Energy-optimal predictive control of discrete-time port-Hamiltonian systems: Closed-loop practical stability
Abstract
We study a dissipativity-based model predictive control (MPC) scheme for energy-optimal constrained output stabilization of a discrete-time nonlinear SISO port-Hamiltonian system described by difference and differential representation. For the optimal control problem to be solved in each MPC step, we establish a measure turnpike behavior. The turnpike set in our work is obtained from the underlying port-Hamiltonian structure without assuming existence of steady-states or periodic orbits. In particular, unlike existing results which typically establish the turnpike property w.r.t. a controlled forward invariant set such as optimal steady-states or optimal periodic orbits, we do not require the turnpike set to be forward control invariant. For MPC, we establish recursive feasibility and show practical stability to the turnpike set w.r.t. the MPC closed loop leveraging both dissipativity and the port-Hamiltonian structure. Finally, we demonstrate our results using two numerical examples.
Related
- Optimal Riesz mean inequalities for the Coulomb Hamiltonian
- Fourth-Order Energy-Consistent Average Vector Field Discrete Gradient Methods for Dissipative Hamiltonian Systems
- Exponential stability of port-Hamiltonian systems with unstructured, measurable Hamiltonian densities
- Input-to-state stability of second-order port-Hamiltonian systems under nonlinear dynamic boundary feedback
- The supersymmetric Scarf I Hamiltonian with reflections and its discrete para-Bannai--Ito version
BibTeX
@misc{singh2026energyoptimal,
title = {{Energy-optimal predictive control of discrete-time port-Hamiltonian systems: Closed-loop practical stability}},
author = {Vaibhav Kumar Singh and Manuel Schaller and Timm Faulwasser and Karl Worthmann},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25920},
eprint = {2609.25920},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25920},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Energy-optimal predictive control of discrete-time port-Hamiltonian systems: Closed-loop practical stability
AU - Vaibhav Kumar Singh
AU - Manuel Schaller
AU - Timm Faulwasser
AU - Karl Worthmann
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.25920
UR - https://arxiv.org/abs/2609.25920
AB - We study a dissipativity-based model predictive control (MPC) scheme for energy-optimal constrained output stabilization of a discrete-time nonlinear SISO port-Hamiltonian system described by difference and differential representation. For the optimal control problem to be solved in each MPC step, we establish a measure turnpike behavior. The turnpike set in our work is obtained from the underlying port-Hamiltonian structure without assuming existence of steady-states or periodic orbits. In particular, unlike existing results which typically establish the turnpike property w.r.t. a controlled forward invariant set such as optimal steady-states or optimal periodic orbits, we do not require the turnpike set to be forward control invariant. For MPC, we establish recursive feasibility and show practical stability to the turnpike set w.r.t. the MPC closed loop leveraging both dissipativity and the port-Hamiltonian structure. Finally, we demonstrate our results using two numerical examples.
ER -