Co-Learning Port-Hamiltonian Systems and Optimal Energy-Shaping Control

A team from Michigan State University—Ankur Kamboj, Biswadip Dey, and Vaibhav Srivastava—has introduced a novel physics-informed learning framework for energy-shaping control of port-Hamiltonian (pH) systems. The approach, detailed in a preprint on arXiv (2604.26172), co-learns a pH system model and an optimal energy-balancing passivity-based controller (EB-PBC) through alternating optimization with policy-aware data collection. At each iteration, the system model is refined using trajectory data gathered under the current control policy, and the controller is re-optimized on the updated model. Both components are parameterized by neural networks that embed the pH dynamics and EB-PBC structure, ensuring interpretability in terms of energy interactions.

The learned controller renders the closed-loop system inherently passive and provably stable, exploiting passive plant dynamics without canceling the natural potential. A key innovation is dissipation regularization, which enforces strict energy decay during training, enhancing robustness to sim-to-real gaps. The framework was validated on state-regulation and swing-up tasks for planar and torsional pendulum systems, demonstrating its effectiveness in real-world control scenarios. This work bridges machine learning and control theory, offering a data-driven path to designing stable, energy-aware controllers for complex physical systems.