{"ID":2824135,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.24493","arxiv_id":"2512.24493","title":"Bayesian Safety Guarantees for Port-Hamiltonian Systems with Learned Energy Functions","abstract":"Control barrier functions for port-Hamiltonian systems inherit model uncertainty when the Hamiltonian is learned from data. We show how to propagate this uncertainty into a safety filter with independently tunable credibility budgets. To propagate this uncertainty, we employ a two-stage Bayesian approach. First, posterior prediction over the Hamiltonian yields credible bands for the energy storage, producing Bayesian barriers whose safe sets are high-probability inner approximations of the true allowable set with credibility $1 - (η_{\\mathrm{ptB}})$. Independently, a drift credible ellipsoid accounts for vector field uncertainty in the CBF inequality with credibility $1 - (η_{\\rm dr})$. Since energy and drift uncertainties enter through disjoint credible sets, the end-to-end safety guarantee is at least $1 - (η_{\\rm dr} + η_{\\mathrm{ptB}})$. Experiments on a mass-spring oscillator with a GP-learned Hamiltonian show that the proposed filter preserves safety despite limited and noisy observations. Moreover, we show that the proposed framework yields a larger safe set than an unstructured GP-CBF alternative on a planar manipulator.","short_abstract":"Control barrier functions for port-Hamiltonian systems inherit model uncertainty when the Hamiltonian is learned from data. We show how to propagate this uncertainty into a safety filter with independently tunable credibility budgets. To propagate this uncertainty, we employ a two-stage Bayesian approach. First, poster...","url_abs":"https://arxiv.org/abs/2512.24493","url_pdf":"https://arxiv.org/pdf/2512.24493v2","authors":"[\"Chi Ho Leung\",\"Philip E. Paré\"]","published":"2025-12-30T22:24:37Z","proceeding":"eess.SY","tasks":"[\"eess.SY\",\"cs.RO\"]","methods":"[]","has_code":false}