From Raw Data to Safety: Reducing Conservatism by Set Expansion

TL;DR

This paper introduces a data-driven set expansion method for safety filters that reduces conservatism and handles unknown or time-delay systems using minimal data, validated through simulations.

Contribution

It extends previous data-driven safety filters by proposing online and offline set expansion techniques that significantly reduce conservatism in safety guarantees.

Findings

Expanded safe sets are notably larger in simulations.

Safety filters remain effective with extremely short prediction horizons.

Method handles unknown and time-delay systems with a single data batch.

Abstract

In response to safety concerns associated with learning-based algorithms, safety filters have been proposed as a modular technique. Generally, these filters heavily rely on the system's model, which is contradictory if they are intended to enhance a data-driven or end-to-end learning solution. This paper extends our previous work, a purely Data-Driven Safety Filter (DDSF) based on Willems' lemma, to an extremely short-sighted and non-conservative solution. Specifically, we propose online and offline sample-based methods to expand the safe set of DDSF and reduce its conservatism. Since this method is defined in an input-output framework, it can systematically handle both unknown and time-delay LTI systems using only one single batch of data. To evaluate its performance, we apply the proposed method to a time-delay system under various settings. The simulation results validate the effectiveness of the set expansion algorithm in generating a notably large input-output safe set, resulting in safety filters that are not conservative, even with an extremely short prediction horizon.