Finite-time adaptive control for uncertain switched port-controlled Hamiltonian systems

Authors

Zi-Ming Wang, Xudong Zhao, Xiaodi Li, Airong Wei

Abstract

In this paper, the finite-time boundedness (FTB) and H ∞ control are discussed for a class of uncertain switched port-controlled Hamiltonian (PCH) systems via adaptive control strategies. In view of the mode-dependent matching principle, the energy-based multiple Lyapunov functions method and the mode-dependent average dwell time (MDADT) approach, sufficient conditions on the FTB are obtained for uncertain switched PCH systems by employing a set of adaptive mode-dependent state feedback controllers. Furthermore, to solve the finite-time H ∞ control for the system under consideration, a new set of mode-dependent state feedback controllers are designed to restrain both the structured uncertainties and disturbances, and sufficient conditions on the H ∞ control problem are derived for the system under a new MDADT scheme. Finally, the numerical simulations are presented to illustrate the effectiveness of the proposed finite-time adaptive control methods.

Keywords

Uncertain switched port-controlled Hamiltonian systems; Energy-based multiple Lyapunov functions; Mode-dependent average dwell time; Finite-time adaptive control

Citation

• Journal: Communications in Nonlinear Science and Numerical Simulation
• Year: 2023
• Volume: 119
• Issue:
• Pages: 107129
• Publisher: Elsevier BV
• DOI: 10.1016/j.cnsns.2023.107129

BibTeX

@article{Wang_2023,
  title={{Finite-time adaptive control for uncertain switched port-controlled Hamiltonian systems}},
  volume={119},
  ISSN={1007-5704},
  DOI={10.1016/j.cnsns.2023.107129},
  journal={Communications in Nonlinear Science and Numerical Simulation},
  publisher={Elsevier BV},
  author={Wang, Zi-Ming and Zhao, Xudong and Li, Xiaodi and Wei, Airong},
  year={2023},
  pages={107129}
}

Download the bib file

References

• Maschke BM, Schaft AJ. Port-controlled Hamiltonian systems: Modeling origins and system theoretic properties. In: Proceedings of the IFAC symposium on NOLCOS (282–288). Bordeaux, France; 1992.
• Zhang, X., Lu, Z., Yuan, X., Wang, Y. & Shen, X. L2-Gain Adaptive Robust Control for Hybrid Energy Storage System in Electric Vehicles. IEEE Trans. Power Electron. 36, 7319–7332 (2021) – 10.1109/tpel.2020.3041653
• Cai, L., He, Z. & Hu, H. A New Load Frequency Control Method of Multi-Area Power System via the Viewpoints of Port-Hamiltonian System and Cascade System. IEEE Trans. Power Syst. 32, 1689–1700 (2017) – 10.1109/tpwrs.2016.2605007
• van der Schaft, A. & Jeltsema, D. Limits to Energy Conversion. IEEE Trans. Automat. Contr. 67, 532–538 (2022) – 10.1109/tac.2021.3075652
• Haddad, W. M., Rajpurohit, T. & Jin, X. Energy-based feedback control for stochastic port-controlled Hamiltonian systems. Automatica 97, 134–142 (2018) – 10.1016/j.automatica.2018.07.031
• Shen, T., Ortega, R., Lu, Q., Mei, S. & Tamura, K. Adaptive L2 Disturbance Attenuation Of Hamiltonian Systems With Parametric Perturbation And Application To Power Systems. Asian Journal of Control 5, 143–152 (2003) – 10.1111/j.1934-6093.2003.tb00105.x
• 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
• Wang, Y., Li, C. & Cheng, D. Generalized Hamiltonian realization of time-invariant nonlinear systems. Automatica 39, 1437–1443 (2003) – 10.1016/s0005-1098(03)00132-8
• El‐Ferik, S., Qureshi, A. & Lewis, F. L. Robust neuro‐adaptive cooperative control of multi‐agent port‐controlled Hamiltonian systems. Adaptive Control & Signal 30, 488–510 (2015) – 10.1002/acs.2589
• Ahmad, M. A., Azuma, S., Baba, I. & Sugie, T. Switching Controller Design for Hybrid Electric Vehicles. SICE Journal of Control, Measurement, and System Integration 7, 273–282 (2014) – 10.9746/jcmsi.7.273
• Lian, J. & Li, C. Event-Triggered Sliding Mode Control of Uncertain Switched Systems via Hybrid Quantized Feedback. IEEE Trans. Automat. Contr. 66, 2809–2816 (2021) – 10.1109/tac.2020.3009199
• Zhou, L., Pan, R. & Xiao, X. Synchronization of a class of switched nonlinear systems based on quantized sampled-data. Communications in Nonlinear Science and Numerical Simulation 70, 170–180 (2019) – 10.1016/j.cnsns.2018.10.018
• Branicky, M. S. Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Automat. Contr. 43, 475–482 (1998) – 10.1109/9.664150
• Hespanha, Stability of switched systems with average dwell time. (1999)
• Jiang, B., Lou, Y. & Lu, J. Input-to-state stability of delayed systems with bounded-delay impulses. MMC 2, 44–54 (2022) – 10.3934/mmc.2022006
• Zhao, X., Zhang, L., Shi, P. & Liu, M. Stability and Stabilization of Switched Linear Systems With Mode-Dependent Average Dwell Time. IEEE Trans. Automat. Contr. 57, 1809–1815 (2012) – 10.1109/tac.2011.2178629
• Li, X., Lin, X., Li, S. & Zou, Y. Finite-time stability of switched nonlinear systems with finite-time unstable subsystems. Journal of the Franklin Institute 352, 1192–1214 (2015) – 10.1016/j.jfranklin.2014.12.011
• Wang, Y.-E., Sun, X.-M. & Mazenc, F. Stability of switched nonlinear systems with delay and disturbance. Automatica 69, 78–86 (2016) – 10.1016/j.automatica.2016.02.015
• Long, L., Wang, Z. & Zhao, J. Switched adaptive control of switched nonlinearly parameterized systems with unstable subsystems. Automatica 54, 217–228 (2015) – 10.1016/j.automatica.2015.02.004
• Xie, X., Zhou, Q., Yue, D. & Li, H. Relaxed Control Design of Discrete-Time Takagi–Sugeno Fuzzy Systems: An Event-Triggered Real-Time Scheduling Approach. IEEE Trans. Syst. Man Cybern, Syst. 48, 2251–2262 (2018) – 10.1109/tsmc.2017.2737542
• Su, X., Wen, Y., Shi, P., Wang, S. & Assawinchaichote, W. Event-Triggered Fuzzy Control for Nonlinear Systems via Sliding Mode Approach. IEEE Trans. Fuzzy Syst. 29, 336–344 (2021) – 10.1109/tfuzz.2019.2952798
• Fei, Z., Shi, S., Ahn, C. K. & Basin, M. V. Finite-Time Control for Switched T–S Fuzzy Systems via a Dynamic Event-Triggered Mechanism. IEEE Trans. Fuzzy Syst. 29, 3899–3909 (2021) – 10.1109/tfuzz.2020.3029292
• Zhu, L. & Feng, G. Necessary and sufficient conditions for stability of switched nonlinear systems. Journal of the Franklin Institute 352, 117–137 (2015) – 10.1016/j.jfranklin.2014.10.011
• Zhu, H. & Hou, X. Robust H∞ control for uncertain switched nonlinear polynomial systems: Parameterization of controller approach. Intl J Robust & Nonlinear 28, 4931–4950 (2018) – 10.1002/rnc.4296
• Wang, Z.-M., Wei, A., Zhao, X., Mu, R. & Zhang, X. Control design for switched port-controlled Hamiltonian systems with unstabilizable modes: An improved mode-dependent average dwell time scheme. Nonlinear Analysis: Hybrid Systems 38, 100944 (2020) – 10.1016/j.nahs.2020.100944
• Wang, Z., Sun, J., Chen, J. & Bai, Y. Finite‐time stability of switched nonlinear time‐delay systems. Intl J Robust & Nonlinear 30, 2906–2919 (2020) – 10.1002/rnc.4928
• Kamenkov, On stability of motion over a finite interval of time. J Appl Math Mech USSR (1953)
• Amato, F., Ariola, M. & Dorato, P. Finite-time control of linear systems subject to parametric uncertainties and disturbances. Automatica 37, 1459–1463 (2001) – 10.1016/s0005-1098(01)00087-5
• 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
• Li, M., Sun, L. & Yang, R. Finite-time H∞ control for a class of discrete-time nonlinear singular systems. Journal of the Franklin Institute 355, 5384–5393 (2018) – 10.1016/j.jfranklin.2018.05.033
• Lin, X., Li, S. & Zou, Y. Finite‐time stability of switched linear systems with subsystems which are not finite‐time stable. IET Control Theory & Appl 8, 1137–1146 (2014) – 10.1049/iet-cta.2013.0648
• Zhang, T., Li, X. & Song, S. Finite-Time Stabilization of Switched Systems Under Mode-Dependent Event-Triggered Impulsive Control. IEEE Trans. Syst. Man Cybern, Syst. 52, 5434–5442 (2022) – 10.1109/tsmc.2021.3124998
• Wang, Z.-M., Wei, A., Zong, G., Zhao, X. & Li, H. 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, 11807–11829 (2020) – 10.1016/j.jfranklin.2019.11.055
• Xiang, Z., Sun, Y.-N. & Mahmoud, M. S. Robust finite-time H∞ control for a class of uncertain switched neutral systems. Communications in Nonlinear Science and Numerical Simulation 17, 1766–1778 (2012) – 10.1016/j.cnsns.2011.09.022
• Zhang, L., Wang, S., Karimi, H. R. & Jasra, A. Robust Finite-Time Control of Switched Linear Systems and Application to a Class of Servomechanism Systems. IEEE/ASME Trans. Mechatron. 20, 2476–2485 (2015) – 10.1109/tmech.2014.2385796
• He, S., Ai, Q., Ren, C., Dong, J. & Liu, F. Finite-Time Resilient Controller Design of a Class of Uncertain Nonlinear Systems With Time-Delays Under Asynchronous Switching. IEEE Trans. Syst. Man Cybern, Syst. 49, 281–286 (2019) – 10.1109/tsmc.2018.2798644
• Lv, X., Niu, Y. & Song, J. Finite-time boundedness of uncertain Hamiltonian systems via sliding mode control approach. Nonlinear Dyn 104, 497–507 (2021) – 10.1007/s11071-021-06292-8
• Wei, A., Wang, Z., Mu, R. & Zhang, X. Finite‐time adaptive control for port‐controlled Hamiltonian systems with parametric perturbations. Adaptive Control & Signal 36, 802–817 (2022) – 10.1002/acs.3373
• Li, Y., Niu, B., Zong, G., Zhao, J. & Zhao, X. Command filter-based adaptive neural finite-time control for stochastic nonlinear systems with time-varying full-state constraints and asymmetric input saturation. International Journal of Systems Science 53, 199–221 (2021) – 10.1080/00207721.2021.1943562
• Niu, Global adaptive control of switched uncertain nonlinear systems: An improved MDADT method. Automatica (2020)
• Zhang, H., Wang, H., Niu, B., Zhang, L. & Ahmad, A. M. Sliding-mode surface-based adaptive actor-critic optimal control for switched nonlinear systems with average dwell time. Information Sciences 580, 756–774 (2021) – 10.1016/j.ins.2021.08.062