Control of port-Hamiltonian systems with minimal energy supply

Authors

Manuel Schaller, Friedrich Philipp, Timm Faulwasser, Karl Worthmann, Bernhard Maschke

Abstract

We investigate optimal control of linear port-Hamiltonian systems with control constraints, in which one aims to perform a state transition with minimal energy supply. Decomposing the state space into dissipative and non-dissipative (i.e. conservative) subspaces, we show that the set of reachable states is bounded w.r.t. the dissipative subspace. We prove that the optimal control problem exhibits the turnpike property with respect to the non-dissipative subspace, i.e., for varying initial conditions and time horizons optimal state trajectories evolve close to the conservative subspace most of the time. We analyze the corresponding steady-state optimization problem and prove that all optimal steady states lie in the non-dissipative subspace. We conclude this paper by illustrating these results by a numerical example from mechanics.

Keywords

Dissipativity; Minimal energy supply; Optimal control; Port-Hamiltonian systems; Turnpike property

Citation

• Journal: European Journal of Control
• Year: 2021
• Volume: 62
• Issue:
• Pages: 33–40
• Publisher: Elsevier BV
• DOI: 10.1016/j.ejcon.2021.06.017
• Note: 2021 European Control Conference Special Issue

BibTeX

@article{Schaller_2021,
  title={{Control of port-Hamiltonian systems with minimal energy supply}},
  volume={62},
  ISSN={0947-3580},
  DOI={10.1016/j.ejcon.2021.06.017},
  journal={European Journal of Control},
  publisher={Elsevier BV},
  author={Schaller, Manuel and Philipp, Friedrich and Faulwasser, Timm and Worthmann, Karl and Maschke, Bernhard},
  year={2021},
  pages={33--40}
}

Download the bib file

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