Data-based Low-conservative Nonlinear Safe Control Learning
This work addresses the problem of excessive conservatism in safe control for nonlinear systems with uncertainties, which is incremental as it builds on existing methods by reducing conservatism through geometry-aware formulations.
The paper tackles the problem of safe control for nonlinear discrete-time systems with uncertainties by developing a data-driven framework that constructs a data-consistent closed-loop representation for controller synthesis and safety certification. The result is a significant improvement in nonlinearity tolerance and the size of the certified safe set, as shown in simulation results.
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.