On Stabilization of Mixed Dimensional Parameter Port Hamiltonian Systems Via Energy Shaping

Authors

Abstract

For systems described by Port-Hamiltonian (PH) equations, the Control by Interconnection method, based on the existence of Casimir functions, provides a simple and elegant procedure for stabilization of nonlinear systems with finite dissipation. This work explores the possibility of extending this technique to the case where the plant contains an infinite-dimensional subsystem. Conditions for the existence of Casimir functions reveal the constraints for the application of the design procedure. A simple example of an RLC circuit coupled with an infinite-dimensional transmission line illustrates the main ideas of this paper.

Keywords

Aerodynamic Force; Dirac Structure; Casimir Function; Dissipative Element; Total Energy Function

Citation

ISBN: 9783319209876
Publisher: Springer International Publishing
DOI: 10.1007/978-3-319-20988-3_16

BibTeX

@inbook{Rodr_guez_Cort_s_2015,
  title={{On Stabilization of Mixed Dimensional Parameter Port Hamiltonian Systems Via Energy Shaping}},
  ISBN={9783319209883},
  ISSN={1610-7411},
  DOI={10.1007/978-3-319-20988-3_16},
  booktitle={{Mathematical Control Theory I}},
  publisher={Springer International Publishing},
  author={Rodríguez-Cortés, H.},
  year={2015},
  pages={303--320}
}

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References

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