Work

Energy-Optimal Control of Discrete-Time Port-Hamiltonian Systems

Year: 2025

Type: article

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 work, 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.

Source: IEEE Control Systems Letters

DOI: 10.1109/lcsys.2025.3579391

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

Institutions: Brandenburg University of Technology Cottbus-Senftenberg, University of Groningen, Chemnitz University of Technology, Technische Universität Ilmenau

Language: English

Topic: Control and Stability of Dynamical Systems

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Nederlandse Organisatie voor Wetenschappelijk Onderzoek, Ministry of Education and Research, Romania

Awards: G3269320301, Optimierungsbasierte und datengetriebene Steuerung und Regelung unter Nutzung portHamiltonscher Strukturen, TeSoPs: Technologically and Socially feasible transition Pathways for local energy system integration