Data-based Low-conservative Nonlinear Safe Control Learning

TL;DR

This paper introduces a data-driven safe control method for nonlinear systems that reduces conservatism by embedding nonlinearities and disturbances directly into invariance conditions, enabling larger safe sets.

Contribution

It proposes a geometry-aware difference-of-convex formulation and vertex-dependent controllers for less conservative, data-driven safety certification of nonlinear systems.

Findings

Certifies substantially larger safe sets.

Improves nonlinearity tolerance in safety guarantees.

Enlarges certifiable invariant sets with data-driven methods.

Abstract

This paper develops a data-driven safe control framework for nonlinear discrete-time systems with parametric uncertainty and additive disturbances. The proposed approach constructs a data-consistent closed-loop representation that enables controller synthesis and safety certification directly from data. Unlike existing methods that treat unmodeled nonlinearities as global worst-case uncertainties using Lipschitz bounds, the proposed approach embeds nonlinear terms directly into the invariance conditions via a geometry-aware difference-of-convex formulation. This enables facet- and direction-specific convexification, avoiding both nonlinearity cancellation and the excessive conservatism induced by uniform global bounds. We further propose a vertex-dependent controller construction that enforces convexity and contractivity conditions locally on the active facets associated with each vertex, thereby enlarging the class of certifiable invariant sets. For systems subject to additive disturbances, disturbance effects are embedded directly into the verification conditions through optimized, geometry-dependent bounds, rather than via uniform margin inflation, yielding less conservative robust safety guarantees. As a result, the proposed methods can certify substantially larger safe sets, naturally accommodate joint state and input constraints, and provide data-driven safety guarantees. The simulation results show a significant improvement in both nonlinearity tolerance and the size of the certified safe set.