Control barrier functions (CBFs) have recently been introduced as a systematic tool to ensure safety by establishing set invariance. When combined with a control Lyapunov function (CLF), they form a safety-critical control mechanism. However, the effectiveness of CBFs and CLFs is closely tied to the system model. In practice, model uncertainty can jeopardize safety and stability guarantees and may lead to undesirable performance. In this paper, we develop a safe learning-based control strategy for switching systems in the face of uncertainty. We focus on the case that a nominal model is available for a true underlying switching system. This uncertainty results in piecewise residuals for each switching surface, impacting the CLF and CBF constraints. We introduce a batch multi-output Gaussian process (MOGP) framework to approximate these piecewise residuals, thereby mitigating the adverse effects of uncertainty. A particular structure of the covariance function enables us to convert the MOGP-based chance constraints CLF and CBF into second-order cone constraints, which leads to a convex optimization. We analyze the feasibility of the resulting optimization and provide the necessary and sufficient conditions for feasibility. The effectiveness of the proposed strategy is validated through a simulation of a switching adaptive cruise control system.

翻译：控制障碍函数（CBF）近期被引入作为一种系统化工具，通过建立集合不变性来确保安全性。当与控制李雅普诺夫函数（CLF）结合时，它们构成了安全关键控制机制。然而，CBF和CLF的有效性与系统模型紧密相关。在实践中，模型不确定性可能危及安全性和稳定性保证，并导致不良性能。本文针对存在不确定性的切换系统，开发了一种基于学习的安全控制策略。我们聚焦于真实底层切换系统存在名义模型的情形。这种不确定性会导致每个切换面上的分段残差，进而影响CLF和CBF约束。我们引入一种批处理多输出高斯过程（MOGP）框架来近似这些分段残差，从而减轻不确定性的不利影响。协方差函数的特定结构使我们能够将基于MOGP的CLF和CBF机会约束转化为二阶锥约束，进而形成凸优化问题。我们分析了该优化问题的可行性，并给出了可行性的充要条件。通过切换自适应巡航控制系统的仿真验证了所提策略的有效性。