New PHS-DP framework simplifies trajectory tracking without PDEs

A team led by Jinjun Jia introduced Port-Hamiltonian Systems with Dissipation Potential (PHS-DP), a new framework that addresses a long-standing limitation in port-Hamiltonian control. Traditional methods rely on damping matrices to modify momentum-dependent dynamics, forcing engineers to solve a difficult matching partial differential equation (PDE) for trajectory tracking. PHS-DP replaces the damping matrix with scalar convex dissipation potentials, creating separate scalar objects for momentum and auxiliary state channels. This restores variational symmetry between stored and dissipated energy, enabling a new control strategy called Dual Potential Shaping Control (DPSC). DPSC achieves trajectory tracking by sequentially shaping potential energy and dissipation potentials without altering the interconnection structure. The closed-loop cascade contracts via a hierarchical argument, and the matching condition is automatically satisfied for any admissible choice of shaped potentials—no PDE solving required.

Unlike existing PDE-free energy shaping methods that sacrifice the port-Hamiltonian closed-loop structure and lose physical interpretability, PHS-DP preserves the interconnection structure and maintains a transparent energy-based interpretation throughout the design. The authors validated their approach on a magnetic levitation system, demonstrating tracking performance comparable to timed IDA-PBC but with substantially reduced design complexity. This work offers a practical path for modeling and controlling complex physical systems (e.g., robotics, power systems) while retaining the clarity of energy-based reasoning. The paper is available on arXiv (2605.12971).