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.

翻译：针对从数据中学习Hamiltonian的port-Hamiltonian系统，控制障碍函数会继承模型不确定性。我们展示了如何将该不确定性传播至具有独立可调置信度预算的安全性滤波器中。为传播该不确定性，我们采用两阶段贝叶斯方法：首先，对Hamiltonian的后验预测给出能量存储的置信带，从而生成贝叶斯障碍函数，其安全集以至少$1 - (η_{\mathrm{ptB}})$的置信度为真实容许集的高概率内逼近；独立地，漂移置信椭球以至少$1 - (η_{\rm dr})$的置信度刻画CBF不等式中的向量场不确定性。由于能量与漂移不确定性通过不相交的置信集引入，端到端安全性保证至少为$1 - (η_{\rm dr} + η_{\mathrm{ptB}})$。在采用高斯过程学习Hamiltonian的质量-弹簧振荡器上的实验表明，尽管观测有限且含噪，所提滤波仍能保持安全性。进一步，在平面机械臂上，该框架比无结构GP-CBF方法产生更大的安全集。