aiqbench analysis
This research addresses critical safety challenges in learning-based control by integrating Bayesian uncertainty quantification into port-Hamiltonian systems. The authors demonstrate a two-stage approach that propagates model uncertainty through energy storage and vector field dynamics to provide rigorous, high-probability safety guarantees even with noisy data. For readers focused on reliable AI deployment in physical systems, this work offers a principled method to maintain stability when using Gaussian Process-learned Hamiltonians.
Bayesian Safety Guarantees for Port-Hamiltonian Systems with Learned Energy Functions
arXiv:2512.24493v3 Announce Type: replace-cross 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 $1 - (\eta_{\mathrm{ptB}})$. Independently, a drift credible ellipsoid accounts for vector field uncertainty in the CBF inequality with credibility $1 - (\eta_{\rm dr})$. Since energy and drift uncertainties enter through disjoint credible sets, the end-to-end safety guarantee is at least $1 - (\eta_{\rm dr} + \eta_{\mathrm{ptB}})$. Experiments on a mass-spring oscillator with a GP-learned Hamiltonian show that the proposed filter preserves safety despite limited and noisy observations.
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 $1 - (\eta_{\mathrm{ptB}})$. Independently, a drift credible ellipsoid accounts for vector field uncertainty in the CBF inequality with credibility $1 - (\eta_{\rm dr})$. Since energy and drift uncertainties enter through disjoint credible sets, the end-to-end safety guarantee is at least $1 - (\eta_{\rm dr} + \eta_{\mathrm{ptB}})$. Experiments on a mass-spring oscillator with a GP-learned Hamiltonian show that the proposed filter preserves safety despite limited and noisy observations.
Systems and Control (eess.SY); Robotics (cs.RO)
arXiv:2512.24493 [eess.SY]
(or arXiv:2512.24493v3 [eess.SY] for this version)
https://doi.org/10.48550/arXiv.2512.24493 Focus to learn more arXiv-issued DOI via DataCite
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