Energy-based control for hybrid port-controlled Hamiltonian systems

Authors

Wassim M. Haddad, Sergey G. Nersesov, VijaySekhar Chellaboina

Abstract

In this paper we develop an energy-based hybrid control framework for hybrid port-controlled Hamiltonian systems. In particular, we obtain constructive sufficient conditions for hybrid feedback stabilization that provide a shaped energy function for the closed-loop system, while preserving a hybrid Hamiltonian structure at the closed-loop level. Furthermore, an inverse optimal hybrid feedback control framework is developed that characterizes a class of globally stabilizing energy-based controllers that guarantee hybrid sector and gain margins to multiplicative input uncertainty of hybrid Hamiltonian systems.

Keywords

Port-controlled Hamiltonian systems; Hybrid systems; Impulsive dynamical systems; Energy functions; Energy-based control; Optimal control

Citation

• Journal: Automatica
• Year: 2003
• Volume: 39
• Issue: 8
• Pages: 1425–1435
• Publisher: Elsevier BV
• DOI: 10.1016/s0005-1098(03)00113-4

BibTeX

@article{Haddad_2003,
  title={{Energy-based control for hybrid port-controlled Hamiltonian systems}},
  volume={39},
  ISSN={0005-1098},
  DOI={10.1016/s0005-1098(03)00113-4},
  number={8},
  journal={Automatica},
  publisher={Elsevier BV},
  author={Haddad, Wassim M. and Nersesov, Sergey G. and Chellaboina, VijaySekhar},
  year={2003},
  pages={1425--1435}
}

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References

• Antsaklis, P. J. & Nerode, A. Hybrid Control Systems: An Introductory Discussion to the Special Issue. IEEE Trans. Automat. Contr. 43, 457–460 (1998) – 10.1109/tac.1998.664148
• Brogliato, (1999)
• Impacts in Mechanical Systems. Lecture Notes in Physics (Springer Berlin Heidelberg, 2000). doi:10.1007/3-540-45501-9 – 10.1007/3-540-45501-9
• Chellaboina, V., Bhat, S. P. & Haddad, W. M. An invariance principle for nonlinear hybrid and impulsive dynamical systems. Nonlinear Analysis: Theory, Methods & Applications 53, 527–550 (2003) – 10.1016/s0362-546x(02)00316-4
• Haddad, W. M. & Chellaboina, V. Dissipativity theory and stability of feedback interconnectionsfor hybrid dynamical systems. Mathematical Problems in Engineering 7, 299–335 (2001) – 10.1155/s1024123x01001661
• Haddad, On the equivalence between dissipativity and optimality of nonlinear hybrid controllers. International Journal of Hybrid Systems (2001)
• Haddad, W. M. et al. Non-linear impulsive dynamical systems. Part I: Stability and dissipativity. International Journal of Control 74, 1631–1658 (2001) – 10.1080/00207170110081705
• Haddad, W. M., Chellaboina, V. & Kablar, N. A. Non-linear impulsive dynamical systems. Part II: Stability of feedback interconnections and optimality. International Journal of Control 74, 1659–1677 (2001) – 10.1080/00207170110080959
• Lakshmikantham, (1989)
• Ortega, R., van der Schaft, A. J. & Maschke, B. M. Stabilization of port-controlled Hamiltonian systems via energy balancing. Lecture Notes in Control and Information Sciences 239–260 (1999) doi:10.1007/1-84628-577-1_13 – 10.1007/1-84628-577-1_13
• Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Energy-shaping of port-controlled Hamiltonian systems by interconnection. Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304) vol. 2 1646–1651 – 10.1109/cdc.1999.830260
• 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
• Yang, (2001)