# Feasibility Analysis and Regularity Characterization of Distributionally Robust Safe Stabilizing Controllers

arXiv: https://arxiv.org/abs/2311.05813 · HTML: https://mlsanity.com/paper/2311.05813/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Nov 2023.

## Built on by (most cited first, 3 of 3)

- [Neural Configuration-Space Barriers for Manipulation Planning and Control](https://mlsanity.com/paper/2503.04929/) (2025)
- [Distributionally Robust Policy and Lyapunov-Certificate Learning](https://mlsanity.com/paper/2404.03017/) (2024)
- [A Unified Perspective on Conformal Prediction and Wasserstein Distributionally Robust Optimization for Uncertainty Quantification](https://mlsanity.com/paper/2608.29789/) (2026)

## Abstract (arXiv)

This paper studies the well-posedness and regularity of safe stabilizing optimization-based controllers for control-affine systems in the presence of model uncertainty. When the system dynamics contain unknown parameters, a finite set of samples can be used to formulate distributionally robust versions of control barrier function and control Lyapunov function constraints. Control synthesis with such distributionally robust constraints can be achieved by solving a (convex) second-order cone program (SOCP). We provide one necessary and two sufficient conditions to check the feasibility of such optimization problems, characterize their computational complexity and numerically show that they are significantly faster to check than direct use of SOCP solvers. Finally, we also analyze the regularity of the resulting control laws.