Port-Transversal Barriers: Graph-Theoretic Safety for Port-Hamiltonian Systems

TL;DR

This paper introduces a graph-theoretic framework for analyzing safety constraints in port-Hamiltonian systems, linking energy compartment structure to barrier function design.

Contribution

It establishes a novel graph-based method to determine safety barrier feasibility and designs candidate barrier functions based on system topology.

Findings

Shortest-path distance bounds the relative degree of safety constraints.

No smooth static feedback can reduce the relative degree if no path exists.

Barrier functions of relative degree one can be constructed under certain connectivity conditions.

Abstract

We study port-Hamiltonian systems with energy functions that split into local storage terms. From the interconnection and dissipation structure, we construct a graph on the energy compartments. From this graph, we show that the shortest-path distance from a constrained compartment to the nearest actuated one gives a lower bound on the relative degree of the corresponding safety constraint. We also show that no smooth static feedback can reduce it when no path exists. When the relative degree exceeds one and the immediate graph neighbors of the constrained compartment is connected to at least one input port, we reshape the constraint by subtracting their shifted local storages, producing a candidate barrier function of relative degree one. We then identify sufficient regularity conditions that recover CBF feasibility under bounded inputs. We validate the framework on an LC ladder network, where the enforceability of a capacitor charge constraint depends only on the input topology.