Distributionally Robust Safety Under Arbitrary Uncertainties: A Safety Filtering Approach

• URL: http://arxiv.org/abs/2605.12974v2
• Date: Mon, 18 May 2026 23:59:03 GMT
• Title: Distributionally Robust Safety Under Arbitrary Uncertainties: A Safety Filtering Approach
• Abstract summary: We study how to ensure probabilistic safety for nonlinear systems under distributional ambiguity.<n>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.<n>We validate our method through simulations across three systems, from a Dubins vehicle to a high-speed racing car and a fighter jet.
• Score: 11.107547000695646
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this work, 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 through simulations 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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