Adaptive parallel simultaneous stabilization of a set of uncertain port‐controlled hamiltonian systems subject to actuator saturation

Authors

Abstract

This paper investigates adaptive parallel simultaneous stabilization (APSS) of a set of uncertain nonlinear port‐controlled Hamiltonian (PCH) systems subject to actuator saturation and proposes a number of results on the design of the APSS controllers. First, the case of two PCH systems is studied. Using both the dissipative Hamiltonian structural and saturated actuator properties, the two systems are combined to generate an augmented PCH system, with which, some results on the control designs are then obtained. When there are external disturbances in the two systems, anH ∞ APSS controller is designed for the systems. Second, the case of more than two uncertain PCH systems subject to actuator saturation is investigated, and several new results are proposed for the APSS problem. Finally, an illustrative example is presented to show that the adaptive stabilization controllers obtained in this paper work very well. Copyright © 2013 John Wiley & Sons, Ltd.

Citation

Journal: International Journal of Adaptive Control and Signal Processing
Year: 2014
Volume: 28
Issue: 11
Pages: 1128–1144
Publisher: Wiley
DOI: 10.1002/acs.2433

BibTeX

@article{Wei_2013,
  title={{Adaptive parallel simultaneous stabilization of a set of uncertain port‐controlled hamiltonian systems subject to actuator saturation}},
  volume={28},
  ISSN={1099-1115},
  DOI={10.1002/acs.2433},
  number={11},
  journal={International Journal of Adaptive Control and Signal Processing},
  publisher={Wiley},
  author={Wei, Airong and Wang, Yuzhen},
  year={2013},
  pages={1128--1144}
}

Download the bib file

References

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
Transient stabilization of multimachine power systems with nontrivial transfer conductances. IEEE Trans. Automat. Contr. 50, 60–75 (2005) – 10.1109/tac.2004.840477
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
Maschke, B., Ortega, R. & Van Der Schaft, A. J. Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation. IEEE Trans. Automat. Contr. 45, 1498–1502 (2000) – 10.1109/9.871758
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
Van der Schaft AJ, L2‐Gain and Passivity Techniques in Nonlinear Control (1999)
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
Yuzhen Wang, Daizhan Cheng, Chunwen Li & You Ge. Dissipative hamiltonian realization and energy-based L/sub 2/-disturbance attenuation control of multimachine power systems. IEEE Trans. Automat. Contr. 48, 1428–1433 (2003) – 10.1109/tac.2003.815037
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
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
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
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
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
Advanced Strategies in Control Systems with Input and Output Constraints. Lecture Notes in Control and Information Sciences (Springer Berlin Heidelberg, 2007). doi:10.1007/978-3-540-37010-9 – 10.1007/978-3-540-37010-9
Gomes da Silva JM, Antiwindup design with guaranteed regions of stability: an LMI‐based approach. IEEE Transactions on Automatic Control (2005)
Montagner, V. F., Oliveira, R. C. L. F., Peres, P. L. D., Tarbouriech, S. & Queinnec, I. Gain-Scheduled Controllers for Linear Parameter-Varying Systems with Saturating Actuators: LMI-based Design. 2007 American Control Conference 6067–6072 (2007) doi:10.1109/acc.2007.4282551 – 10.1109/acc.2007.4282551
Castelan, E. B., Corso, J., Moreno, U. F. & De Pieri, E. R. STABILITY AND STABILIZATION OF A CLASS OF UNCERTAIN NONLINEAR DISCRETE-TIME SYSTEMS WITH SATURATING ACTUATORS. IFAC Proceedings Volumes 40, 518–523 (2007) – 10.3182/20071017-3-br-2923.00083
Wei, A., Wang, Y. & Hu, X. Estimate of Domain of Attraction for a Class of Port‐Controlled Hamiltonian Systems Subject to Both Actuator Saturation and Disturbances. Asian Journal of Control 14, 1108–1112 (2011) – 10.1002/asjc.392
Ho-Mock-Qai, B. & Dayawansa, W. P. Simultaneous Stabilization of Linear and Nonlinear Systems by Means of Nonlinear State Feedback. SIAM J. Control Optim. 37, 1701–1725 (1999) – 10.1137/s0363012997315610
Wu, J.-L. Simultaneous stabilization for a collection of single-input nonlinear systems. IEEE Trans. Automat. Contr. 50, 328–337 (2005) – 10.1109/tac.2005.843877
Blondel, V. Simultaneous Stabilization of Linear Systems. Lecture Notes in Control and Information Sciences (Springer Berlin Heidelberg, 1994). doi:10.1007/3-540-19862-8 – 10.1007/3-540-19862-8
Kabamba, P. T. & Yang, C. Simultaneous controller design for linear time-invariant systems. IEEE Trans. Automat. Contr. 36, 106–111 (1991) – 10.1109/9.62275
Miller, D. E. & Tongwen Chen. Simultaneous stabilization with near-optimal H∞ performance. IEEE Trans. Automat. Contr. 47, 1986–1998 (2002) – 10.1109/tac.2002.805687
Schmitendorf, W. E. & Hollot, C. V. Simultaneous stabilization via linear state feedback control. IEEE Trans. Automat. Contr. 34, 1001–1005 (1989) – 10.1109/9.35818
Wang, Y., Feng, G. & Cheng, D. Simultaneous stabilization of a set of nonlinear port-controlled Hamiltonian systems. Automatica 43, 403–415 (2007) – 10.1016/j.automatica.2006.09.008
Sun, W., Lin, Z. & Wang, Y. Global asymptotic and finite-gain \(L_{2}\) stabilization of port-controlled Hamiltonian systems subject to actuator saturation. 2009 American Control Conference 1894–1898 (2009) doi:10.1109/acc.2009.5160232 – 10.1109/acc.2009.5160232
Wei, A. & Wang, Y. Stabilization and \(H_{\infty}\) control of nonlinear port-controlled Hamiltonian systems subject to actuator saturation. Automatica 46, 2008–2013 (2010) – 10.1016/j.automatica.2010.08.001
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