Authors

Hannes Gernandt, Manuel Schaller

Abstract

In this note, we consider port-Hamiltonian structures in numerical optimal control of ordinary differential equations. By introducing a novel class of nonlinear monotone port-Hamiltonian (pH) systems, we show that the primal–dual gradient method may be viewed as an infinite-dimensional nonlinear pH system. The monotonicity and the particular block structure arising in the optimality system is used to prove exponential stability of the dynamics towards its equilibrium, which is a critical point of the first-order optimality conditions. Leveraging the port-based modeling, we propose an optimization-based controller in a suboptimal receding horizon control fashion. To this end, the primal–dual gradient based optimizer-dynamics is coupled to a pH plant dynamics in a power-preserving manner. We show that the resulting model is again monotone pH system and prove that the closed-loop exhibits local exponential convergence towards the equilibrium.

Keywords

Monotone operator; Port-Hamiltonian system; Optimal control; Passivity; Primal–dual gradient method; Control-by-interconnection

Citation

BibTeX

@article{Gernandt_2025,
  title={{Port-Hamiltonian structures in infinite-dimensional optimal control: Primal–Dual gradient method and control-by-interconnection}},
  volume={197},
  ISSN={0167-6911},
  DOI={10.1016/j.sysconle.2025.106030},
  journal={Systems & Control Letters},
  publisher={Elsevier BV},
  author={Gernandt, Hannes and Schaller, Manuel},
  year={2025},
  pages={106030}
}

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References