Estimate of domain of attraction for a class of Port-Controlled Hamiltonian systems subject to both actuator saturation and disturbance

Authors

Abstract

This paper investigates the estimate of domain of attraction for a class of nonlinear Port-Controlled Hamiltonian (PCH) systems subject to both actuator saturation and disturbances. Firstly, two conditions are established to determine whether an ellipsoid is contractively invariant for the systems only with actuator saturation, with which the biggest ellipsoid contained in the domain of attraction can be found and a new estimation method is presented. It is shown that the proposed conditions can be expressed in the form of the linear matrix inequality optimization problem with constraints. Secondly, the obtained conditions are extended to estimate the domain of attraction of the systems subject to both actuator saturation and disturbances, and a new estimation method is proposed. Study of an illustrative example shows that the methods proposed in this paper work very well in estimating the domain of attraction for some classes of nonlinear PCH systems with actuator saturation and/or disturbances.

Citation

Journal: 2010 8th World Congress on Intelligent Control and Automation
Year: 2010
Volume:
Issue:
Pages: 957–962
Publisher: IEEE
DOI: 10.1109/wcica.2010.5554406

BibTeX

@inproceedings{Wei_2010,
  title={{Estimate of domain of attraction for a class of Port-Controlled Hamiltonian systems subject to both actuator saturation and disturbance}},
  DOI={10.1109/wcica.2010.5554406},
  booktitle={{2010 8th World Congress on Intelligent Control and Automation}},
  publisher={IEEE},
  author={Wei, Airong and Wang, Yuzhen},
  year={2010},
  pages={957--962}
}

Download the bib file

References

Hu, T. & Lin, Z. Control Systems with Actuator Saturation. (Birkhäuser Boston, 2001). doi:10.1007/978-1-4612-0205-9 – 10.1007/978-1-4612-0205-9
Zongli Lin, Saberi, A. & Stoorvogel, A. A. Semiglobal stabilization of linear discrete-time systems subject to input saturation, via linear feedback-an ARE-based approach. IEEE Trans. Automat. Contr. 41, 1203–1207 (1996) – 10.1109/9.533685
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
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
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
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
shen, Adaptive L2disturbance attenuation of Hamiltonian systems with parameter perturbations and application to power systems. Proc of the 39th IEEE Conference on Decision and Control (2000)
Stoorvogel, A. A., Saberi, A. & Weiland, S. On external semi-global stochastic stabilization of linear systems with input saturation. 2007 American Control Conference 5845–5850 (2007) doi:10.1109/acc.2007.4282930 – 10.1109/acc.2007.4282930
Sussmann, H. J., Sontag, E. D. & Yang, Y. A general result on the stabilization of linear systems using bounded controls. IEEE Trans. Automat. Contr. 39, 2411–2425 (1994) – 10.1109/9.362853
van der schaft, L2-Gain and Passivity Techniques in Nonlinear Control (1999)
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
castelan, Stability and stabilization of a class of nonlinear systems with saturating actuators. Proc of the 16th IFAC World Congress (2005)
Escobar, G., van der Schaft, A. J. & Ortega, R. A Hamiltonian viewpoint in the modeling of switching power converters. Automatica 35, 445–452 (1999) – 10.1016/s0005-1098(98)00196-4
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
gomes da silva, Antiwindup design with guaranteed regions of stability: An LMI-based approach. IEEE Trans on Automatic Control (2005)
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
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
Hindi, H. & Boyd, S. Analysis of linear systems with saturation using convex optimization. Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171) vol. 1 903–908 – 10.1109/cdc.1998.760808
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
Wang, Y., Feng, G., Cheng, D. & Liu, Y. Adaptive \(L_{2}\) disturbance attenuation control of multi-machine power systems with SMES units. Automatica 42, 1121–1132 (2006) – 10.1016/j.automatica.2006.03.014
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
wei, Parallel simultaneous stabilization of a set of Port-Controlled Hamiltonian systems subject to actuator saturation. Accepted by Journal of Systems Science and Complexity (2009)
Zhou, B. & Duan, G.-R. On Analytical Approximation of the Maximal Invariant Ellipsoids for Linear Systems With Bounded Controls. IEEE Trans. Automat. Contr. 54, 346–353 (2009) – 10.1109/tac.2008.2007879