用贝叶斯方法为学习的能量函数提供安全保证，提升系统鲁棒性。
Bayesian Safety Guarantees for Port-Hamiltonian Systems with Learned Energy Functions
- 基于两阶段贝叶斯推断，量化能量函数与系统漂移的不确定性。
- 在质点弹簧系统上验证：即使数据有限且含噪，仍能保持安全。
- 相比无结构方法，安全区域更大，适合需高可靠性的控制场景。
当端口-哈密顿系统中的哈密顿量从数据中学习时，控制屏障函数会继承模型不确定性。本文提出一种两阶段贝叶斯方法，将该不确定性传播至安全滤波器，并可独立设置可信度预算。首先，对哈密顿量的后验预测生成能量存储的可信区间，构建贝叶斯屏障，其安全集为真实允许集的高概率内逼近，可信度为 $1 - \eta_{\mathrm{ptB}}$。其次，通过漂移可信椭球处理控制屏障函数不等式中的向量场不确定性，可信度为 $1 - \eta_{\rm dr}$。由于能量与漂移不确定性由互斥的可信集表示，整体安全保证至少为 $1 - (\eta_{\rm dr} + \eta_{\mathrm{ptB}})$。实验表明，在使用高斯过程（GP）学习哈密顿量的质点弹簧振子系统中，所提滤波器在有限且含噪观测下仍能保持安全。此外，在平面机械臂上，该框架产生的安全集大于无结构的GP-CBF方法。
原文摘要 · Abstract (English)
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.
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