Robust Data-Driven Invariant Sets for Nonlinear Systems
This addresses the challenge of robust control for unknown nonlinear systems under noise and constraints, offering a data-driven alternative to model-based methods.
The paper tackles the problem of synthesizing robust invariant sets for nonlinear systems by introducing a purely data-driven framework that computes polytopic contractive sets from noisy measurements, proving that enforcing a contractiveness condition over vertices guarantees robust invariance.
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 λ contractiveness into the data-driven setting. Crucially, we prove that enforcing this condition strictly over the vertices of the consistency set guarantees robust invariance.