canonical form; actuator fault; sensor fault; fault estimation; parameter adaptive laws; partial differential equations observer canonical form; actuator fault; sensor fault; fault estimation; parameter adaptive laws; partial differential equations
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MDPI and ACS Style

Yuan, Y.; Xu, X.; Dubljevic, S. Adaptive Fault Estimation for Hyperbolic PDEs. Mathematics 2021, 9, 1613. https://doi.org/10.3390/math9141613

AMA Style

Yuan Y, Xu X, Dubljevic S. Adaptive Fault Estimation for Hyperbolic PDEs. Mathematics. 2021; 9(14):1613. https://doi.org/10.3390/math9141613

Chicago/Turabian Style

Yuan, Yuan, Xiaodong Xu, and Stevan Dubljevic. 2021. "Adaptive Fault Estimation for Hyperbolic PDEs" Mathematics 9, no. 14: 1613. https://doi.org/10.3390/math9141613

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