This paper investigates the fault detection problem for a class of semi-linear partial differential equation (PDE) systems. Specifically, the complexities of the studied system, that is, nonlinearity, stochasticity and external disturbance, are considered and reconstructed as the Takagi-Sugeno (T-S) fuzzy model. The primary purpose of this paper is to construct a fuzzy asynchronous fault detection filter for detecting the random fault signals that can be described by a Markov process. In particular, to save network transmission resources, an adaptive event-triggered mechanism (AETM) can be employed to dynamically select the triggered signal by designing an adaptive threshold before the input signal is transmitted to the filter. Furthermore, by applying the Lyapunov stability theory, the stochastic theory and several inequality transformation techniques, sufficient conditions are obtained for the asymptotic stability of the augmented system in the form of linear matrix inequality, and the desired filter’s parameters can be obtained in explicit form. A high-speed aerospace fin temperature distribution model is presented to illustrate the effectiveness of the described scheme by comparisons.
RoshanravanSShamaghdariS.Simultaneous fault detection and isolation and fault-tolerant control using supervisory control technique: asynchronous switching approach. Proc IMechE, Part I: J Systems and Control Engineering2020; 234(8): 900–911.
2.
BhargavRBhaljaBRGuptaCP.Novel fault detection and localization algorithm for low-voltage DCmicrogrid. IEEE Trans Ind Inform2020; 16(7): 4498–4511.
3.
SuXShiPWuL, et al. Fault detection filtering for nonlinear switched stochastic systems. IEEE Trans Automat Contr2016; 61(5): 1310–1315.
4.
QuanYGuoHHuangY, et al. Observer-based distributed fault detection and isolation for multi-agent systems with time delays and disturbances. Proc IMechE, Part I: J Systems and Control Engineering2023; 237(3): 479–489.
5.
NingZYuJPanY, et al. Adaptive event-triggered fault detection for fuzzy stochastic systems with missing measurements. IEEE Trans Fuzzy Syst2018; 26(4): 2201–2212.
6.
ZhangZNingZZhangK, et al. Zonotopic fault detection for discrete-time systems with limited communication capability and sensor nonlinearity. J Franklin Inst2022; 359(11): 5733–5749.
7.
MaYWangZMeslemN, et al. An improved zonotopic approach applied to fault detection for Takagi-Sugeno fuzzy systems. IEEE Trans Fuzzy Syst2023; 31(11): 3762–3774.
8.
ShenMMaYParkJH, et al. Fuzzy tracking control for Markov jump systems with mismatched faults by iterative proportional-integral observers. IEEE Trans Fuzzy Syst2022; 30(2): 542–554.
9.
YangHJiangYYinS.Adaptive fuzzy fault-tolerant control for Markov jump systems with additive and multiplicative actuator faults. IEEE Trans Fuzzy Syst2021; 29(4): 772–785.
10.
ZhaoALiJLeiY, et al. Distributed robust output feedback control of uncertain fractional-order reaction-diffusion systems. Proc IMechE, Part I: J Systems and Control Engineering2023; 237(1): 86–101.
11.
ChenSVazquezRKrsticM.Folding bilateral backstepping output-feedback control design for an unstable parabolic PDE. IEEE Trans Automat Contr2022; 67(5): 2389–2404.
12.
ZhangZSongXSunX, et al. Hybrid-driven-based fuzzy secure filtering for nonlinear parabolic partial differential equation systems with cyber attacks. Int J Adapt Control Signal Process2023; 37(2): 380–398.
13.
WangMSongXSongS, et al. Diagnostic observer-based fault detection for nonlinear parabolic PDE systems via dual sampling approaches. J Franklin Inst2020; 357(12): 8203–8228.
14.
ZhangJYuanCZengW, et al. Fault detection of a class of nonlinear uncertain parabolic PDE systems. IEEE Control Syst Letters2020; 5(4): 1459–1464.
15.
TaiWTengQZhouY, et al. Chaos synchronization of stochastic reaction-diffusion time-delay neural networks via non-fragile output-feedback control. Appl Math Comput2019; 354: 115–127.
16.
WuHNZhangXM.Boundary static output feedback control for nonlinear stochastic parabolic partial differential systems via fuzzy-model-based approach. IEEE Trans Fuzzy Syst2019; 28(10): 2581–2591.
17.
EngblomSFermLHellanderA, et al. Simulation of stochastic reaction-diffusion processes on unstructured meshes. SIAM J Sci Comput2009; 31(3): 1774–1797.
18.
ShiJSunHHouL.Observer-based Takagi-Sugeno fuzzy sampled-data dynamic positioning controller design for unmanned surface vehicle with external disturbances and actuator faults. Proc IMechE, Part I: J Systems and Control Engineering2023; 237(2): 294–313.
19.
LiTFChangXHParkJH.Control design for parabolic PDE systems via T-S fuzzy model. IEEE Trans Syst Man Cybern Syst2022; 52(6): 3671–3679.
20.
KangWZhangJLamHK.Subpredictor-based fuzzy control design for a reaction-diffusion equation. IEEE Trans Fuzzy Syst2022; 30(11): 4728–4740.
21.
ZhangXWWuHN.Fuzzy stabilization design for semilinear parabolic PDE systems with mobile actuators and sensors. IEEE Trans Fuzzy Syst2019; 28(3): 474–486.
22.
ZhangZSongXSunX.Dynamic event-triggered fuzzy filtering for semi-linear parabolic PDE systems: a reduced-order approach. Int J Control Autom Syst2024; 22(2): 406–418.
23.
SongXWangMZhangB, et al. Event-triggered reliable fuzzy filtering for nonlinear parabolic PDE systems with Markovian jumping sensor faults. Inform Sci2020; 510: 50–69.
24.
EspitiaNKarafyllisIKrsticM.Event-triggered boundary control of constant-parameter reaction-diffusion PDEs: a small-gain approach. Automatica2021; 128: 109562.
25.
WangJKrsticM.Event-triggered output-feedback backstepping control of sandwich hyperbolic PDE systems. IEEE Trans Automat Contr2022; 67(1): 220–235.
26.
ShenMGuYParkJH, et al. Composite control of linear systems with event-triggered inputs and outputs. IEEE Trans Circuits Syst2021; 69(3): 1154–1158.
27.
WangJKrsticM.Adaptive event-triggered PDE control for load-moving cable systems. Automatica2020; 129: 109637.
28.
ZhangRZengDParkJH, et al. Adaptive event-triggered synchronization of reaction-diffusion neural networks. IEEE Trans Neural Netw Learn Syst2020; 32(8): 3723–3735.
29.
JiaJZhangXZhengL, et al. Event-triggered fuzzy control for vehicle nonlinear suspension systems with time delay. Proc IMechE, Part I: J Systems and Control Engineering2022; 236(10): 1865–1878.
30.
ShenMGuYZhuS, et al. Mismatched quantized output-feedback control of fuzzy markov jump systems with a dynamic guaranteed cost triggering scheme. IEEE Trans Fuzzy Syst2024; 32(4): 1681–1692.
31.
ShenMWangXZhuS, et al. Data-driven event-triggered adaptive dynamic programming control for nonlinear systems with input saturation. IEEE Trans Cybern2023; 54(2): 1178–1188.
32.
SongXZhangQSongS, et al. Improved event-triggered control for a chemical tubular reactor with singular perturbations. J Process Control2022; 112: 49–56.
33.
SongXZhangQSongS, et al. Event-triggered underactuated control for networked coupled PDE-ODE systems with singular perturbations. IEEE Syst J2023; 17(3): 4474–4484.
34.
WangYXiaYAhnCK, et al. Exponential stabilization of Takagi-Sugeno fuzzy systems with aperiodic sampling: an aperiodic adaptive event-triggered method. IEEE Trans Syst Man Cybern Syst2019; 49(2): 444–454.
35.
OksendalB.Stochastic differential equations. Math Gaz1985; 77(480): 65–84.
36.
Bar AmNFridmanE.Network-based filtering of parabolic systems. Automatica2014; 50(12): 3139–3146.
37.
WangJWWuHN.Exponential pointwise stabilization of semilinear parabolic distributed parameter systems via the Takagi-S ugeno fuzzy PDE model. IEEE Trans Fuzzy Syst2016; 26(1): 155–173.
38.
TsaiSHWangJWSongES, et al. Robust control for nonlinear hyperbolic PDE systems based on the polynomial fuzzy model. IEEE Trans Cybern2019; 51(7): 3789–3801.
39.
WuKLiuXShiP, et al. Boundary control of linear stochastic reaction-diffusion systems. Int J Robust Nonlinear Control2019; 29(1): 268–282.
40.
WangZPZhangXWuHN, et al. Fuzzy boundary control for nonlinear delayed DPSs under boundary measurements. IEEE Trans Cybern2021; 53(3): 1547–1556.
41.
GahinetPNemirovskiiALaubA, et al. LMI control toolbox for use with Matlab. Natick, MA: Math Works, 1995.
42.
YadavVPadhiRBalakrishnanSN.Robust/optimal temperature profile control of a high-speed aerospace vehicle using neural networks. IEEE Trans Neural Netw2007; 18(4): 1115–1128.
43.
SongXZhangQWangM, et al. Distributed estimation for nonlinear PDE systems using space-sampling approach: applications to high-speed aerospace vehicle. Nonlinear Dyn2021; 106(4): 3183–3198.
