This study focuses on the funnel tracking control for a class of singular systems (SSs) with unknown disturbances by integrating the uncertainty and disturbance estimator (UDE). First, a dynamic prescribed convergence rate dependent on both the funnel boundaries and tracking error is proposed to guarantee that the output tracking error strictly stays within the predefined performance funnel. Subsequently, an anti-disturbance funnel controller is designed by integrating this convergence rate with the UDE method. Notably, the UDE estimates and compensates for the bias of the error system instead of directly canceling disturbances, thereby ensuring both asymptotic tracking performance and transient performance. Finally, numerical and practical simulations demonstrate the efficacy of the proposed approach.
DuanG.Analysis and design of descriptor linear systems. Springer, 2010.
2.
XuSLamJ.Robust control and filtering of singular systems. Springer, 2006.
3.
DuHLiSQianC.Finite-time attitude tracking control of spacecraft with application to attitude synchronization. IEEE Trans Automat Control2011; 56(11): 2711–2717.
4.
LiZDengJLuR, et al. Trajectory-tracking control of mobile robot systems incorporating neural-dynamic optimized model predictive approach. IEEE Trans Syst Man Cybern Syst2016; 46(6): 740–749.
5.
LiuGP.Tracking control of multi-agent systems using a networked predictive PID tracking scheme. IEEE-CAA J Automat Sin2023; 10(1): 216–225.
6.
CuiLYangHMaJ, et al. Disturbance observer based ground vehicle tracking control under intermittent feedback for quadrotor. IEEE Trans Ind Electron2024; 71(10): 12964–12972.
7.
WangXWangYSunQ, et al. Adaptive robust control of unmanned tracked vehicles for trajectory tracking based on constraint modeling and analysis. Nonlinear Dyn2024; 112(11): 9117–9135.
8.
ZhangDHanQLZhangXM.Network-based modeling and proportional-integral control for direct-drive-wheel systems in wireless network environments. IEEE Trans Cybern2020; 50(6): 2462–2474.
9.
ZengHBZhuZJPengTS, et al. Robust tracking control design for a class of nonlinear networked control systems considering bounded package dropouts and external disturbance. IEEE Trans Fuzzy Syst2024; 32(6): 3608–3617.
10.
AbdullahAA.H∞ model following control of linear parameter-varying descriptor systems. Optim Control Appl Methods2022; 43(3): 943–961.
ShenHPengCYanH, et al. Data-driven near optimization for fast sampling singularly perturbed systems. IEEE Trans Automat Contr2024; 69(7): 4689–4694.
13.
ShenHWangYYanH, et al. Data-driven single-loop policy iteration control of uncertain singularly perturbed systems. IEEE Trans Automat Contr2025; 70(12): 8314–8320.
14.
RsetamKCaoZManZ, et al. Gpio-based continuous sliding mode control for networked control systems under communication delays with experiments on servo motors. IEEE-CAA J Automat Sin2025; 12(1): 99–113.
15.
ZengQZhaoJ.Disturbance observer-based event-triggered control of vehicle suspension with finite-time prescribed performance. IEEE Trans Transp Electrification2024; 10(1): 277–287.
16.
ZhongQCReesD.Control of uncertain LTI systems based on an uncertainty and disturbance estimator. J Dyn Syst Meas Control2004; 126(4): 905–910.
17.
ZhongQKupermanAStobartRK.Design of UDE-based controllers from their two-degree-of-freedom nature. Int J Robust Nonlinear Control2011; 21(17): 1994–2008.
18.
KupermanA.Design of α -filter-based UDE controllers considering finite control bandwid. Nonlinear Dyn2015; 81: 411–416.
19.
RenBZhongQCDaiJ.Asymptotic reference tracking and disturbance rejection of UDE-based robust control. IEEE Trans Ind Electron2017; 64(4): 3166–3176.
20.
XuRWangXSunK, et al. Stabilization of LTI systems with both uncertainties and external disturbances via DE-based control method. J Franklin Inst2024; 361(17): 107293.
21.
YanHDingKZhaoY, et al. Extended dissipative sampling control for singular systems with time-varying delay. Int J Syst Sci2025; 56: 2978–2990.
22.
NajariyanMParizN.Stability and controllability of fuzzy singular dynamical systems. J Franklin Inst2022; 359(15): 8171–8187.
23.
ChangXHWangXYHouLW.New LMI approach to H∞ control of discrete-time singular systems. Appl Math Comput2024; 474: 128703.
24.
LiMChenWShaoY.Mixed H∞-based finite-time passive filtering for a class of uncertain nonlinear singular systems. Optim Control Appl Methods2024; 45(3): 1122–1139.
25.
LiuHZhaoFChenX, et al. Observer-based finite-time H∞ sliding mode control of stochastic nonlinear singular systems and its applications. Nonlinear Dyn2022; 108(4): 3595–3604.
26.
LiuXLiaoX.Fixed-time control for a class of nonlinear PH-DAE systems. IEEE Trans Syst Man Cybernet Syst2023; 53(8): 5161–5173.
27.
LiuXYangR.Predefined-time adaptive robust control of a class of nonlinear singular systems. Proc Inst Mech Eng J Syst Control Eng2025; 239(1): 3–15.
28.
BechlioulisCPRovithakisGA.Robust adaptive control of feedback linearizable MIMO nonlinear systems with prescribed performance. IEEE Trans Automat Contr2008; 53(9): 2090–2099.
29.
BuXWuXZhuF, et al. Novel prescribed performance neural control of a flexible air-breathing hypersonic vehicle with unknown initial errors. ISA Trans2015; 59: 149–159.
30.
WangYHuJLiJ, et al. Improved prescribed performance control for nonaffine pure-feedback systems with input saturation. Int J Robust Nonlinear Control2019; 29(6): 1769–1788.
31.
BikasLNRovithakisGA.Prescribed performance under input saturation for uncertain strict-feedback systems: A switching control approach. Automatica2024; 165: 111663.
32.
IlchmannARyanEPSangwinCJ.Tracking with prescribed transient behaviour. ESAIM Control Optim Calc Var2002; 7(20): 471–493.
33.
HopfeNIlchmannARyanEP.Funnel control with saturation: Linear MIMO systems. IEEE Trans Automat Contr2010; 55(2): 532–538.
34.
BergerT.Input-constrained funnel control of nonlinear systems. IEEE Trans Automat Contr2024; 69(8): 5368–5382.
35.
LongLWangFChenZ.Global event-triggered funnel control of switched nonlinear systems via switching multiple Lyapunov functions. IEEE Trans Cybern2024; 54(11): 6731–6741.
36.
XuGXiaYZhaiD, et al. Adaptive sliding mode disturbance observer–based funnel trajectory tracking control of quadrotor with external disturbances. IET Control Theory Appl2021; 15(13): 1778–1788.
37.
WangSLiSChenQ, et al. Funnel tracking control for nonlinear servo drive systems with unknown disturbances. ISA Trans2022; 128(b): 328–335.
38.
LiSZhangJLiM, et al. Disturbance observer-based neural adaptive command filtered backsstepping funnel-like control for the chaotic pmsm with asymmetric prescribed performance constraints. Int J Robust Nonlinear Control2025; 35(3): 1183–1200.
