On finite-time stability and stabilization of nonlinear port-controlled Hamiltonian systems

Authors

YuZhen Wang, Gang Feng

Abstract

The finite-time stability and stabilization of nonlinear port-controlled Hamiltonian (PCH) systems are investigated in this paper, and a number of new results are proposed. Firstly, by exploiting the Hamiltonian structural properties, a proper form of the Hamiltonian function is obtained, based on which a finite-time stability criterion is then presented for a class of Hamiltonian systems. Secondly, using the obtained stability criterion and the so-called “energy shaping plus damping injection” technique, the continuous finite-time stabilization problem is studied for the PCH system, and several global stabilization results are provided. Finally, the continuous robust finite-time stabilization of the PCH system with external disturbances is investigated, and two results on designing global robust finite-time stabilizers are obtained. Study of several examples with numerical simulations shows that the control design approach developed in this paper works very well.

Keywords

PCH system; finite-time stability; finite-time stabilization; robust stabilization

Citation

• Journal: Science China Information Sciences
• Year: 2013
• Volume: 56
• Issue: 10
• Pages: 1–14
• Publisher: Springer Science and Business Media LLC
• DOI: 10.1007/s11432-012-4600-0

BibTeX

@article{Wang_2012,
  title={{On finite-time stability and stabilization of nonlinear port-controlled Hamiltonian systems}},
  volume={56},
  ISSN={1869-1919},
  DOI={10.1007/s11432-012-4600-0},
  number={10},
  journal={Science China Information Sciences},
  publisher={Springer Science and Business Media LLC},
  author={Wang, YuZhen and Feng, Gang},
  year={2012},
  pages={1--14}
}

Download the bib file

References

• B M Maschke, Proceedings of the IFAC Symposium on NOLCOS, Bordeaux (1992)
• A J Schaft van der, Archive füur Elektronik und Übertragungstechnik (1995)
• 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
• Ortega, R., Spong, M. W., Gomez-Estern, F. & Blankenstein, G. Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment. IEEE Trans. Automat. Contr. 47, 1218–1233 (2002) – 10.1109/tac.2002.800770
• 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
• 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
• Dalsmo, M. & van der Schaft, A. On Representations and Integrability of Mathematical Structures in Energy-Conserving Physical Systems. SIAM J. Control Optim. 37, 54–91 (1998) – 10.1137/s0363012996312039
• 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
• A J Schaft van der, L2-gain and Passivity Techniques in Nonlinear Control (1999)
• 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
• 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, Y. Z., Song, Y. H. & Li, X. Novel energy-based Lyapunov function for controlled power systems. IEEE Power Eng. Rev. 20, 55–57 (2000) – 10.1109/39.841351
• Xi, Z., Cheng, D., Lu, Q. & Mei, S. Nonlinear decentralized controller design for multimachine power systems using Hamiltonian function method. Automatica 38, 527–534 (2002) – 10.1016/s0005-1098(01)00233-3
• Viola, G., Ortega, R., Banavar, R., Acosta, J. A. & Astolfi, A. Total Energy Shaping Control of Mechanical Systems: Simplifying the Matching Equations Via Coordinate Changes. IEEE Trans. Automat. Contr. 52, 1093–1099 (2007) – 10.1109/tac.2007.899064
• Zaborszky, J., Subramanian, A., Tzyh-Jong Tarn & Keh-Ming Lu. A new state space for emergency control in the interconnected power system. IEEE Trans. Automat. Contr. 22, 505–517 (1977) – 10.1109/tac.1977.1101582
• Hong, Y. Finite-time stabilization and stabilizability of a class of controllable systems. Systems & Control Letters 46, 231–236 (2002) – 10.1016/s0167-6911(02)00119-6
• Yigwruang Hong, Jie Huang & Yangsheng Xu. On an output feedback finite-time stabilization problem. IEEE Trans. Automat. Contr. 46, 305–309 (2001) – 10.1109/9.905699
• Bhat, S. P. & Bernstein, D. S. Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Trans. Automat. Contr. 43, 678–682 (1998) – 10.1109/9.668834
• Bhat, S. P. & Bernstein, D. S. Finite-Time Stability of Continuous Autonomous Systems. SIAM J. Control Optim. 38, 751–766 (2000) – 10.1137/s0363012997321358
• Haimo, V. T. Finite Time Controllers. SIAM J. Control Optim. 24, 760–770 (1986) – 10.1137/0324047
• Yiguang Hong, Jiankui Wang & Daizhan Cheng. Adaptive finite-time control of nonlinear systems with parametric uncertainty. IEEE Trans. Automat. Contr. 51, 858–862 (2006) – 10.1109/tac.2006.875006
• Huang, X., Lin, W. & Yang, B. Global finite-time stabilization of a class of uncertain nonlinear systems. Automatica 41, 881–888 (2005) – 10.1016/j.automatica.2004.11.036
• Ji Li & Chunjiang Qian. Global finite-time stabilization by dynamic output feedback for a class of continuous nonlinear systems. IEEE Trans. Automat. Contr. 51, 879–884 (2006) – 10.1109/tac.2006.874991
• Orlov, Y. Finite Time Stability and Robust Control Synthesis of Uncertain Switched Systems. SIAM J. Control Optim. 43, 1253–1271 (2004) – 10.1137/s0363012903425593
• Daizhan Cheng & Martin, C. Stabilization of nonlinear systems via designed center manifold. IEEE Trans. Automat. Contr. 46, 1372–1383 (2001) – 10.1109/9.948465
• Rosier, L. Homogeneous Lyapunov function for homogeneous continuous vector field. Systems & Control Letters 19, 467–473 (1992) – 10.1016/0167-6911(92)90078-7
• 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