Robust Data-Driven Invariant Sets for Nonlinear Systems

TL;DR

This paper introduces a data-driven method to compute robust invariant sets for unknown nonlinear systems using finite noisy data, avoiding explicit model identification.

Contribution

It extends a known contractiveness condition into a data-driven framework, ensuring robust invariance through vertex enforcement on the consistency set.

Findings

The method guarantees robust invariance for nonlinear systems under noise.

It constructs a geometric boundary encapsulating all compatible system dynamics.

The approach does not require explicit system model identification.

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.