Uncertainties arising in various control systems, such as robots that are subject to unknown disturbances or environmental variations, pose significant challenges for ensuring system safety, such as collision avoidance. At the same time, safety specifications are getting more and more complex, e.g., by composing multiple safety objectives through Boolean operators resulting in non-smooth descriptions of safe sets. Control Barrier Functions (CBFs) have emerged as a control technique to provably guarantee system safety. In most settings, they rely on an assumption of having deterministic dynamics and smooth safe sets. This paper relaxes these two assumptions by extending CBFs to encompass control systems with stochastic dynamics and safe sets defined by non-smooth functions. By explicitly considering the stochastic nature of system dynamics and accommodating complex safety specifications, our method enables the design of safe control strategies in uncertain and complex systems. We provide formal guarantees on the safety of the system by leveraging the theoretical foundations of stochastic CBFs and non-smooth safe sets. Numerical simulations demonstrate the effectiveness of the approach in various scenarios.

翻译：各类控制系统中存在的不确定性（例如受未知扰动或环境变化影响的机器人系统）给确保系统安全性（如避碰）带来了重大挑战。与此同时，安全规范日益复杂，例如通过布尔运算符组合多个安全目标，导致安全集呈现非光滑描述。控制障碍函数（CBFs）作为一种可证明保证系统安全性的控制技术应运而生。在多数场景下，该技术依赖确定性动力学与光滑安全集的假设。本文通过扩展CBFs以涵盖随机动力学系统及非光滑函数定义的安全集，放宽了这两项假设。通过显式考虑系统动力学的随机特性并兼容复杂安全规范，我们的方法能够在不确定与复杂系统中设计安全控制策略。基于随机CBFs与非光滑安全集的理论基础，我们提供了系统安全性的形式化保证。数值仿真验证了该方法在多种场景下的有效性。