In this paper, the problem of finite-time stabilization for a class of nonlinear parabolic distributed parameter systems (DPSs) is addressed, in which a Round-Robin scheduling controller is proposed to input feedback signal. In order to easily design controller, a finite element technique based on Galerkin’s method is applied to DPSs, the approximate finite-dimensional nonlinear systems are obtained. To control the nonlinear DPSs, a Takagi-Sugeno (T-S) fuzzy controller is given based on the finite-dimensional systems. Then, a fuzzy scheduling controller is designed to address the finite-time stability problem under an optimal performance level. Finally, a classical chemical model subjected to the Fisher equation is given to show the effectiveness of the proposed control method.
WangJW.Observer-based boundary control of semi-linear parabolic PDEs with non-collocated distributed event-triggered observation. J Franklin Inst2019; 356(17): 10405–10420.
4.
WangJWWuHNSunCY.Local exponential stabilization via boundary feedback controllers for a class of unstable semi-linear parabolic distributed parameter processes. J Franklin Inst2017; 354(13): 5221–5244.
5.
WangJWLiHX.Static collocated piecewise fuzzy control design of quasi-linear parabolic PDE systems subject to periodic boundary conditions. IEEE Trans Fuzzy Syst2019; 27(7): 1479–1492.
6.
SongXManJSongS, et al. Finite-time fault estimation and tolerant control for nonlinear interconnected distributed parameter systems with Markovian switching channels. IEEE Trans Circuits Syst I: Reg Pap2022; 69(3): 1347–1359.
7.
SongXWangMAhnCK, et al. Finite-time H∞ asynchronous control for nonlinear Markov jump distributed parameter systems via quantized fuzzy output-feedback approach. IEEE Trans Cybern2020; 50(9): 4098–4109.
8.
SongXWangMSongS, et al. Event-triggered reliable H∞ control for a class of nonlinear distributed parameter systems within a finite-time interval. J Franklin Inst2020; 357(16): 11368–11393.
9.
WangJWWangJM.Spatiotemporal adaptive state feedback control of a linear parabolic partial differential equation. Int J Robust Nonlinear Control2023; 33(6): 3850–3873.
10.
YaoMWeiGDingD, et al. Output-feedback control for stochastic impulsive systems under round-robin protocol. Automatica2022; 143: 110394.
11.
WangYWangZZouL, et al. H∞ PID control for discrete-time fuzzy systems with infinite-distributed delays under round-Robin Communication Protocol. IEEE Trans Fuzzy Syst2022; 30(6): 1875–1888.
12.
WangZPWuHN.Finite dimensional guaranteed cost sampled-data fuzzy control for a class of nonlinear distributed parameter systems. Inf Sci2016; 327: 21–39.
13.
JiHZhangHCuiB.Finite-dimensional guaranteed cost sampled-data fuzzy control of markov jump distributed parameter systems via T–S fuzzy model. IET Control Theory Appl2018; 12(15): 2098–2108.
14.
WangZPWuHN.Sampled-data fuzzy control with guaranteed cost for nonlinear parabolic PDE systems via static output feedback. IEEE Trans Fuzzy Syst2020; 28(10): 2452–2465.
15.
WangZPWuHNLiHX.Estimator-based H∞ sampled-data fuzzy control for nonlinear parabolic PDE systems. IEEE Trans Syst Man Cybern Syst2020; 50(7): 2491–2500.
16.
WangCZhangHYangS, et al. Fuzzy-model-based finite-time control of nonlinear spacecrafts over a distributed sensor network. J Franklin Inst2023; 360(4): 2729–2750.
17.
GuK. An integral inequality in the stability problem of time-delay systems. In: Proceedings of the 39th IEEE conference on decision and control, 2000, vol. 3, pp.2805–2810.
18.
ParkPKoJWJeongC.Reciprocally convex approach to stability of systems with time-varying delays. Automatica2011; 47(1): 235–238.
19.
PetersenIRHollotCV.A riccati equation approach to the stabilization of uncertain linear systems. Automatica1986; 22(4): 397–411.
20.
ChenJXuSLiY, et al. Improvement on stability conditions for continuous-time T–S fuzzy systems. J Franklin Inst2016; 353(10): 2218–2236.
21.
ChenJParkJHXuS.Stability analysis for neural networks with time-varying delay via improved techniques. IEEE Trans Syst Man Cybern Syst2019; 49(12): 4495–4500.
22.
ZhangHLiuJXuS.H-infinity load frequency control of networked power systems via an event-triggered scheme. IEEE Trans Ind Electron2020; 67(8): 7104–7113.
