This study develops four enhanced adaptive finite-time control strategies for high-order nonlinear maritime systems, addressing critical limitations in conventional backstepping controllers when applied to vehicles operating under uncertain oceanic conditions. The research proposes four advanced control strategies: multilayer adaptive control, neural network-based adaptive control, model predictive control (MPC) combined with backstepping, and event-triggered control employing barrier Lyapunov functions. These methods have been validated through simulations on a third-order nonlinear system and a cart-pendulum system. Comprehensive MATLAB simulations on third-order nonlinear systems demonstrate substantial performance improvements: the neural network controller achieves 88% faster convergence with 93.4% higher tracking accuracy, the MPC-backstepping approach reduces control energy by 32.7%, and the event-triggered method cuts computational load by 93% while maintaining strict state constraints. Quantitative analysis reveals steady-state error reductions from 0.085 to 0.014 (83.5% improvement) and settling time decreases from 1.2 s to 0.144 s (88% improvement) compared to conventional finite-time backstepping controllers. Furthermore, the proposed controllers were experimentally validated on practical applications, including robotic manipulators, quadrotor UAVs, and industrial hydraulic systems, exhibiting outstanding performance in highly nonlinear and noisy environments.
AframA.Janabi-SharifiF. (2014). Theory and applications of HVAC control systems–A review of model predictive control (MPC).Building and Environment, 72, 343–355. https://doi.org/10.1016/j.buildenv.2013.11.016
2.
AhmadiM., et al. (2019). Safe policy synthesis in multi-agent POMDPs via discrete-time barrier functions. In 2019 IEEE 58th Conference on Decision and Control (CDC) (pp. 4797–4803). IEEE.
3.
AliR., et al. (2017). VMR: virtual machine replacement algorithm for QoS and energy-awareness in cloud data centers. In 2017 IEEE International Conference on Computational Science and Engineering (CSE) and IEEE International Conference on Embedded and Ubiquitous Computing (EUC). Vol. 2 (pp. 230–233). IEEE.
4.
AmesA. D.CooganS.EgerstedtM.NotomistaG.SreenathK.TabuadaP. (2019). Control barrier functions: Theory and applications. IEEE Control Systems Magazine, 39(2), 127–157. https://doi.org/10.23919/ECC.2019.8796030
5.
BhatS. P.BernsteinD. S. (2000). Finite-time stability of continuous autonomous systems. SIAM Journal on Control and Optimization, 38(3), 751–766. https://doi.org/10.1137/S0363012997321358
6.
ChenC., et al. (2020). Deep learning on computational-resource-limited platforms: A survey. Mobile Information Systems, 2020(1), 8454327.
7.
ChenW. H.BallanceD. J.O'ReillyJ. (2000). Model predictive control of nonlinear systems: Computational burden and stability. IEE Proceedings-Control Theory and Applications, 147(4), 387–394. https://doi.org/10.1049/ip-cta:20000379
8.
DiG., et al. (2022). An experiment study on the identification of noise sensitive individuals and the influence of noise sensitivity on perceived annoyance. Applied Acoustics, 185, 108394. https://doi.org/10.1016/j.apacoust.2021.108394
9.
GautamA. (2024). Computationally efficient trajectory tracking control of AUVs with nonlinear model predictive control using neural-based dynamics modeling. Journal of Advanced Marine Engineering and Technology, 48(4), 207–218. https://doi.org/10.5916/jamet.2024.48.4.207
10.
GeS. S.WangC. (2004). Adaptive neural control of uncertain MIMO nonlinear systems. IEEE Transactions on Neural Networks, 15(3), 674–692. https://doi.org/10.1109/TNN.2004.826130
11.
HeemelsW. P.JohanssonK. H.TabuadaP. (2012). An introduction to event-triggered and self-triggered control. In 2012 ieee 51st ieee conference on decision and control (cdc) (pp. 3270–3285). IEEE.
12.
HwangS.-k.JungB.-g. (2023). A proposal for robust control performance on cascade control using IMC-based PID control and genetic algorithm. Journal of Advanced Marine Engineering and Technology, 47(1), 23–33. https://doi.org/10.5916/jamet.2023.47.1.23
13.
KöhlerJ.MüllerM. A.AllgöwerF. (2024). Analysis and design of model predictive control frameworks for dynamic operation—an overview.Annual Reviews in Control, 57, 100929. https://doi.org/10.1016/j.arcontrol.2023.100929
LinW. S.ChenC. S. (2002). Robust adaptive sliding mode control using fuzzy modelling for a class of uncertain MIMO nonlinear systems. IEE Proceedings-Control Theory and Applications, 149(3), 193–202. https://doi.org/10.1049/ip-cta:20020236
18.
MayneD. Q.RawlingsJ. B.RaoC. V.ScokaertP. O. (2000). Constrained model predictive control: Stability and optimality. Automatica, 36(6), 789–814. https://doi.org/10.1016/S0005-1098(99)00214-9
19.
MercorelliP. (2018). Fuzzy based control of a nonholonomic car-like robot for drive assistant systems. In 2018 19th international Carpathian control conference (ICCC) (pp. 434–439). IEEE.
20.
MinH., et al. (2019). Adaptive finite-time control for high-order nonlinear systems with multiple uncertainties and its application.IEEE Transactions on Circuits and Systems I: Regular Papers, 67(5), 1752–1761. https://doi.org/10.1109/TCSI.2019.2958327
21.
NakayamaS.KobayashiK.YamashitaY. (2024). Lyapunov-based approach to event-triggered control with self-triggered sampling.Advanced Robotics, 38(9–10), 603–609. https://doi.org/10.1080/01691864.2024.2321181
22.
NascimentoC. A. O.GiudiciR.GuardaniR. (2000). Neural network based approach for optimization of industrial chemical processes. Computers & Chemical Engineering, 24(9–10), 2303–2314. https://doi.org/10.1016/S0098-1354(00)00587-1
23.
PhamD.-A.AhnJ.-K.HanS.-H. (2024). Application of improved sliding mode and artificial neural networks in robot control.Applied Sciences, 14(12), 5304. https://doi.org/10.3390/app14125304
24.
PhamD.-A.HanS.-H. (2022). Design of combined neural network and fuzzy logic controller for marine rescue drone trajectory-tracking.Journal of Marine Science and Engineering, 10(11), 1716. https://doi.org/10.3390/jmse10111716
25.
PhamD.-A.HanS.-H. (2023a). Enhancing underwater robot manipulators with a hybrid sliding mode controller and neural-fuzzy algorithm.Journal of Marine Science and Engineering, 11(12), 2312. https://doi.org/10.3390/jmse11122312
26.
PhamD.-A.HanS.-H. (2023b). Designing a ship autopilot system for operation in a disturbed environment using the adaptive neural fuzzy inference system.Journal of Marine Science and Engineering, 11(7), 1262. https://doi.org/10.3390/jmse11071262
27.
PhamD.-A.HanS.-H.KongK.-J. (2025). Time-specified adaptive robust control framework for managing nonlinear system uncertainties.Applied Sciences, 15(6), 3226. https://doi.org/10.3390/app15063226
28.
SarkarT.RakhlinA. (2019). Near optimal finite time identification of arbitrary linear dynamical systems. In International Conference on Machine Learning (pp. 5610–5618). PMLR.
29.
SchwenzerM., et al. (2021). Review on model predictive control: An engineering perspective.The International Journal of Advanced Manufacturing Technology, 117(5), 1327–1349. https://doi.org/10.1007/s00170-021-07682-3
30.
SeraleG.FiorentiniM.CapozzoliA.BernardiniD.BemporadA. (2018). Model predictive control (MPC) for enhancing building and HVAC system energy efficiency: Problem formulation, applications and opportunities. Energies, 11(3), 631. https://doi.org/10.3390/en11030631
31.
SharafianA., et al. (2025). Resilience to deception attacks in consensus tracking control of incommensurate fractional-order power systems via adaptive RBF neural network. Expert Systems with Applications, 283, 127763. https://doi.org/10.1016/j.eswa.2025.127763
32.
ShengZ.MaQ.XuS. (2023). Prescribed-time output feedback control for high-order nonlinear systems. IEEE Transactions on Circuits and Systems II: Express Briefs, 70(7), 2460–2464. https://doi.org/10.1109/TCSII.2023.3241160
33.
SunZ. Y.LiuC.SuS. F.SunW. (2021). Global finite-time stabilization for uncertain systems with unknown measurement sensitivity. IEEE Transactions on Cybernetics, 52(8), 7602–7611. https//doi.org/10.1109/TCYB.2020.3041923
34.
SunilL., et al. (2024). Event Triggered and Self Triggered Formation Control of Multi Agent Systems. In 2024 2nd International Conference on Recent Trends in Microelectronics, Automation, Computing and Communications Systems (ICMACC) (pp. 281–285). IEEE.
35.
VaidyanathanS.AzarA. T. (2021). An introduction to backstepping control. In Backstepping control of nonlinear dynamical systems (pp. 1–32). Academic Press.
36.
WangY., et al. (2022). Safety performance boundary identification of highly automated vehicles: A surrogate model-based gradient descent searching approach. IEEE Transactions on Intelligent Transportation Systems, 23(12), 23809–23820. https://doi.org/10.1109/TITS.2022.3191088
37.
YaoY., et al. (2024). A novel prescribed-time control approach of state-constrained high-order nonlinear systems.IEEE Transactions on Systems, Man, and Cybernetics: Systems, 54(5), 2941–2951. https://doi.org/10.1109/TSMC.2024.3352905
ZhangK.ZhouB.DuanG.-R. (2024). Global consensus of double-integrator multiagent systems with input saturation by fully distributed event-triggered and self-triggered controls.IEEE Transactions on Automatic Control, 69(9), 6269–6276. https://doi.org/10.1109/TAC.2024.3374256
40.
ZhaoL.JiaY. (2015). Finite-time attitude tracking control for a rigid spacecraft using time-varying terminal sliding mode techniques.International Journal of Control, 88(6), 1150–1162. https://doi.org/10.1080/00207179.2014.996854
41.
ZhaoX., et al. (2015). Intelligent tracking control for a class of uncertain high-order nonlinear systems.IEEE transactions on Neural Networks and Learning Systems, 27(9), 1976–1982. https://doi.org/10.1109/TNNLS.2015.2460236
42.
ZhouJ., et al. (2008). Adaptive backstepping control. Springer Berlin Heidelberg.
