Adaptive Stabilization and \( H_{\infty} \) Control for Switched Nonlinear Port-Controlled Hamiltonian Systems with Parameter Perturbations

Authors

Abstract

The problems of adaptive stabilization and \( H_{\infty} \) control for switched nonlinear port-controlled Hamiltonian systems with parameter perturbations are investigated via the multiple Lyapunov functions method. Firstly, based on reasonable assumptions, an adaptive feedback law is designed and sufficient conditions are obtained for the stabilization of the switched system. Secondly, when the external disturbance is considered, an adaptive \( H_{\infty} \) feedback controller is given to solve the \( H_{\infty} \) control for the switched system. Finally, a numerical example is presented to illustrate the effectiveness of the proposed method.

Citation

Journal: 2018 37th Chinese Control Conference (CCC)
Year: 2018
Volume:
Issue:
Pages: 891–896
Publisher: IEEE
DOI: 10.23919/chicc.2018.8482605

BibTeX

@inproceedings{Wang_2018,
  title={{Adaptive Stabilization and &lt;tex&gt;$H_{\infty}$&lt;/tex&gt; Control for Switched Nonlinear Port-Controlled Hamiltonian Systems with Parameter Perturbations}},
  DOI={10.23919/chicc.2018.8482605},
  booktitle={{2018 37th Chinese Control Conference (CCC)}},
  publisher={IEEE},
  author={Wang, Zi-Ming and Wei, Airong and Shen, Haixia},
  year={2018},
  pages={891--896}
}

Download the bib file

References

Zhu, L. & Wang, Y. Study on the stability of switched dissipative Hamiltonian systems. SCI CHINA SER F 49, 578–591 (2006) – 10.1007/s11432-006-2005-7
Wei, A. & Wang, Y. Stabilization and H∞ control of nonlinear port-controlled Hamiltonian systems subject to actuator saturation. Automatica 46, 2008–2013 (2010) – 10.1016/j.automatica.2010.08.001
Fujimoto, K., Sakurama, K. & Sugie, T. Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations. Automatica 39, 2059–2069 (2003) – 10.1016/j.automatica.2003.07.005
Laila, D. S. & Astolfi, A. Construction of discrete-time models for port-controlled Hamiltonian systems with applications. Systems & Control Letters 55, 673–680 (2006) – 10.1016/j.sysconle.2005.09.012
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
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
Lu, X., Zhang, X. & Sun, L. Finite-time H ∞ control for nonlinear discrete Hamiltonian descriptor systems. Journal of the Franklin Institute 354, 6138–6151 (2017) – 10.1016/j.jfranklin.2017.07.013
van der schaft, L2 -Gain and passivity techniques in nonlinear control (1999)
Li, H. & Wei, A. Stabilization and H∞ Control of Nonlinear Switched Hamiltonian Systems Subject to Actuator Saturation. Asian Journal of Control 19, 951–960 (2016) – 10.1002/asjc.1428
Hernandez‐Vargas, E., Colaneri, P., Middleton, R. & Blanchini, F. Discrete‐time control for switched positive systems with application to mitigating viral escape. Intl J Robust & Nonlinear 21, 1093–1111 (2011) – 10.1002/rnc.1628
Tang, L. & Zhao, J. Neural network based adaptive prescribed performance control for a class of switched nonlinear systems. Neurocomputing 230, 316–321 (2017) – 10.1016/j.neucom.2016.12.011
Wang, X., Li, H., Zong, G. & Zhao, X. Adaptive fuzzy tracking control for a class of high-order switched uncertain nonlinear systems. Journal of the Franklin Institute 354, 6567–6587 (2017) – 10.1016/j.jfranklin.2017.08.008
Wu, C. & Liu, X. External stability of switching control systems. Systems & Control Letters 106, 24–31 (2017) – 10.1016/j.sysconle.2017.05.008
Liu, Z., Zhang, X., Lu, X. & Liu, Q. Stabilization of positive switched delay systems with all modes unstable. Nonlinear Analysis: Hybrid Systems 29, 110–120 (2018) – 10.1016/j.nahs.2018.01.004
Li, T. & Parsa, L. Design, Control, and Analysis of a Fault-Tolerant Soft-Switching DC–DC Converter for High-Power High-Voltage Applications. IEEE Trans. Power Electron. 33, 1094–1104 (2018) – 10.1109/tpel.2017.2684832
Hajiahmadi, M., De Schutter, B. & Hellendoorn, H. Robust H<inf>∞</inf> control for switched nonlinear systems with application to high-level urban traffic control. 52nd IEEE Conference on Decision and Control 899–904 (2013) doi:10.1109/cdc.2013.6759996 – 10.1109/cdc.2013.6759996
Niu, B. & Zhao, J. Stabilization and -gain analysis for a class of cascade switched nonlinear systems: An average dwell-time method. Nonlinear Analysis: Hybrid Systems 5, 671–680 (2011) – 10.1016/j.nahs.2011.05.005