Wasserstein Distributionally Robust Control Barrier Function using Conditional Value-at-Risk with Differentiable Convex Programming

• URL: http://arxiv.org/abs/2309.08700v1
• Date: Fri, 15 Sep 2023 18:45:09 GMT
• Title: Wasserstein Distributionally Robust Control Barrier Function using Conditional Value-at-Risk with Differentiable Convex Programming
• Authors: Alaa Eddine Chriat and Chuangchuang Sun
• Abstract summary: Control Barrier functions (CBFs) have attracted extensive attention for designing safe controllers for real-world safety-critical systems. We present distributional robust CBF to achieve resilience under distributional shift. We also provide an approximate variant of DR-CBF for higher-order systems.
• Score: 4.825619788907192
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Control Barrier functions (CBFs) have attracted extensive attention for designing safe controllers for their deployment in real-world safety-critical systems. However, the perception of the surrounding environment is often subject to stochasticity and further distributional shift from the nominal one. In this paper, we present distributional robust CBF (DR-CBF) to achieve resilience under distributional shift while keeping the advantages of CBF, such as computational efficacy and forward invariance. To achieve this goal, we first propose a single-level convex reformulation to estimate the conditional value at risk (CVaR) of the safety constraints under distributional shift measured by a Wasserstein metric, which is by nature tri-level programming. Moreover, to construct a control barrier condition to enforce the forward invariance of the CVaR, the technique of differentiable convex programming is applied to enable differentiation through the optimization layer of CVaR estimation. We also provide an approximate variant of DR-CBF for higher-order systems. Simulation results are presented to validate the chance-constrained safety guarantee under the distributional shift in both first and second-order systems.

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