Finite-time stabilization and H∞ control of Port-controlled Hamiltonian systems with disturbances and saturation

Authors

Baozeng Fu, Qingzhi Wang, Ping Li

Abstract

The finite-time stabilization and finite-timeH∞control problems of Port-controlled Hamiltonian (PCH) systems with disturbances and input saturation (IS) are studied in this paper. First, by designing an appropriate output feedback, a strictly dissipative PCH system is obtained and finite-time stabilization result for nominal system is given. Second, with the help of the Hamilton function method and truncation inequality technique, a novel output feedback controller is developed to make the PCH system finite-time stable when IS occurs. Further, a finite-timeH∞controller is designed to attenuate disturbances for PCH systems with IS, and sufficient conditions are presented. Finally, a numerical example and a circuit example are given to reveal the feasibility of the obtained theoretical results.

Citation

• Journal: PLOS ONE
• Year: 2021
• Volume: 16
• Issue: 8
• Pages: e0255797
• Publisher: Public Library of Science (PLoS)
• DOI: 10.1371/journal.pone.0255797

BibTeX

@article{Fu_2021,
  title={{Finite-time stabilization and H∞ control of Port-controlled Hamiltonian systems with disturbances and saturation}},
  volume={16},
  ISSN={1932-6203},
  DOI={10.1371/journal.pone.0255797},
  number={8},
  journal={PLOS ONE},
  publisher={Public Library of Science (PLoS)},
  author={Fu, Baozeng and Wang, Qingzhi and Li, Ping},
  editor={Zhu, Yanzheng},
  year={2021},
  pages={e0255797}
}

Download the bib file

References

• Cheng, D. & Spurgeon, S. Stabilization of Hamiltonian systems with dissipation. International Journal of Control 74, 465–473 (2001) – 10.1080/00207170010010551
• Cheng, D., Astolfi, A. & Ortega, R. On feedback equivalence to port controlled Hamiltonian systems. Systems & Control Letters 54, 911–917 (2005) – 10.1016/j.sysconle.2005.02.005
• WW Sun, Distributed estimation for stochastic Hamiltonian systems with fading wireless channels. IEEE Trans Cybern (2020)
• Liu, X. & Liao, X. Fixed-time stabilization control for port-Hamiltonian systems. Nonlinear Dyn 96, 1497–1509 (2019) – 10.1007/s11071-019-04867-0
• Maschke, B. M. & van der Schaft, A. J. Port-Controlled Hamiltonian Systems: Modelling Origins and Systemtheoretic Properties. IFAC Proceedings Volumes 25, 359–365 (1992) – 10.1016/s1474-6670(17)52308-3
• AJ van der Schaft, The Hamiltonian formulation of energy conserving physical systems with external ports. Archive fur Elektronik und ubertragungstechnik (1995)
• HS Yu, Nonlinear control of induction motors based on state error PCH and energy-shaping principle. Nonlinear Dynam (2013)
• Fu, B., Li, S., Guo, L., Yang, J. & Lan, Q. Finite-time stabilization of port-controlled Hamiltonian systems with nonvanishing disturbances. Transactions of the Institute of Measurement and Control 40, 2973–2981 (2017) – 10.1177/0142331217712381
• Sun, W., Wu, Y. & Wang, L. Trajectory tracking of constrained robotic systems via a hybrid control strategy. Neurocomputing 330, 188–195 (2019) – 10.1016/j.neucom.2018.11.008
• Sun, W. & Fu, B. Adaptive control of time‐varying uncertain non‐linear systems with input delay: a Hamiltonian approach. IET Control Theory & Appl 10, 1844–1858 (2016) – 10.1049/iet-cta.2015.1165
• Cao, Z., Hou, X. & Zhao, W. A Family of Robust Simultaneous Controllers With Tuning Parameters Design for a Set of Port‐Controlled Hamiltonian Systems. Asian Journal of Control 19, 151–163 (2016) – 10.1002/asjc.1341
• Fu, B., Li, S., Yang, J. & Guo, L. Global output regulation for a class of single input Port-controlled Hamiltonian disturbed systems. Applied Mathematics and Computation 325, 322–331 (2018) – 10.1016/j.amc.2017.12.046
• Xu, T., Yu, H., Yu, J. & Meng, X. Adaptive Disturbance Attenuation Control of Two Tank Liquid Level System With Uncertain Parameters Based on Port-Controlled Hamiltonian. IEEE Access 8, 47384–47392 (2020) – 10.1109/access.2020.2979352
• Liu, X. & Liao, X. Fixed-Time $\mathcal {H}_{\infty }$ Control for Port-Controlled Hamiltonian Systems. IEEE Trans. Automat. Contr. 64, 2753–2765 (2019) – 10.1109/tac.2018.2874768
• Fu, B., Li, S., Wang, X. & Guo, L. Output feedback based simultaneous stabilization of two Port-controlled Hamiltonian systems with disturbances. Journal of the Franklin Institute 356, 8154–8166 (2019) – 10.1016/j.jfranklin.2019.02.039
• BZ Fu, Nonlinear disturbance observer-based control for a class of port-controlled Hamiltonian disturbed systems. IEEE Access (2018)
• Ortega, R., Spong, M. W., Gomez-Estern, F. & Blankenstein, G. Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment. IEEE Trans. Automat. Contr. 47, 1218–1233 (2002) – 10.1109/tac.2002.800770
• Ren, Y. & Sun, W. Robust adaptive control for robotic systems with input time-varying delay using Hamiltonian method. IEEE/CAA J. Autom. Sinica 5, 852–859 (2018) – 10.1109/jas.2016.7510055
• Bhat, S. P. & Bernstein, D. S. Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Trans. Automat. Contr. 43, 678–682 (1998) – 10.1109/9.668834
• YZ Wang, Finite-time stabilization of Port-controlled Hamiltonian systems with application to nonlinear affine systems. Proc Amer Control Conf (2008)
• Lan, Q., Li, S. & Yang, J. Finite‐time tracking control for a class of nonlinear systems with multiple mismatched disturbances. Intl J Robust & Nonlinear 30, 4095–4111 (2020) – 10.1002/rnc.4989
• Li, S. & Tian, Y.-P. Finite-time stability of cascaded time-varying systems. International Journal of Control 80, 646–657 (2007) – 10.1080/00207170601148291
• Wang, X., Wang, G. & Li, S. Distributed Finite-Time Optimization for Integrator Chain Multiagent Systems With Disturbances. IEEE Trans. Automat. Contr. 65, 5296–5311 (2020) – 10.1109/tac.2020.2979274
• Du, H., He, Y. & Cheng, Y. Finite-Time Synchronization of a Class of Second-Order Nonlinear Multi-Agent Systems Using Output Feedback Control. IEEE Trans. Circuits Syst. I 61, 1778–1788 (2014) – 10.1109/tcsi.2013.2295012
• WW Zhu, Design of output-based finite-time convergent composite controller for a class of perturbed second-order nonlinear systems. IEEE Trans Syst Man Cybern-Syst (2020)
• Li, X., Yang, X. & Song, S. Lyapunov conditions for finite-time stability of time-varying time-delay systems. Automatica 103, 135–140 (2019) – 10.1016/j.automatica.2019.01.031
• SH Li, Continuous finite-time output regulation for disturbed systems under mismatching condition. IEEE Trans Autom Control (2014)
• Song, J., Niu, Y. & Zou, Y. Finite-Time Stabilization via Sliding Mode Control. IEEE Trans. Automat. Contr. 62, 1478–1483 (2017) – 10.1109/tac.2016.2578300
• Zong, G., Wang, R., Zheng, W. & Hou, L. Finite‐timeH ∞ control for discrete‐time switched nonlinear systems with time delay. Intl J Robust & Nonlinear 25, 914–936 (2013) – 10.1002/rnc.3121
• Sun, L., Feng, G. & Wang, Y. Finite-time stabilization and \(H_{\infty}\) control for a class of nonlinear Hamiltonian descriptor systems with application to affine nonlinear descriptor systems. Automatica 50, 2090–2097 (2014) – 10.1016/j.automatica.2014.05.031
• Lin, X., Li, X., Zou, Y. & Li, S. Finite-time stabilization of switched linear systems with nonlinear saturating actuators. Journal of the Franklin Institute 351, 1464–1482 (2014) – 10.1016/j.jfranklin.2013.11.013
• Wei, A. & Wang, Y. Stabilization and \(H_{\infty}\) control of nonlinear port-controlled Hamiltonian systems subject to actuator saturation. Automatica 46, 2008–2013 (2010) – 10.1016/j.automatica.2010.08.001
• Y Ren, Adaptive neural network boundary control for a flexible manipulator with input constraints and model uncertainties. IEEE Trans Cybern (2020)
• Y Ren, Adaptive fault-tolerant boundary control for a flexible string with unknown dead-zone and actuator fault. IEEE Trans Cybern (2021)
• Ma, L., Zong, G., Zhao, X. & Huo, X. Observed-based adaptive finite-time tracking control for a class of nonstrict-feedback nonlinear systems with input saturation. Journal of the Franklin Institute 357, 11518–11544 (2020) – 10.1016/j.jfranklin.2019.07.021
• Lin, X., Huang, S., Li, S. & Zou, Y. Finite-time feedback control of an input-delay system with nonlinear saturating actuators. Transactions of the Institute of Measurement and Control 40, 3059–3067 (2017) – 10.1177/0142331217713836
• WW Sun, Adaptive neural network control for full-state constrained robotic manipulator with actuator saturation and time-varying delays. IEEE Trans Neural Netw Learn Syst (2021)
• Sun, W. W. Stabilization analysis of time-delay Hamiltonian systems in the presence of saturation. Applied Mathematics and Computation 217, 9625–9634 (2011) – 10.1016/j.amc.2011.04.044
• Hong, Y. & Jiang, Z.-P. Finite-Time Stabilization of Nonlinear Systems With Parametric and Dynamic Uncertainties. IEEE Trans. Automat. Contr. 51, 1950–1956 (2006) – 10.1109/tac.2006.886515
• Wang, Z.-M., Wei, A. & Zhang, X. Stability analysis and control design based on average dwell time approaches for switched nonlinear port-controlled Hamiltonian systems. Journal of the Franklin Institute 356, 3368–3397 (2019) – 10.1016/j.jfranklin.2019.02.024
• TL Shen, H∞ control theory and its applications (1996)