用鲁棒过滤机制让复杂系统在不确定性下依然安全可靠。
Distributionally Robust Safety Under Arbitrary Uncertainties: A Safety Filtering Approach
- 通过切换主控与备份策略实现安全防护，降低计算负担。
- 基于样本的验证方法在有限数据下保证失败率低于阈值。
- 适用于自动驾驶、飞行器等高动态系统的安全控制。
我们研究了在分布模糊性下的非线性系统概率安全性保障问题。提出一种基于备份的安全过滤框架，通过在高性能主策略与可认证的备份策略间切换来确保安全。针对分布结构未知且真实分布不可知的任意不确定性，采用基于Wasserstein模糊集的分布鲁棒（DR）建模方式。不在线求解高维DR轨迹优化问题，而是利用备份式安全过滤的结构，将安全认证简化为对主备策略切换时间的一维搜索。进一步设计了一种具有有限样本保证的采样认证程序，将经验失败概率与基于Wasserstein的膨胀阈值进行比较。在三种系统上进行了验证：从杜宾车辆到高速赛车，再到战斗机，充分展示了方法的广泛适用性和计算高效性。
原文摘要 · Abstract (English)
We study how to ensure probabilistic safety for nonlinear systems under distributional ambiguity. Our approach builds on a backup-based safety filtering framework that switches between a high-performance nominal policy and a certified backup policy to ensure safety. To handle arbitrary uncertainties from ambiguous distributions, i.e., where the distribution is not of specific structure and the true distribution is unknown, we adopt a distributionally robust (DR) formulation using Wasserstein ambiguity sets. Rather than solving a high-dimensional DR trajectory optimization problem online, we exploit the structure of backup-based safety filtering to reduce safety certification to a one-dimensional search over the switching time between nominal and backup policies. We then develop a sampling-based certification procedure with finite-sample guarantees, where empirical failure probabilities are compared against a Wasserstein-inflated threshold. We validate our method across three systems, from a Dubins vehicle to a high-speed racing car and a fighter jet, demonstrating the broad applicability and computational efficiency.
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