On estimation of attraction domain for port-controlled Hamiltonian systems subject to actuator saturation

Authors

Abstract

This paper investigates the estimation of domain of attraction for nonlinear port-controlled Hamiltonian (PCH) systems with actuator saturation (AS). Several conditions are established under which an ellipsoid is contractively invariant, and thus can be employed to find the biggest ellipsoid contained in the domain of attraction. It is shown that the proposed conditions can be expressed in the form of the linear matrix inequalities (LMIs) optimization problem with constraints. Study of an illustrative example shows that the proposed method works very well in estimating the domain of attraction for some classes of nonlinear PCH systems with AS.

Keywords

PCH system; Actuator saturation; Domain of attraction; Set invariance

Citation

Journal: Journal of Control Theory and Applications
Year: 2012
Volume: 10
Issue: 2
Pages: 195–200
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/s11768-012-9296-6

BibTeX

@article{Wei_2012,
  title={{On estimation of attraction domain for port-controlled Hamiltonian systems subject to actuator saturation}},
  volume={10},
  ISSN={1993-0623},
  DOI={10.1007/s11768-012-9296-6},
  number={2},
  journal={Journal of Control Theory and Applications},
  publisher={Springer Science and Business Media LLC},
  author={Wei, Airong and Wang, Yuzhen},
  year={2012},
  pages={195--200}
}

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References

Hu, T., Lin, Z. & Chen, B. M. An analysis and design method for linear systems subject to actuator saturation and disturbance. Automatica 38, 351–359 (2002) – 10.1016/s0005-1098(01)00209-6
Saberi, A., Zongli Lin & Teel, A. R. Control of linear systems with saturating actuators. IEEE Trans. Automat. Contr. 41, 368–378 (1996) – 10.1109/9.486638
J. M. Gomes da Silva, IEEE Transactions on Automatic Control (2005)
Milani, B. E. A. Piecewise-affine Lyapunov functions for discrete-time linear systems with saturating controls. Automatica 38, 2177–2184 (2002) – 10.1016/s0005-1098(02)00193-0
Pittet, C., Tarbouriech, S. & Burgat, C. Stability regions for linear systems with saturating controls via circle and Popov criteria. Proceedings of the 36th IEEE Conference on Decision and Control vol. 5 4518–4523 – 10.1109/cdc.1997.649683
H. Hindi, Proceedings of the 37th IEEE Conference on Decision and Control (1998)
Blanchini, F. Ultimate boundedness control for uncertain discrete-time systems via set-induced Lyapunov functions. IEEE Trans. Automat. Contr. 39, 428–433 (1994) – 10.1109/9.272351
Yong-Yan Cao & Zongli Lin. Robust stability analysis and fuzzy-scheduling control for nonlinear systems subject to actuator saturation. IEEE Trans. Fuzzy Syst. 11, 57–67 (2003) – 10.1109/tfuzz.2002.806317
Coutinho, D. F. & da Silva, J. M. G. Estimating the Region of Attraction of Nonlinear Control Systems with Saturating Actuators. 2007 American Control Conference 4715–4720 (2007) doi:10.1109/acc.2007.4282430 – 10.1109/acc.2007.4282430
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
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
Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica 38, 585–596 (2002) – 10.1016/s0005-1098(01)00278-3
Wang, Y., Feng, G., Cheng, D. & Liu, Y. Adaptive L2 disturbance attenuation control of multi-machine power systems with SMES units. Automatica 42, 1121–1132 (2006) – 10.1016/j.automatica.2006.03.014
Shen, T., Ortega, R., Lu, Q., Mei, S. & Tamura, K. Adaptive L/sub 2/ disturbance attenuation of Hamiltonian systems with parametric perturbation and application to power systems. Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187) vol. 5 4939–4944 – 10.1109/cdc.2001.914715
Xi, Z. & Cheng, D. Passivity-based stabilization and H 8 control of the Hamiltonian control systems with dissipation and its applications to power systems. International Journal of Control 73, 1686–1691 (2000) – 10.1080/00207170050201762
Boyd, S., El Ghaoui, L., Feron, E. & Balakrishnan, V. Linear Matrix Inequalities in System and Control Theory. (1994) doi:10.1137/1.9781611970777 – 10.1137/1.9781611970777
Hu, T. & Lin, Z. On enlarging the basin of attraction for linear systems under saturated linear feedback. Systems & Control Letters 40, 59–69 (2000) – 10.1016/s0167-6911(00)00002-5