Estimating and enlarging the domain of attraction in IDA-PBC

Authors

Abstract

Interconnection and damping assignment passivity- based control (IDA-PBC) is a nonlinear state feedback technique that endows the closed-loop system with a port-Hamiltonian (PH) structure. The assigned energy function qualifies as a Lyapunov function and thus can be used to estimate the domain of attraction (DA). However, determining the largest bounded sublevel set of a general energy function which is contained in the DA is a difficult task. In this paper, a numerical algorithm is developed to cope with this problem without formulating conditions on the energy function. Moreover, an optimization procedure is proposed to determine a controller parametrization which maximizes the estimated DA, while simultaneously taking account of desired closed-loop performance. An illustrative example is included, where also a comparison to a linear state feedback controller is presented.

Citation

Journal: 2012 IEEE 51st IEEE Conference on Decision and Control (CDC)
Year: 2012
Volume:
Issue:
Pages: 1852–1858
Publisher: IEEE
DOI: 10.1109/cdc.2012.6426473

BibTeX

@inproceedings{Kloiber_2012,
  title={{Estimating and enlarging the domain of attraction in IDA-PBC}},
  DOI={10.1109/cdc.2012.6426473},
  booktitle={{2012 IEEE 51st IEEE Conference on Decision and Control (CDC)}},
  publisher={IEEE},
  author={Kloiber, Tobias and Kotyczka, Paul},
  year={2012},
  pages={1852--1858}
}

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References

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