Data-driven Reachability Verification with Probabilistic Guarantees under Koopman Spectral Uncertainty

TL;DR

A novel data-driven framework that addresses this challenge by leveraging Koopman operator theory, and encodes model uncertainty from finite data directly into Koopman spectral representation with quantifiable error bounds, thereby offering a significant advantage in scalability and applicability.

Abstract

Providing rigorous reachability guarantees for unknown complex systems is a crucial and challenging task. In this paper, we present a novel data-driven framework that addresses this challenge by leveraging Koopman operator theory. Instead of operating in the state space, the proposed method encodes model uncertainty from finite data directly into Koopman spectral representation with quantifiable error bounds. Leveraging this spectral information, we systematically determine time intervals within which trajectories from the initial set are guaranteed, with a prescribed probability, to reach the target set. This enables the rigorous reachability verification without explicit computation of reachable sets, thereby offering a significant advantage in scalability and applicability. We finally validate the effectiveness of the proposed framework through case studies on representative dynamical systems.