Providing safety guarantees for learning-based controllers is important for real-world applications. One approach to realizing safety for arbitrary control policies is safety filtering. If necessary, the filter modifies control inputs to ensure that the trajectories of a closed-loop system stay within a given state constraint set for all future time, referred to as the set being positive invariant or the system being safe. Under the assumption of fully known dynamics, safety can be certified using control barrier functions (CBFs). However, the dynamics model is often either unknown or only partially known in practice. Learning-based methods have been proposed to approximate the CBF condition for unknown or uncertain systems from data; however, these techniques do not account for input constraints and, as a result, may not yield a valid CBF condition to render the safe set invariant. In this work, we study conditions that guarantee control invariance of the system under input constraints and propose an optimization problem to reduce the conservativeness of CBF-based safety filters. Building on these theoretical insights, we further develop a probabilistic learning approach that allows us to build a safety filter that guarantees safety for uncertain, input-constrained systems with high probability. We demonstrate the efficacy of our proposed approach in simulation and real-world experiments on a quadrotor and show that we can achieve safe closed-loop behavior for a learned system while satisfying state and input constraints.

翻译：为基于学习的控制器提供安全保障对于实际应用至关重要。实现任意控制策略安全性的一种方法是安全过滤。必要时，过滤器会修改控制输入，确保闭环系统的轨迹在任意未来时刻均维持在给定的状态约束集内，这被称为该集合为正不变性或系统安全。在完全已知动力学假设下，可通过控制屏障函数（CBF）认证安全性。然而实际中动力学模型往往未知或仅部分已知。已有研究提出基于学习的方法，从数据中近似未知或不确定系统的CBF条件，但这些技术未考虑输入约束，因此可能无法生成有效的CBF条件来保证安全集合的不变性。本文研究了在输入约束下保证系统控制不变性的条件，并提出一种优化问题以减少基于CBF的安全过滤器的保守性。基于这些理论见解，我们进一步开发了概率学习方法，能够构建高概率保证不确定输入约束系统安全的安全过滤器。通过四旋翼飞行器的仿真与真实世界实验，我们验证了所提方法的有效性，表明能在满足状态与输入约束的同时实现学习系统的安全闭环行为。