Adaptive IDA‐PBC for Underactuated Mechanical Systems With Unknown Time‐Varying Disturbances

Authors

Jose Guadalupe Romero, Emmanuel Nuño

Abstract

                                  Interconnection and Damping Assignment Passivity‐Based Control (IDA‐PBC) has been one of the most employed algorithms to stabilize underactuated port‐Hamiltonian systems. However, IDA‐PBC cannot handle input disturbances. Disturbances can cause a drift in the desired equilibrium and can generate unstable behaviors. In this paper, we propose to include an adaptive term to estimate the disturbance in the IDA‐PBC for underactuated mechanical systems. Under the assumption that the disturbance is composed of a finite sum of sinusoidal functions with                    unknown                    frequencies and amplitudes, we design an estimation algorithm that is based on the internal model for which we estimate, exponentially, the frequencies and the magnitudes of the disturbances. As it is typical in IDA‐PBC, we show that the desired control objective is achieved provided that the desired output is detectable.                  

Citation

• Journal: International Journal of Adaptive Control and Signal Processing
• Year: 2026
• Volume:
• Issue:
• Pages:
• Publisher: Wiley
• DOI: 10.1002/acs.70076

BibTeX

@article{Romero_2026,
  title={{Adaptive IDA‐PBC for Underactuated Mechanical Systems With Unknown Time‐Varying Disturbances}},
  ISSN={1099-1115},
  DOI={10.1002/acs.70076},
  journal={International Journal of Adaptive Control and Signal Processing},
  publisher={Wiley},
  author={Romero, Jose Guadalupe and Nuño, Emmanuel},
  year={2026}
}

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References

• Ortega R, van der Schaft A, Maschke B, Escobar G (2002) Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica 38(4):585–596. https://doi.org/10.1016/s0005-1098(01)00278- – 10.1016/s0005-1098(01)00278-3
• Ortega R, Spong MW, Gomez-Estern F, Blankenstein G (2002) Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment. IEEE Trans Automat Contr 47(8):1218–1233. https://doi.org/10.1109/tac.2002.80077 – 10.1109/tac.2002.800770
• Meshram RV, Bhagwat M, Khade S, Wagh SR, Stankovic AM, Singh NM (2019) Port-Controlled Phasor Hamiltonian Modeling and IDA-PBC Control of Solid-State Transformer. IEEE Trans Contr Syst Technol 27(1):161–174. https://doi.org/10.1109/tcst.2017.276186 – 10.1109/tcst.2017.2761866
• Mattioni M, Moreschini A, Monaco S, Normand-Cyrot D (2022) Quaternion-Based Attitude Stabilization via Discrete-Time IDA-PBC. IEEE Control Syst Lett 6:2665–2670. https://doi.org/10.1109/lcsys.2022.317350 – 10.1109/lcsys.2022.3173509
• Harandi MRJ, Namvar M, Taghirad HD (2023) Stabilization of Robots With Actuator Constraints via Interconnection and Damping Assignment. IEEE Trans Contr Syst Technol 31(6):2945–2952. https://doi.org/10.1109/tcst.2023.327390 – 10.1109/tcst.2023.3273902
• Zhang T, Xia J (2019) Interconnection and Damping Assignment Passivity-Based Impedance Control of a Compliant Assistive Robot for Physical Human–Robot Interactions. IEEE Robot Autom Lett 4(2):538–545. https://doi.org/10.1109/lra.2019.289143 – 10.1109/lra.2019.2891434
• Salamat B, Elsbacher G, Tonello AM (2025) Energy Shaping Control in Underactuated Robot Systems With Underactuation Degree Two. IEEE Robot Autom Lett 10(3):2734–2741. https://doi.org/10.1109/lra.2025.353468 – 10.1109/lra.2025.3534688
• Donaire A, Junco S (2009) On the addition of integral action to port-controlled Hamiltonian systems. Automatica 45(8):1910–1916. https://doi.org/10.1016/j.automatica.2009.04.00 – 10.1016/j.automatica.2009.04.006
• Donaire A, Romero JG, Ortega R, Siciliano B, Crespo M (2016) Robust IDA-PBC for underactuated mechanical systems subject to matched disturbances. Int J Robust Nonlinear Control 27(6):1000–1016. https://doi.org/10.1002/rnc.361 – 10.1002/rnc.3615
• Romero JG, Donaire A, Ortega R (2013) Robust energy shaping control of mechanical systems. Systems & Control Letters 62(9):770–780. https://doi.org/10.1016/j.sysconle.2013.05.01 – 10.1016/j.sysconle.2013.05.011
• Ferguson J., Matched Disturbance Rejection for a Class of Nonlinear Systems. International Journal of Robust and Nonlinear Control (2019)
• Ferguson J, Wu D, Ortega R (2020) On Matched Disturbance Suppression for Port-Hamiltonian Systems. IEEE Control Syst Lett 4(4):892–897. https://doi.org/10.1109/lcsys.2020.299426 – 10.1109/lcsys.2020.2994262
• Franco E, Arpenti P, Donaire A (2023) Integral passivity‐based control of underactuated mechanical systems with state‐dependent matched disturbances. Intl J Robust & Nonlinear 34(5):3565–3585. https://doi.org/10.1002/rnc.715 – 10.1002/rnc.7151
• Franco E, Chen K (2025) Integral IDA-PBC for underactuated mechanical systems with unmeasured actuator dynamics and time-varying matched disturbances. European Journal of Control 85:101256. https://doi.org/10.1016/j.ejcon.2025.10125 – 10.1016/j.ejcon.2025.101256
• Franco E, Arpenti P, Donaire A, Ruggiero F (2024) Integral IDA-PBC for Underactuated Mechanical Systems Subject to Matched and Unmatched Disturbances. IEEE Control Syst Lett 8:568–573. https://doi.org/10.1109/lcsys.2024.339947 – 10.1109/lcsys.2024.3399474
• {“status”:”error” – 10.1109/tac.2018.2797191
• {“status”:”error” – 10.1002/rnc.1200
• Lu B, Fang Y, Sun N (2018) Continuous Sliding Mode Control Strategy for a Class of Nonlinear Underactuated Systems. IEEE Trans Automat Contr 63(10):3471–3478. https://doi.org/10.1109/tac.2018.279488 – 10.1109/tac.2018.2794885
• Ovalle L, Rios H, Llama M, Fridman L (2022) Continuous Sliding-Mode Output-Feedback Control for Stabilization of a Class of Underactuated Systems. IEEE Trans Automat Contr 67(2):986–992. https://doi.org/10.1109/tac.2021.307517 – 10.1109/tac.2021.3075179
• Boiko I, Fridman L (2005) Analysis of chattering in continuous sliding-mode controllers. IEEE Trans Automat Contr 50(9):1442–1446. https://doi.org/10.1109/tac.2005.85465 – 10.1109/tac.2005.854655
• Rosales A, Shtessel Y, Fridman L, Panathula CB (2017) Chattering Analysis of HOSM Controlled Systems: Frequency Domain Approach. IEEE Trans Automat Contr 62(8):4109–4115. https://doi.org/10.1109/tac.2016.261955 – 10.1109/tac.2016.2619559
• Bou Serhal RE, Khalil HK (2012) Application of the extended high gain observer to underactuated mechanical systems. 2012 American Control Conference (ACC) 4727–473 – 10.1109/acc.2012.6315215
• Anderle M., High Gain Observer for Embedded Acrobot. IFAC Proceedings (2014)
• Ferretti G. M. G., Adaptive Composition of Torque Disturbances in an Industrial Robot. IFAC Proceedings (2002)
• Ortega R, Romero JG, Aranovskiy S (2022) A new least squares parameter estimator for nonlinear regression equations with relaxed excitation conditions and forgetting factor. Systems & Control Letters 169:105377. https://doi.org/10.1016/j.sysconle.2022.10537 – 10.1016/j.sysconle.2022.105377
• Ortega R, Bobtsov A, Nikolaev N, Schiffer J, Dochain D (2021) Generalized parameter estimation-based observers: Application to power systems and chemical–biological reactors. Automatica 129:109635. https://doi.org/10.1016/j.automatica.2021.10963 – 10.1016/j.automatica.2021.109635
• Arpenti P, Ruggiero F, Lippiello V (2022) A Constructive Methodology for the IDA-PBC of Underactuated 2-DoF Mechanical Systems with Explicit Solution of PDEs. Int J Control Autom Syst 20(1):283–297. https://doi.org/10.1007/s12555-020-0839- – 10.1007/s12555-020-0839-1
• van der Schaft A (2017) L2-Gain and Passivity Techniques in Nonlinear Control. Springer International Publishin – 10.1007/978-3-319-49992-5
• Romero JG, Ortega R, Nuño E, Bobtsov A (2025) Robust adaptive consensus of perturbed Euler–Lagrange agents with unknown time varying disturbances. Automatica 174:112170. https://doi.org/10.1016/j.automatica.2025.11217 – 10.1016/j.automatica.2025.112170
• Byrnes CI, Priscoli FD, Isidori A (1997) Output Regulation of Uncertain Nonlinear Systems. Birkhäuser Bosto – 10.1007/978-1-4612-2020-6
• Bobtsov AA, Kolyubin SA, Pyrkin AA (2010) Compensation of unknown multi-harmonic disturbances in nonlinear plants with delayed control. Autom Remote Control 71(11):2383–2394. https://doi.org/10.1134/s000511791011010 – 10.1134/s000511791011010x
• Marino R, Tomei P (2002) Global estimation of n unknown frequencies. IEEE Trans Automat Contr 47(8):1324–1328. https://doi.org/10.1109/tac.2002.80076 – 10.1109/tac.2002.800761
• Tao G (2003) Adaptive Control Design and Analysi – 10.1002/0471459100
• D. Mahindrakar A, Astolfi A, Ortega R, Viola G (2006) Further constructive results on interconnection and damping assignment control of mechanical systems: the Acrobot example. Int J Robust Nonlinear Control 16(14):671–685. https://doi.org/10.1002/rnc.108 – 10.1002/rnc.1088
• Zhang M., Proceedings of the IEEE International Conference on Robotics and Automation (2001)