Distributionally Robust Safety Under Arbitrary Uncertainties: A Safety Filtering Approach

2026-05-13

AI Summary

This work proposes a distributionally robust safe control framework for nonlinear systems under distributional ambiguity—where the true disturbance distribution is unknown and lacks structural assumptions—by leveraging a backup policy switching strategy. The approach constructs probabilistic safety guarantees using Wasserstein ambiguity sets and reduces the high-dimensional trajectory optimization problem to a one-dimensional search over switching times, substantially improving computational efficiency. Additionally, a sampling-based verification mechanism with finite-sample theoretical guarantees is developed to ensure reliable safety certification. Experimental evaluations on three distinct systems—Dubins vehicles, high-speed race cars, and fighter jets—demonstrate that the method achieves broad applicability, strong safety assurances, and high computational performance.

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.

Problem

• distributional ambiguity
• probabilistic safety
• nonlinear systems
• Wasserstein ambiguity sets
• safety certification

Innovation

• distributionally robust optimization
• safety filtering
• Wasserstein ambiguity sets
• backup policy
• probabilistic safety