Distributionally robust Lyapunov–Barrier Networks for safe and stable control under uncertainty

Abstract

This paper addresses the challenge of simultaneously achieving stability and safety in nonlinear control systems subject to uncertain parameters. We propose distributionally robust Lyapunov–Barrier networks (DR-LBNs), a novel framework that unifies control Lyapunov functions, control barrier functions, and distributionally robust optimization. By modeling parametric uncertainties through a Wasserstein-based ambiguity set, proposed approach offers high-probability guarantees on both asymptotic stability and forward invariance of a safe set, even when the true distribution of uncertainties is unknown or shifts from training to deployment. We formalize key theoretical results on probabilistic stability, universal approximation of Lyapunov and barrier functions, and sample complexity. In numerical evaluations, the DR-LBN approach outperforms both a simple baseline controller and a worst-case robust distribution method in terms of safety margins, convergence speed, and control effort.