Disturbance rejection for disturbed Port-controlled Hamiltonian systems based on sliding-mode control approach

Authors

Baozeng Fu, Xiaojie Liu, Qingzhi Wang

Abstract

For a class of Port-controlled Hamiltonian systems with nonvanishing disturbances, this paper investigates its disturbance rejection and stabilization problems via two kinds of sliding-mode control (SMC) approaches. Firstly, a new framework is developed to construct the integral sliding surface, which is dependent on the structure of the Hamiltonian system, and then a SMC law is developed to asymptotically stabilize the Hamiltonian system with better disturbance rejection capability. Secondly, in order to further reduce the chattering phenomenon and maintain the system nominal performance, a novel sliding surface is proposed based on the nonlinear disturbance observer (NDOB) and then a disturbance estimation-based SMC law is designed, which can effectively counteract disturbances and make the closed-loop Hamiltonian system asymptotically stable. Finally, a simulation example clarifies the effectiveness of the two SMC approaches, and the superiority of the NDOB-based SMC approach is also illustrated by comparisons.

Keywords

asymptotic stability, disturbance rejection, integral sliding surface, nonlinear disturbance observer, port-controlled hamiltonian systems, sliding-mode control

Citation

• Journal: Journal of the Franklin Institute
• Year: 2026
• Volume: 363
• Issue: 5
• Pages: 108510
• Publisher: Elsevier BV
• DOI: 10.1016/j.jfranklin.2026.108510

BibTeX

@article{Fu_2026,
  title={{Disturbance rejection for disturbed Port-controlled Hamiltonian systems based on sliding-mode control approach}},
  volume={363},
  ISSN={0016-0032},
  DOI={10.1016/j.jfranklin.2026.108510},
  number={5},
  journal={Journal of the Franklin Institute},
  publisher={Elsevier BV},
  author={Fu, Baozeng and Liu, Xiaojie and Wang, Qingzhi},
  year={2026},
  pages={108510}
}

Download the bib file

References

• Maschke, Port-controlled Hamiltonian systems: modeling origins and systemtheoretic properties. (1992)
• Schaft, The Hamiltonian formulation of energy conserving physical systems with external ports. Arch. f¨1r Elektronik und ¨1bertragungstechnik (1995)
• Yang R, Sun L, Zhang G, Zhang Q (2019) Finite-time stability and stabilization of nonlinear singular time-delay systems via Hamiltonian method. Journal of the Franklin Institute 356(12):5961–5992. https://doi.org/10.1016/j.jfranklin.2019.04.03 – 10.1016/j.jfranklin.2019.04.033
• Lv X, Niu Y, Song J (2021) Finite-time boundedness of uncertain Hamiltonian systems via sliding mode control approach. Nonlinear Dyn 104(1):497–507. https://doi.org/10.1007/s11071-021-06292- – 10.1007/s11071-021-06292-8
• (2005) Transient stabilization of multimachine power systems with nontrivial transfer conductances. IEEE Trans Automat Contr 50(1):60–75. https://doi.org/10.1109/tac.2004.84047 – 10.1109/tac.2004.840477
• Wang Z-M, Zhao X, Li X, Wei A (2023) Finite-time adaptive control for uncertain switched port-controlled Hamiltonian systems. Communications in Nonlinear Science and Numerical Simulation 119:107129. https://doi.org/10.1016/j.cnsns.2023.10712 – 10.1016/j.cnsns.2023.107129
• Chen Y, Liu Q (2024) Fixed-time stabilization and \(H_{\infty}\) control of time-delay port-controlled Hamiltonian systems. European Journal of Control 77:100996. https://doi.org/10.1016/j.ejcon.2024.10099 – 10.1016/j.ejcon.2024.100996
• Sun W, Lv X, Qiu M (2022) Distributed Estimation for Stochastic Hamiltonian Systems With Fading Wireless Channels. IEEE Trans Cybern 52(6):4897–4906. https://doi.org/10.1109/tcyb.2020.302354 – 10.1109/tcyb.2020.3023547
• Izydorek M, Janczewska J, Soares P (2022) A convergence result for mountain pass periodic solutions of perturbed Hamiltonian systems. Commun Contemp Math 25(06). https://doi.org/10.1142/s021919972250011 – 10.1142/s0219199722500110
• Wang, Adaptive neural networks control for MIMO nonlinear systems with unmeasured states and unmodeled dynamics. Appl. Math. Comput. (2021)
• Tong, Finite-time synchronization and energy consumption prediction for multilayer fractional-order networks. IEEE Trans. Circuits Syst. II, Exp. Briefs (2023)
• Fu B, Li S, Wang X, Guo L (2019) Output feedback based simultaneous stabilization of two Port-controlled Hamiltonian systems with disturbances. Journal of the Franklin Institute 356(15):8154–8166. https://doi.org/10.1016/j.jfranklin.2019.02.03 – 10.1016/j.jfranklin.2019.02.039
• Chen G, Du G, Xia J, Xie X, Park JH (2023) Controller Synthesis of Aperiodic Sampled-Data Networked Control System With Application to Interleaved Flyback Module Integrated Converter. IEEE Trans Circuits Syst I 70(11):4570–4580. https://doi.org/10.1109/tcsi.2023.329594 – 10.1109/tcsi.2023.3295940
• Li, Interval stability/stabilization and H∞ feedback control for linear impulsive stochastic systems. Appl. Math. Comput. (2023)
• Chen G, Xia J, Park JH, Shen H, Zhuang G (2022) Robust Sampled-Data Control for Switched Complex Dynamical Networks With Actuators Saturation. IEEE Trans Cybern 52(10):10909–10923. https://doi.org/10.1109/tcyb.2021.306981 – 10.1109/tcyb.2021.3069813
• Ma Z, Tong D, Chen Q, Zhou W (2025) Fixed/Prescribed-Time Synchronization and Energy Consumption for Kuramoto-Oscillator Networks. IEEE Trans Cybern 55(7):3379–3389. https://doi.org/10.1109/tcyb.2025.355610 – 10.1109/tcyb.2025.3556103
• Wang Z-M, Wei A, Zong G, Zhao X, Li H (2020) Finite-time stabilization and \(\boldsymbol{\mathcal{H}}_{\infty}\) control for a class of switched nonlinear port-controlled Hamiltonian systems subject to actuator saturation. Journal of the Franklin Institute 357(16):11807–11829. https://doi.org/10.1016/j.jfranklin.2019.11.05 – 10.1016/j.jfranklin.2019.11.055
• Zhang M, Borja P, Ortega R, Liu Z, Su H (2018) PID Passivity-Based Control of Port-Hamiltonian Systems. IEEE Trans Automat Contr 63(4):1032–1044. https://doi.org/10.1109/tac.2017.273228 – 10.1109/tac.2017.2732283
• Lin, Resilient H∞ dynamic output feedback controller design for USJSs with time-varying delays. Appl. Math. Comput. (2021)
• Shi, PPLXth moment exponential synchronization for delayed multi-agent systems with L vy noise and Markov switching. IEEE Trans. Circuits Syst. II, Exp. Briefs (2024)
• Qi W, Zong G, Karim HR (2018) Observer-Based Adaptive SMC for Nonlinear Uncertain Singular Semi-Markov Jump Systems With Applications to DC Motor. IEEE Trans Circuits Syst I 65(9):2951–2960. https://doi.org/10.1109/tcsi.2018.279725 – 10.1109/tcsi.2018.2797257
• Wang H, Pan Y, Li S, Yu H (2019) Robust Sliding Mode Control for Robots Driven by Compliant Actuators. IEEE Trans Contr Syst Technol 27(3):1259–1266. https://doi.org/10.1109/tcst.2018.279958 – 10.1109/tcst.2018.2799587
• Edwards C, Spurgeon S (1998) Sliding Mode Contro – 10.1201/9781498701822
• Utkin V (1977) Variable structure systems with sliding modes. IEEE Trans Automat Contr 22(2):212–222. https://doi.org/10.1109/tac.1977.110144 – 10.1109/tac.1977.1101446
• Fujimoto K, Sakata N, Maruta I, Ferguson J (2021) A Passivity Based Sliding Mode Controller for Simple Port-Hamiltonian Systems. IEEE Control Syst Lett 5(3):839–844. https://doi.org/10.1109/lcsys.2020.300532 – 10.1109/lcsys.2020.3005327
• Cao Z, Niu Y, Song J (2020) Finite-Time Sliding-Mode Control of Markovian Jump Cyber-Physical Systems Against Randomly Occurring Injection Attacks. IEEE Trans Automat Contr 65(3):1264–1271. https://doi.org/10.1109/tac.2019.292615 – 10.1109/tac.2019.2926156
• Fu B, Che W, Wang Q, Liu Y, Yu H (2024) Improved sliding-mode control for a class of disturbed systems based on a disturbance observer. Journal of the Franklin Institute 361(6):106699. https://doi.org/10.1016/j.jfranklin.2024.10669 – 10.1016/j.jfranklin.2024.106699
• Liu M, Xu N, Niu B, Alotaibi ND (2025) Sliding-mode surface-based fixed-time adaptive critic tracking control for zero-sum game of switched nonlinear systems. Mathematics and Computers in Simulation 229:78–95. https://doi.org/10.1016/j.matcom.2024.09.02 – 10.1016/j.matcom.2024.09.025
• Du H, Chen X, Wen G, Yu X, Lu J (2018) Discrete-Time Fast Terminal Sliding Mode Control for Permanent Magnet Linear Motor. IEEE Trans Ind Electron 65(12):9916–9927. https://doi.org/10.1109/tie.2018.281594 – 10.1109/tie.2018.2815942
• Yao D, Li H, Lu R, Shi Y (2022) Event-based distributed sliding mode formation control of multi-agent systems and its applications to robot manipulators. Information Sciences 614:87–103. https://doi.org/10.1016/j.ins.2022.09.05 – 10.1016/j.ins.2022.09.059
• Ding S, Mei K, Li S (2019) A New Second-Order Sliding Mode and Its Application to Nonlinear Constrained Systems. IEEE Trans Automat Contr 64(6):2545–2552. https://doi.org/10.1109/tac.2018.286716 – 10.1109/tac.2018.2867163
• Song, Dynamic event-triggered sliding mode control: dealing with slow sampling singularly perturbed systems. IEEE Trans. Circuits Syst. II, Exp. Briefs (2020)
• Zhai, Fast-exponential sliding mode control of robotic manipulator with super-twisting method. IEEE Trans. Circuits Syst. II, Exp. Briefs (2022)
• Fu B, Che W, Liu Y, Wang Q, Yu H (2023) Novel sliding‐mode control for a class of second‐order systems with mismatched disturbances. Intl J Robust & Nonlinear 34(2):1277–1291. https://doi.org/10.1002/rnc.702 – 10.1002/rnc.7028
• Liu Z, Su H, Pan S (2012) A New Adaptive Sliding Mode Control of Uncertain Nonlinear Systems. Asian Journal of Control 16(1):198–208. https://doi.org/10.1002/asjc.65 – 10.1002/asjc.657
• Ferrara, Advanced and optimization based sliding mode control: theory and applications. (2019)
• Guo Z, Wang Z, Li S (2022) Global finite-time set stabilization of spacecraft attitude with disturbances using second-order sliding mode control. Nonlinear Dyn 108(2):1305–1318. https://doi.org/10.1007/s11071-022-07245- – 10.1007/s11071-022-07245-5
• Yang J, Li S, Yu X (2013) Sliding-Mode Control for Systems With Mismatched Uncertainties via a Disturbance Observer. IEEE Trans Ind Electron 60(1):160–169. https://doi.org/10.1109/tie.2012.218384 – 10.1109/tie.2012.2183841
• Chen W-H (2004) Disturbance Observer Based Control for Nonlinear Systems. IEEE/ASME Trans Mechatron 9(4):706–710. https://doi.org/10.1109/tmech.2004.83903 – 10.1109/tmech.2004.839034
• Wen-Hua Chen, Ballance DJ, Gawthrop PJ, O’Reilly J (2000) A nonlinear disturbance observer for robotic manipulators. IEEE Trans Ind Electron 47(4):932–938. https://doi.org/10.1109/41.85797 – 10.1109/41.857974
• Chen W-H (2003) Nonlinear Disturbance Observer-Enhanced Dynamic Inversion Control of Missiles. Journal of Guidance, Control, and Dynamics 26(1):161–166. https://doi.org/10.2514/2.502 – 10.2514/2.5027
• Li, (2014)
• Chen W-H, Yang J, Guo L, Li S (2016) Disturbance-Observer-Based Control and Related Methods—An Overview. IEEE Trans Ind Electron 63(2):1083–1095. https://doi.org/10.1109/tie.2015.247839 – 10.1109/tie.2015.2478397
• Yang J, Chen W-H, Li S, Guo L, Yan Y (2017) Disturbance/Uncertainty Estimation and Attenuation Techniques in PMSM Drives—A Survey. IEEE Trans Ind Electron 64(4):3273–3285. https://doi.org/10.1109/tie.2016.258341 – 10.1109/tie.2016.2583412
• Hou Q, Ding S (2022) Finite-Time Extended State Observer-Based Super-Twisting Sliding Mode Controller for PMSM Drives With Inertia Identification. IEEE Trans Transp Electrific 8(2):1918–1929. https://doi.org/10.1109/tte.2021.312364 – 10.1109/tte.2021.3123646
• Bhat SP, Bernstein DS (1998) Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Trans Automat Contr 43(5):678–682. https://doi.org/10.1109/9.66883 – 10.1109/9.668834
• Khalil, (2002)
• Labbadi M, Efimov D (2025) Delayed High Order Sliding Mode Control Using Implicit Lyapunov Function Approach. Intl J Robust & Nonlinear 35(17):7282–7294. https://doi.org/10.1002/rnc.7005 – 10.1002/rnc.70053