A class of port-controlled Hamiltonian systems

Authors

Abstract

In this paper, we examine a particular class of port-controlled Hamiltonian systems for which the equations can be written in a form that is very similar to the equations of a linear passive system. We examine the passivity of such a system around an equilibrium point (u0,x0), which generates the output y0. We show that under some mild assumptions, a new Hamiltonian can be found such that the system is again passive with respect to the new supply rate (y-y0)^T(u-u0).

Citation

Journal: Proceedings of the 44th IEEE Conference on Decision and Control
Year: 2006
Volume:
Issue:
Pages: 5630–5632
Publisher: IEEE
DOI: 10.1109/cdc.2005.1583059

BibTeX

@inproceedings{Jayawardhana,
  title={{A class of port-controlled Hamiltonian systems}},
  DOI={10.1109/cdc.2005.1583059},
  booktitle={{Proceedings of the 44th IEEE Conference on Decision and Control}},
  publisher={IEEE},
  author={Jayawardhana, B. and Weiss, G.},
  pages={5630--5632}
}

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References

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
Jayawardhana, B. Tracking and disturbance rejection for passive nonlinear systems. Proceedings of the 44th IEEE Conference on Decision and Control 3333–3338 doi:10.1109/cdc.2005.1582676 – 10.1109/cdc.2005.1582676
dugundji, Topology (1966)
showalter, Monotone Operators in Banach Space and Nonlinear Partial Differential Equations (1996)
van der Schaft, A. L2 - Gain and Passivity Techniques in Nonlinear Control. Communications and Control Engineering (Springer London, 2000). doi:10.1007/978-1-4471-0507-7 – 10.1007/978-1-4471-0507-7
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
Ortega, R., Loría, A., Nicklasson, P. J. & Sira-Ramírez, H. Passivity-Based Control of Euler-Lagrange Systems. Communications and Control Engineering (Springer London, 1998). doi:10.1007/978-1-4471-3603-3 – 10.1007/978-1-4471-3603-3