We study safe control for dynamical systems whose continuous-time dynamics are learned with Gaussian processes (GPs), focusing on mechanical and port-Hamiltonian systems where safety is naturally expressed via energy constraints. The availability of a GP Hamiltonian posterior naturally raises the question of how to systematically exploit this structure to design an energy-aware control barrier function with high-probability safety guarantees. We address this problem by developing a Bayesian-CBF framework and instantiating it with energy-aware Bayesian-CBFs (EB-CBFs) that construct conservative energy-based barriers directly from the Hamiltonian and vector-field posteriors, yielding safety filters that minimally modify a nominal controller while providing probabilistic energy safety guarantees. Numerical simulations on a mass-spring system demonstrate that the proposed EB-CBFs achieve high-probability safety under noisy sampled GP-learned dynamics.

翻译：本研究针对通过高斯过程（GPs）学习连续时间动力学的动态系统，探索其安全控制问题，重点关注机械系统与端口哈密顿系统——这类系统的安全性通常可通过能量约束自然表达。当获得高斯过程哈密顿量后验分布时，一个核心问题是如何系统性地利用该结构来设计具有高概率安全保证的能量感知控制屏障函数。为解决此问题，我们提出了贝叶斯控制屏障函数框架，并通过能量感知贝叶斯控制屏障函数（EB-CBFs）进行实例化。该方法直接从哈密顿量与向量场的后验分布构建基于能量的保守屏障，从而生成安全性滤波器；该滤波器在提供概率性能量安全保证的同时，对标称控制器进行最小程度的修正。在质量-弹簧系统上的数值仿真表明，所提出的EB-CBFs在噪声采样高斯过程学习动力学下能够实现高概率安全性。