Robust Data-Driven Invariant Sets for Nonlinear Systems

Abstract

The synthesis of robust invariant sets for nonlinear systems has traditionally been hindered by the inherent non convexity and a strict reliance on exact analytical models. This paper presents a purely data-driven framework to compute robust polytopic contractive sets for unknown nonlinear systems operating under persistent bounded process noise and state-input constraints. Rather than attempting to identify a single, potentially nominal model, we utilize a finite data set to construct a polytopic consistency set--a rigorous geometric boundary encapsulating all possible system dynamics compatible with the noisy measurements. The core contribution of this work extends an established sufficient condition for {\lambda} contractiveness into the data-driven setting. Crucially, we prove that enforcing this condition strictly over the vertices of the consistency set guarantees robust invariance.