Fixed-time stabilization and H∞ control of time-delay port-controlled Hamiltonian systems

Authors

Yufei Chen, Qihuai Liu

Abstract

In this paper, we investigate the fixed-time stability (FxTS) and fixed-time H ∞ control design of time-delay port-controlled Hamiltonian (PCH) systems. Firstly, we establish an improved FxTS criterion. Secondly, by utilizing this criterion and interconnection and damping assignment passivity-based (IDA-PBC) technique, two new FxTS results are given for PCH systems with the assumption about Hamiltonian functions. Then, a fixed-time H ∞ control design procedure is presented by using a new Lyapunov–Krasovskii (L-K) functional. Finally, the forced mathematical pendulum model with a constant time-delay shows the effectiveness of our results.

Keywords

Port-controlled Hamiltonian; Fixed-time stability; \( H^\infty \)-control; L-K functional method

Citation

• Journal: European Journal of Control
• Year: 2024
• Volume: 77
• Issue:
• Pages: 100996
• Publisher: Elsevier BV
• DOI: 10.1016/j.ejcon.2024.100996

BibTeX

@article{Chen_2024,
  title={{Fixed-time stabilization and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg" display="inline" id="d1e142"><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msub></mml:math> control of time-delay port-controlled Hamiltonian systems}},
  volume={77},
  ISSN={0947-3580},
  DOI={10.1016/j.ejcon.2024.100996},
  journal={European Journal of Control},
  publisher={Elsevier BV},
  author={Chen, Yufei and Liu, Qihuai},
  year={2024},
  pages={100996}
}

Download the bib file

References

• Bhat, S. P. & Bernstein, D. S. Finite-Time Stability of Continuous Autonomous Systems. SIAM J. Control Optim. 38, 751–766 (2000) – 10.1137/s0363012997321358
• Boyd, (1994)
• Chen, Y. & Liu, Q. Stability of port-Hamiltonian systems with mixed time delays subject to input saturation. NAMC 29, 124–145 (2023) – 10.15388/namc.2024.29.33822
• Chen, Y., Liu, Q. & Su, H. Generalized Hamiltonian forms of dissipative mechanical systems via a unified approach. Journal of Geometry and Physics 160, 103976 (2021) – 10.1016/j.geomphys.2020.103976
• Chen, New results on finite-time stability and H∞ control for nonlinear Hamiltonian systems. Asian Journal of Control (2023)
• Farid, Y. & Ruggiero, F. Finite-time extended state observer and fractional-order sliding mode controller for impulsive hybrid port-Hamiltonian systems with input delay and actuators saturation: Application to ball-juggler robots. Mechanism and Machine Theory 167, 104577 (2022) – 10.1016/j.mechmachtheory.2021.104577
• Favache, A., Dos Santos Martins, V. S., Dochain, D. & Maschke, B. Some Properties of Conservative Port Contact Systems. IEEE Trans. Automat. Contr. 54, 2341–2351 (2009) – 10.1109/tac.2009.2028973
• Feng, L., Hu, C., Yu, J., Jiang, H. & Wen, S. Fixed-time Synchronization of Coupled Memristive Complex-valued Neural Networks. Chaos, Solitons & Fractals 148, 110993 (2021) – 10.1016/j.chaos.2021.110993
• Gu, K. An integral inequality in the stability problem of time-delay systems. Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187) vol. 3 2805–2810 – 10.1109/cdc.2000.914233
• Hu, C. & Jiang, H. Special Functions-Based Fixed-Time Estimation and Stabilization for Dynamic Systems. IEEE Trans. Syst. Man Cybern, Syst. 52, 3251–3262 (2022) – 10.1109/tsmc.2021.3062206
• Hu, C., Yu, J., Chen, Z., Jiang, H. & Huang, T. Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks. Neural Networks 89, 74–83 (2017) – 10.1016/j.neunet.2017.02.001
• Kong, F., Ni, H., Zhu, Q., Hu, C. & Huang, T. Fixed-time and predefined-time synchronization of discontinuous neutral-type competitive networks via non-chattering adaptive control strategy. IEEE Trans. Netw. Sci. Eng. 1–12 (2023) doi:10.1109/tnse.2023.3271109 – 10.1109/tnse.2023.3271109
• Kong, F., Zhu, Q. & Huang, T. Improved Fixed-Time Stability Lemma of Discontinuous System and its Application. IEEE Trans. Circuits Syst. I 69, 835–846 (2022) – 10.1109/tcsi.2021.3115097
• Liu, Q., Xie, A. & Wang, C. Contact Extension and Symplectification. Acta Math. Appl. Sin. Engl. Ser. 39, 962–971 (2023) – 10.1007/s10255-023-1093-0
• 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
• Liu, X. & Liao, X. Fixed-time stabilization control for port-Hamiltonian systems. Nonlinear Dyn 96, 1497–1509 (2019) – 10.1007/s11071-019-04867-0
• Liu, X. & Liao, X. Locally Fixed-Time Stabilization and $H_{\infty}$ Control for Memristive Port-Controlled Hamiltonian Systems. 2021 International Conference on Control, Automation and Information Sciences (ICCAIS) 793–798 (2021) doi:10.1109/iccais52680.2021.9624521 – 10.1109/iccais52680.2021.9624521
• Liu, X. & Liao, X. Fixed-Time Control for a Class of Nonlinear PH-DAE Systems. IEEE Trans. Syst. Man Cybern, Syst. 53, 5161–5173 (2023) – 10.1109/tsmc.2023.3258447
• Liu, Q. & Torres, P. J. Orbital dynamics on invariant sets of contact Hamiltonian systems. DCDS-B 27, 5821 (2022) – 10.3934/dcdsb.2021297
• Liu, X. & Zhao, M. Memristor‐based disturbance rejection control for port‐Hamiltonian systems with locally fixed‐time convergence. IET Control Theory & Appl 16, 1326–1340 (2022) – 10.1049/cth2.12307
• Meng, M., Li, X. & Chen, J. Decentralized Nash Equilibria Learning for Online Game With Bandit Feedback. IEEE Trans. Automat. Contr. 69, 4050–4057 (2024) – 10.1109/tac.2023.3342850
• Mohit, M. & Shahrokhi, M. Adaptive fixed-time consensus control for a class of non-strict feedback multi-agent systems subject to input nonlinearities, state constraints, unknown control directions, and actuator faults. European Journal of Control 66, 100649 (2022) – 10.1016/j.ejcon.2022.100649
• Moulay, E., Dambrine, M., Yeganefar, N. & Perruquetti, W. Finite-time stability and stabilization of time-delay systems. Systems & Control Letters 57, 561–566 (2008) – 10.1016/j.sysconle.2007.12.002
• Niamsup, P., Ratchagit, K. & Phat, V. N. Novel criteria for finite-time stabilization and guaranteed cost control of delayed neural networks. Neurocomputing 160, 281–286 (2015) – 10.1016/j.neucom.2015.02.030
• Pasumarthy, R. & Kao, C.-Y. On stability of time delay Hamiltonian systems. 2009 American Control Conference 4909–4914 (2009) doi:10.1109/acc.2009.5160619 – 10.1109/acc.2009.5160619
• Petersen, I. R. & Hollot, C. V. A riccati equation approach to the stabilization of uncertain linear systems. Automatica 22, 397–411 (1986) – 10.1016/0005-1098(86)90045-2
• Polyakov, A. Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems. IEEE Trans. Automat. Contr. 57, 2106–2110 (2012) – 10.1109/tac.2011.2179869
• Pratap, A., Raja, R., Cao, J., Rajchakit, G. & Alsaadi, F. E. Further synchronization in finite time analysis for time-varying delayed fractional order memristive competitive neural networks with leakage delay. Neurocomputing 317, 110–126 (2018) – 10.1016/j.neucom.2018.08.016
• Schiffer, J., Fridman, E., Ortega, R. & Raisch, J. Stability of a class of delayed port-Hamiltonian systems with application to microgrids with distributed rotational and electronic generation. Automatica 74, 71–79 (2016) – 10.1016/j.automatica.2016.07.022
• Wang, Finite-time stabilization of port-controlled Hamiltonian systems with application to nonlinear affine systems. (2008)
• Wang, Z.-M., Wei, A., Zong, G., Zhao, X. & Li, H. Finite-time stabilization andH∞control for a class of switched nonlinear port-controlled Hamiltonian systems subject to actuator saturation. Journal of the Franklin Institute 357, 11807–11829 (2020) – 10.1016/j.jfranklin.2019.11.055
• Wang, Finite-time adaptive control for uncertain switched port-controlled Hamiltonian systems. Communications in Nonlinear Science and Numerical Simulation (2023)
• Yang, R. & Guo, R. Adaptive Finite‐Time Robust Control of Nonlinear Delay Hamiltonian Systems Via Lyapunov‐Krasovskii Method. Asian Journal of Control 20, 332–342 (2017) – 10.1002/asjc.1556
• Yang, R. & Wang, Y. Finite-time stability analysis and H∞ control for a class of nonlinear time-delay Hamiltonian systems. Automatica 49, 390–401 (2013) – 10.1016/j.automatica.2012.11.034
• Zhang, C., Chang, L., Xing, L. & Zhang, X. Fixed-Time Stabilization of a Class of Strict-Feedback Nonlinear Systems via Dynamic Gain Feedback Control. IEEE/CAA J. Autom. Sinica 10, 403–410 (2023) – 10.1109/jas.2023.123408
• Zuo, Z. & Tie, L. A new class of finite-time nonlinear consensus protocols for multi-agent systems. International Journal of Control 87, 363–370 (2013) – 10.1080/00207179.2013.834484