An innovative adaptive tracking control strategy is proposed in this paper for a class of nonlinear systems, which considers input-delay, full state constraints, and unmodeled dynamics simultaneously. To address the system’s unknown nonlinear dynamics, the approximation ability of multi-dimensional Taylor network (MTN) is employed in the controller design process. The effect of input-delay is reduced through the application of Pade approximation. Additionally, the impact of state constraints is mitigated through the introduction of barrier Lyapunov functions (BLFs). To deal with unmodeled dynamics, a dynamic signal is formulated. By integrating the backstepping control strategy with Lyapunov stability theory, it is ensured that all signals in the closed-loop system remain bounded, the tracking error approaches a small region close to the origin, and the full state constraints are not violated. Finally, simulation results are provided to validate the proposed strategy’s effectiveness.
AlattasKAVuMTMofidO, et al. (2022) Barrier function-based nonsingular finite-time tracker for quadrotor UAVs subject to uncertainties and input constraints. Mathematics10(10): 1659.
2.
AlyAAVuMTEl-SousyFFM, et al. (2022) Adaptive neural network-based fixed-time tracking controller for disabilities exoskeleton wheelchair robotic system. Mathematics10(20): 3853.
3.
DengHKrstićM (1997) Stochastic nonlinear stabilization — I: A backstepping design. Systems and Control Letters32(3): 143–150.
4.
FengZGLiRBZhangW, et al. (2024) Neuroadaptive output-feedback tracking control for stochastic nonlower triangular nonlinear systems with dead-zone input. IEEE Transactions on Cybernetics54(12): 7839–7850.
5.
GaoZFLiuDHQianMS (2025) Decentralized adaptive tracking control for interconnected nonlinear systems with unmodeled dynamics and input delays. International Journal of Control98(4): 887–901.
6.
HanYQHeWJLiN, et al. (2021) Adaptive tracking control of a class of nonlinear systems with input delay and dynamic uncertainties using multi-dimensional taylor network. International Journal of Control, Automation and Systems19: 4078–4089.
7.
HaoWJSunJJZongZY, et al. (2025a) Adaptive predefined time tracking control for nonlinear multi-agent systems subject to input saturation: An improved command filtering approach. Nonlinear Dynamics113: 19697–19716.
8.
HaoWJZongZYWeiSZ, et al. (2025b) Adaptive tracking control of nonlinear multi-agent systems subject to multiple constraints via multi-dimensional taylor network. IEEE Transactions on Automation Science and Engineering22: 16913–16924.
9.
HeWJZhuSLLuLT, et al. (2024) Adaptive multi-switching-based global tracking control for switched nonlinear systems with prescribed performance. IEEE Transactions on Automation Science and Engineering21(3): 3243–3252.
10.
JainAKKatiyarA (2023) Robust adaptive control design of nonlinear systems with input delay. International Journal of Adaptive Control and Signal Processing37(5): 1193–1202.
11.
JiangZPPralyL (1998) Design of robust adaptive controllers for nonlinear systems with dynamic uncertainties. Automatica34(7): 825–840.
12.
KhanesarMAKaynakOYinS, et al. (2015) Adaptive indirect fuzzy sliding mode controller for networked control systems subject to time-varying network-induced time delay. IEEE Transactions on Fuzzy Systems23(1): 205–214.
13.
KharratM (2024) Adaptive fault-tolerant control for a class of nonstrict-feedback nonlinear systems with unmodeled dynamics and dead-zone output using multi-dimensional Taylor networks. Nonlinear Dynamics112: 13289–13306.
14.
KongLHHeWLiuZJ, et al. (2023) Adaptive tracking control with global performance for output-constrained MIMO nonlinear systems. IEEE Transactions on Automatic Control68(6): 3760–3767.
15.
KongLHZhangSWuYF, et al. (2025) Adaptive tracking control of constrained nonlinear systems and its application to circuit systems. IEEE Transactions on Circuits and Systems I: Regular Papers72(4): 1731–1740.
16.
KrstićMKanellakopoulosIKokotovićP (1992) Adaptive nonlinear control without overparametrization. Systems and Control Letters19(3): 177–185.
17.
LiDPLiuYJTongSC, et al. (2019) Neural networks-based adaptive control for nonlinear state constrained systems with input delay. IEEE Transactions on Cybernetics49(4): 1249–1258.
18.
LiHYangFSLiuZC (2024a) Command filter-based adaptive predefined-time control for non-strict feedback nonlinear systems with unmodeled dynamics. Journal of the Franklin Institute361(12): 106936.
19.
LiHYWangFL (2025) Adaptive RL control based on projection operator for stochastic nonlinear systems with full state constraints and unmodeled dynamics. Asian Journal of Control. Epub ahead of print 11 July. DOI: 10.1002/asjc.3778.
20.
LiHYWangLJDuHP, et al. (2017) Adaptive fuzzy backstepping tracking control for strict-feedback systems with input delay. IEEE Transactions on Fuzzy Systems25(3): 642–652.
21.
LiNHanYQHeWJ, et al. (2022) Control design for stochastic nonlinear systems with full-state constraints and input delay: A new adaptive approximation method. International Journal of Control, Automation and Systems20(8): 2768–2778.
22.
LiTShiPLiuJP, et al. (2024b) Improved command-filtering-based fixed-time fuzzy adaptive control for uncertain nonlinear systems with full state constraints. IEEE Transactions on Fuzzy Systems32(5): 3286–3292.
23.
LiYHQiangSZhuangXY, et al. (2004) Robust and adaptive backstepping control for nonlinear systems using RBF neural networks. IEEE Transactions on Neural Networks15(3): 693–701.
24.
LiuMRWuLBWuM, et al. (2025) Event-triggered adaptive fault estimation and fault-tolerant control for strict-feedback nonlinear systems with full state constraints. Nonlinear Dynamics113: 2505–2520.
25.
LuLTZhuSLWangDM, et al. (2024) Distributed adaptive fault-tolerant control with prescribed performance for nonlinear multiagent systems. Communications in Nonlinear Science and Numerical Simulation138: 108222.
26.
LvJXJuXZWangCH (2025) Neural network prescribed-time observer-based output-feedback control for uncertain pure-feedback nonlinear systems. Expert Systems with Applications264(10): 125813.
27.
LüSYShenH (2024) Adaptive fuzzy asymptotic tracking control of uncertain nonlinear systems with full state constraints. IEEE Transactions on Fuzzy Systems32(5): 2750–2761.
28.
MaoJLiQWangRH, et al. (2025) Adaptive neural fixed-time sampled-data output-feedback stabilization for a class of nonlinear systems. Applied Mathematics and Computation507: 129550.
29.
MaoJXiangZRHuangSP, et al. (2022) Practical finite-time sampled-data output feedback stabilization for a class of upper-triangular nonlinear systems with input delay. IEEE Transactions on Systems Man and Cybernetics Systems32(12): 6939–6961.
30.
MaoJZouWCGuoJ, et al. (2024) Observer-based finite-time sampled-data control for a class of nonlinear time-delay systems. IEEE Transactions on Systems Man and Cybernetics Systems54(3): 1645–1657.
31.
MokhtareZVuMTMobayenS, et al. (2022) An adaptive barrier function terminal sliding mode controller for partial seizure disease based on the pinsky–rinzel mathematical model. Mathematics10(16): 2940.
32.
NiYWangZHuangX, et al. (2024) Intermittent sampled-data control for local stabilization of neural networks subject to actuator saturation: A work-interval-dependent functional approach. IEEE Transactions on Neural Networks and Learning Systems35(1): 1087–1097.
33.
PengXJHeYLiHY, et al. (2025) Robust time-varying formation control of one-sided Lipschitz nonlinear multiagent system with delays via optimization algorithm. IEEE Transactions on Cybernetics55(4): 1801–1813.
34.
QiuJBJiWQLamHK (2023) A new design of fuzzy affine model-based output feedback control for discrete-time nonlinear systems. IEEE Transactions on Fuzzy Systems31(5): 1434–1444.
35.
SongJHChenYLiuYZ, et al. (2023) Fixed-time fuzzy adaptive fault-tolerant control for strict-feedback nonlinear systems with input delay. IEEE Transactions on Systems, Man, and Cybernetics: Systems53(11): 6999–7010.
36.
TeeKPGeSSTayEH (2009) Barrier Lyapunov functions for the control of output-constrained nonlinear systems. Automatica45(4): 918–927.
37.
TsaiSHLeeWHTanakaK, et al. (2024) Polynomial fuzzy observer-based feedback control for nonlinear hyperbolic PDEs systems. IEEE Transactions on Cybernetics54(9): 5257–5269.
38.
WangCXGaoYZhangZC, et al. (2024a) Output feedback control of stochastic nonlinear systems with external disturbances and inverse dynamics. International Journal of Adaptive Control and Signal Processing38(11): 3615–3635.
39.
WangFLChenKZhenSC, et al. (2024b) Prescribed performance adaptive robust control for robotic manipulators with fuzzy uncertainty. IEEE Transactions on Fuzzy Systems32(3): 1318–1330.
40.
WangGBYanHSZhengXY (2023) Contraction-based stochastic model predictive control for nonlinear systems with input delay using multidimensional taylor network. IEEE Transactions on Automatic Control68(12): 7498–7513.
41.
WangHQShiPLiHY, et al. (2017) Adaptive neural tracking control for a class of nonlinear systems with dynamic uncertainties. IEEE Transactions on Cybernetics47(10): 3075–3087.
42.
WangJHWuYSChenC, et al. (2024c) Adaptive PI event-triggered control for MIMO nonlinear systems with input delay. Information Sciences677: 120817.
43.
WangMYanHCQiuJB, et al. (2024d) Fuzzy-model-based finite frequency fault detection filtering design for two-dimensional nonlinear systems. IEEE/CAA Journal of Automatica Sinica11(10): 2099–2110.
44.
WangNFuZMTaoFZ, et al. (2021) A simplified adaptive tracking control for nonlinear pure-feedback systems with input delay and full-state constraints. International Journal of Adaptive Control and Signal Processing35(12): 2521–2536.
45.
WangNTaoFZFanPY, et al. (2025a) A simplified adaptive fixed time control of pure-feedback stochastic nonlinear systems subject to full state constraints. International Journal of Adaptive Control and Signal Processing39(4): 829–840.
46.
WangSBSunCBChenQ, et al. (2025b) Composite learning fixed-time control for nonlinear servo systems with state constraints and unknown dynamics. IEEE Transactions on Systems, Man, and Cybernetics: Systems55(3): 2332–2342.
47.
WangWWuJLiJ (2024e) Adaptive neural optimised control for stochastic nonlinear systems with time-varying input delay via self-triggered mechanism. International Journal of Systems Science55(2): 176–190.
48.
WangXJNiuBShangZH, et al. (2024f) Distributed resilient adaptive consensus tracking control of nonlinear multi-agent systems dealing with deception attacks via K-filters approach. Automatica169: 111871.
49.
WangZYanLFanY, et al. (2025c) Switching event-triggered-based gain-scheduled control for bipartite synchronization of coupled coopetitive memristive neural networks. IEEE Transactions on Systems, Man, and Cybernetics: Systems55(10): 6951–6963.
50.
XiaXNDuCZhangTP, et al. (2025) Adaptive tracking control of high-order nonlinear systems with unknown time-varying input delay and unmodeled dynamics. Nonlinear Dynamics113: 3543–3561.
51.
XiaXNZhangTPKangGP, et al. (2022) Adaptive control of uncertain nonlinear systems with discontinuous input and time-varying input delay. IEEE Transactions on Systems, Man, and Cybernetics: Systems52(11): 7248–7258.
52.
XiongJChenY (2025) RBFNN-based parameter adaptive sliding mode control for an uncertain TQUAV with time-varying mass. International Journal of Robust and Nonlinear Control35(11): 4658–4668.
53.
XuSHeXQYuQK (2025) Event-triggered adaptive asymptotic tracking control for uncertain nonlinear system with time-varying parameters and full state constraints. Nonlinear Dynamics113: 13297–13311.
54.
YanHSWangGB (2023) Adaptive tracking control for stochastic nonlinear systems with time-varying delays using multi-dimensional Taylor network. ISA Transactions132: 246–257.
55.
YangDSunYRZongGD, et al. (2025) Dynamic event-triggered adaptive tracking control for switched nonlinear system with vanishing control gains. IEEE Transactions on Automation Science and Engineering22: 11693–11705.
56.
YeDCaiYJYangHJ, et al. (2019) Adaptive neural-based control for non-strict feedback systems with full-state constraints and unmodeled dynamics. Nonlinear Dynamics97: 715–732.
57.
YinYTNiuBJiangK, et al. (2022) Event-triggered adaptive decentralised control for switched interconnected nonlinear systems with unmodeled dynamics and full state constraints. International Journal of Systems Science58(3): 1639–1658.
58.
YuXWangGJiaL, et al. (2024) Event-triggered practical fixed-time containment control for stochastic multiagent systems with input delay. IEEE Transactions on Fuzzy Systems32(5): 2762–2774.
59.
ZhaiJCWangHQTaoJQ, et al. (2023) Observer-based adaptive fuzzy finite time control for non-strict feedback nonlinear systems with unmodeled dynamics and input delay. Nonlinear Dynamics111: 1417–1440.
60.
ZhangCHWangLZhangY, et al. (2025) Adaptive event-triggered control combined with high-order backstepping for pure feedback nonlinear systems. IEEE Transactions on Cybernetics55(4): 1884–1892.
