Port-Transversal Barriers: Graph-Theoretic Safety for Port-Hamiltonian Systems
This work addresses safety verification for control systems in engineering domains, but it is incremental as it builds on existing port-Hamiltonian and control barrier function frameworks.
The paper tackles the problem of ensuring safety in port-Hamiltonian systems by deriving a graph-theoretic method to bound the relative degree of safety constraints, showing that enforceability depends on input topology, and validating this on an LC ladder network where capacitor charge constraint enforceability is determined solely by input topology.
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.