Authors

Arijit Sarkar, Vaibhav Kumar Singh, Manuel Schaller, Karl Worthmann

Abstract

In this letter, we study the energy-optimal control of nonlinear port-Hamiltonian (pH) systems in discrete time. For continuous-time pH systems, energy-optimal control problems are strictly dissipative by design. This property, stating that the system to be optimized is dissipative with the cost functional as a supply rate, implies a stable long-term behavior of optimal solutions and enables stability results in predictive control. In this letter, we show that the crucial property of strict dissipativity is not straightforwardly preserved by any energy-preserving integrator such as the implicit midpoint rule. Then, we prove that discretizations via difference and differential representations lead to strictly dissipative discrete-time optimal control problems. Consequently, we rigorously show a stable long-term behavior of optimal solutions in the form of a manifold (subspace) turnpike property. Finally, we validate our findings using two numerical examples.

Citation

  • Journal: IEEE Control Systems Letters
  • Year: 2025
  • Volume: 9
  • Issue:
  • Pages: 1526–1531
  • Publisher: Institute of Electrical and Electronics Engineers (IEEE)
  • DOI: 10.1109/lcsys.2025.3579391

BibTeX

@article{Sarkar_2025,
  title={{Energy-Optimal Control of Discrete-Time Port-Hamiltonian Systems}},
  volume={9},
  ISSN={2475-1456},
  DOI={10.1109/lcsys.2025.3579391},
  journal={IEEE Control Systems Letters},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Sarkar, Arijit and Kumar Singh, Vaibhav and Schaller, Manuel and Worthmann, Karl},
  year={2025},
  pages={1526--1531}
}

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References