Conformal prediction (CP) has been used to obtain probabilistic bounds on the error between a learned dynamics model and the true but unknown system. Such CP bounds can then be embedded into robust control Lyapunov function (CLF) and control barrier function (CBF) frameworks. However, such an approach does not retain stability/safety guarantees because of the distribution shift between the closed-loop trajectory distribution under the deployed CLF/CBF policy and the trajectory distribution from which the CP bound and its guarantees were derived. To address this issue, we propose an episodic framework that iteratively updates the robust conformal CLF/CBF policy while maintaining stability/safety guarantees across episodes. We achieve this by (1) using adversarially robust conformal prediction, and (2) quantifying a distribution shift budget that allows us to control how much the model error can increase across policy updates. This distribution shift budget is derived via a closed-loop trajectory sensitivity analysis, yielding an implicit and an explicit update rule for the CP bound. We analyze convergence of our algorithm, which we demonstrate on three case studies. To the best of our knowledge, these are the first results that provide stability/safety guarantees for robust conformal CBF/CLF policies.

翻译：共形预测已被用于获取学习动力学模型与真实未知系统之间误差的概率界限。此类共形预测界限可嵌入鲁棒控制李雅普诺夫函数和控制势垒函数框架中。然而，由于部署的CLF/CBF策略下的闭环轨迹分布与推导共形预测界限及其保证所用的轨迹分布之间存在分布偏移，该方法无法保留稳定性/安全性保证。为解决该问题，我们提出一种情节式框架，通过迭代更新鲁棒共形CLF/CBF策略，同时保持跨情节的稳定性/安全性保证。具体通过以下两点实现：(1) 采用对抗鲁棒共形预测；(2) 量化分布偏移预算，用以控制策略更新过程中模型误差的增量幅度。该分布偏移预算通过闭环轨迹灵敏度分析推导得出，得到共形预测界限的隐式与显式更新规则。我们分析了算法的收敛性，并通过三个案例研究进行验证。据我们所知，这是首个为鲁棒共形CBF/CLF策略提供稳定性/安全性保证的研究成果。