On feedback equivalence to port controlled Hamiltonian systems

Authors

Daizhan Cheng, Alessandro Astolfi, Romeo Ortega

Abstract

In the last few years port controlled Hamiltonian (PCH) systems have emerged as an interesting class of nonlinear models suitable for a large number of physical applications. In this paper we study the question of feedback equivalence of nonlinear systems to PCH systems. More precisely, we give conditions under which a general nonlinear system can be transformed into a PCH system via static state feedback. We consider the two extreme cases where the target PCH system is completely a priori fixed or completely free, as well as the case where it is only partially predetermined. When the energy function is free a set of partial differential equations needs to be solved, on the other hand, if it is fixed we have to deal with a set of algebraic equations. In the former case, we give some verifiable necessary and sufficient conditions for solvability. As a by-product of our analysis we obtain some stabilization results for nonlinear systems.

Keywords

Hamiltonian systems; Linear-gradient systems; Passivity-based control; Feedback equivalence

Citation

Journal: Systems & Control Letters
Year: 2005
Volume: 54
Issue: 9
Pages: 911–917
Publisher: Elsevier BV
DOI: 10.1016/j.sysconle.2005.02.005

BibTeX

@article{Cheng_2005,
  title={{On feedback equivalence to port controlled Hamiltonian systems}},
  volume={54},
  ISSN={0167-6911},
  DOI={10.1016/j.sysconle.2005.02.005},
  number={9},
  journal={Systems &amp; Control Letters},
  publisher={Elsevier BV},
  author={Cheng, Daizhan and Astolfi, Alessandro and Ortega, Romeo},
  year={2005},
  pages={911--917}
}

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