IDA-PBC for Polynomial Systems: An SOS-based Approach

Authors

Oscar B. Cieza, Johann Reger

Abstract

Algebraic solutions for the Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) problem are introduced for a class of affine polynomial systems. These classes do not involve to solve partial differential equations for the matching condition. The proposed procedure leads to conditions that may be solved by using sum of squares (SOS) and semidefinite programming (SDP). Furthermore, some special parametrizations for the desired Hamiltonian function are analyzed and respective reductions into SOS inequalities are provided. Results are validated on a polynomial second order system and the well-known cart-pole system.

Keywords

Port-Hamiltonian Systems; IDA-PBC; Polynomial Systems; Sum of Squares

Citation

• Journal: IFAC-PapersOnLine
• Year: 2018
• Volume: 51
• Issue: 13
• Pages: 366–371
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2018.07.306
• Note: 2nd IFAC Conference on Modelling, Identification and Control of Nonlinear Systems MICNON 2018- Guadalajara, Jalisco, Mexico, 20–22 June 2018

BibTeX

@article{Cieza_2018,
  title={{IDA-PBC for Polynomial Systems: An SOS-based Approach}},
  volume={51},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2018.07.306},
  number={13},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Cieza, Oscar B. and Reger, Johann},
  year={2018},
  pages={366--371}
}

Download the bib file

References

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