This paper develops a disturbance observer-based adaptive sliding mode control strategy for a class of nonlinear time-delay systems subject to exogenous disturbances and delayed nonlinear uncertainties. A fixed-time nonlinear disturbance observer is designed using dual-power feedback terms to achieve precise estimation of external disturbances. Barrier functions are employed to design an adaptive controller that dynamically adjusts gains for time-delay uncertainty compensation, removing the initial condition dependence of common approaches. The Lyapunov-Razumikhin method is employed to handle large time-varying delays, and the fixed-time convergence of the sliding surface is established through Lyapunov stability theory. The effectiveness of the proposed method is validated through its application to a continuous stirred-tank reactor system and a numerical simulation.
NguyenKD.An adaptive controller for uncertain nonlinear systems with multiple time delays. Automatica2020; 117: 108976.
2.
CuiLPangBJiangZP.Learning-based adaptive optimal control of linear time-delay systems: a policy iteration approach. IEEE Trans Automat Contr2024; 69(1): 629–636.
3.
MaDXingYLiuY, et al. Backstepping control with tunable transformation parameters for a coupled pde rijke tube with boundary input delay. IEEE Trans Autom Sci Eng2025; 22: 12583–12595.
4.
Santos-SanchezOJVelasco-RebolloRERodriguez-GuerreroL, et al. Lyapunov redesign for input and state delays systems by using optimal predictive control and ultimate bound approaches: theory and experiments. IEEE Trans Ind Electron2021; 68(12): 12575–12583.
5.
PengYXuSParkJH.Adaptive fuzzy control for stochastic nonlinear systems with delayed input and delayed state via improved Lyapunov–Krasovskii function. IEEE Trans Fuzzy Syst2025; 33(2): 570–579.
6.
ParkJKwonWParkP.An improved adaptive sliding mode control based on time-delay control for robot manipulators. IEEE Trans Ind Electron2023; 70(10): 10363–10373.
7.
ZhaoYLiXSongS.Observer-based sliding mode control for stabilization of mismatched disturbance systems with or without time delays. IEEE Trans Syst Man Cybern Syst2021; 51(12): 7337–7345.
8.
XuKWangHLiuPX.Adaptive fixed-time control for high-order stochastic nonlinear time-delay systems: an improved Lyapunov-Krasovskii function. IEEE Trans Cybern2024; 54(2): 776–786.
9.
ZhaoSMengQLaiX, et al. An adaptive nonsingular fast terminal sliding mode control method with time-delay estimation for pneumatic soft actuator without specific model. IEEE Trans Ind Inform2025; 21(5): 4061–4071.
10.
JozeslamiMSepestanakiMANafisifarM, et al. Finite-time stabilization of floating offshore wind turbines under wind and wave disturbances by adaptive barrier-function fractional-order sliding mode control. IEEE Trans Sustain Energy2025; 16(4): 2714–2730.
11.
ShaoKZhengJTangR, et al. Barrier function based adaptive sliding mode control for uncertain systems with input saturation. IEEE/ASME Trans Mechatron2022; 27(6): 4258–4268.
12.
JiaCLiuXDuL.Adaptive second-order fixed-time nonsingular terminal sliding mode control based on barrier function for nonlinear systems. IEEE Trans Ind Inform2024; 20(3): 4806–4815.
13.
Cruz-AnconaCDEstradaMAFridmanL. Barrier function-based adaptive Lyapunov redesign for systems without a priori bounded perturbations. IEEE Trans Automat Contr2022; 67(8): 3851–3862.
14.
HuangKXiaWShaoK, et al. Adaptive sliding mode control for vehicle active anti-roll system based on property adjustable barrier function. IEEE Trans Intell Vehicles2025; 10(5): 3124–3133.
15.
YangJLiSYuX.Sliding-mode control for systems with mismatched uncertainties via a disturbance observer. IEEE Trans Ind Electron2013; 60(1): 160–169.
16.
LiangZGaoQShenM, et al. Adaptive integral terminal sliding mode control to improve maneuverability of electric vehicle considering rollover and inputs saturation. IEEE Trans Transp Electrification2025; 11(2): 6012–6024.
17.
LiuYLiHLuR, et al. An overview of finite/fixed-time control and its application in engineering systems. IEEE/CAA J Autom Sin2022; 9(12): 2106–2120.
18.
DengYMoulayELéchappéV, et al. Robust nonsingular predefined-time terminal sliding mode control for perturbed chains of integrators. IEEE Trans Automat Contr2024; 69(12): 8946–8953.
19.
SunJYiJPuZ, et al. Fixed-time sliding mode disturbance observer-based nonsmooth backstepping control for hypersonic vehicles. IEEE Trans Syst Man Cybern Syst2020; 50(11): 4377–4386.
20.
XuKWangHLiuPX.Singularity-free adaptive fixed-time tracking control for mimo nonlinear systems with dynamic uncertainties. IEEE Trans Circuits Syst II Express Briefs2024; 71(3): 1356–1360.
21.
YangYCuiYZhuY, et al. Fixed-time refined disturbance observer-based composite control for periscope-type coarse pointing assembly. IEEE Trans Ind Electron2024; 71(11): 14896–14905.
22.
Van TrieuPVan BinhC.Fixed-time disturbance observer-based fractional-order dynamic surface control of autonomous surface vessel. Proc Inst Mech Eng Part I: J Syst Control Eng2026; 240(2): 289–302.
23.
MaDXiaYShenG, et al. Practical fixed-time disturbance rejection control for quadrotor attitude tracking. IEEE Trans Ind Electron2021; 68(8): 7274–7283.
24.
GaoZLiXWeiZ, et al. Fixed-time secure control for vehicular platoons under deception attacks on both sensor and actuator via adaptive fixed-time disturbance observer. IEEE Internet Things J2025; 12(11): 15828–15839.
25.
LiuXZhangJGuS, et al. Fixed-time dynamic surface disturbance rejection control for pneumatic soft bending actuators. IEEE Trans Circuits Syst I Regul Pap2025; 72(7): 3521–3530.
26.
LiuXZhangXXuF, et al. Fixed-time angle tracking control for multi-dof manipulator driven by pneumatic artificial muscles. IEEE Trans Ind Electron2025; 72(4): 4137–4146.
27.
LongHGuoTZhaoJ.Adaptive disturbance observer-based novel fixed-time nonsingular terminal sliding-mode control for a class of dof nonlinear systems. IEEE Trans Ind Inform2022; 18(9): 5905–5914.
28.
ShaoSWangZXuS, et al. Fixed-time tracking control for quadrotor uav via a novel disturbance observer. Proc Inst Mech Eng Part G: J Aerosp Eng2025; 239(15): 2187–2206.
29.
XuSHeB.Adaptive disturbance observer-based fixed-time prescribed performance sliding-mode control of uncertain robot manipulators. Trans Inst Meas Contr2026; 48(2): 337–348.
30.
LiuKWangRZhengS, et al. Fixed-time disturbance observer-based robust fault-tolerant tracking control for uncertain quadrotor uav subject to input delay. Nonlinear Dyn2022; 107: 2363–2390.
31.
LiuZLiuJZhangO, et al. Adaptive disturbance observer-based fixed-time tracking control for uncertain robotic systems. IEEE Trans Ind Electron2024; 71(11): 14823–14831.
32.
XuRTianDWangZ.Adaptive disturbance observer-based local fixed-time sliding mode control with an improved approach law for motion tracking of piezo-driven microscanning system. IEEE Trans Ind Electron2024; 71(10): 12824–12834.
33.
WuH.Adaptive robust control of uncertain nonlinear systems with nonlinear delayed state perturbations. Automatica2009; 45(8): 1979–1984.
34.
OnyekaAEYanXGMuJ. Sliding mode control of time-delay systems with delayed nonlinear uncertainties. IFAC-PapersOnLine2017; 50(1): 2696–2701.
35.
ZhangXSuHLuR.Second-order integral sliding mode control for uncertain systems with control input time delay based on singular perturbation approach. IEEE Trans Automat Contr2015; 60(11): 3095–3100.
36.
FengJWangWZengHB.Integral sliding mode control for a class of nonlinear multi-agent systems with multiple time-varying delays. IEEE Access2024; 12: 10512–10520.
37.
ShaoKZhengJFuM.Review on the developments of sliding function and adaptive gain in sliding mode control. J Autom Intell2025; 4(4): 266–272.
38.
SunJYangJZengZ.Safety-critical control with control barrier function based on disturbance observer. IEEE Trans Automat Contr2024; 69(7): 4750–4756.
39.
ChenWH.Disturbance observer based control for nonlinear systems. IEEE/ASME Trans Mechatron2004; 9(4): 706–710.
