Data-Driven Abstractions for Control Systems via Random Exploration

TL;DR

This paper introduces a data-driven approach to create symbolic abstractions of control systems using random sampling, providing probabilistic guarantees for control design without requiring full model knowledge.

Contribution

It proposes a novel sampling-based method for abstraction construction with PAC guarantees, bridging the gap between data collection and formal control synthesis.

Findings

Successfully applied to numerical benchmarks

Provides PAC guarantees for abstraction accuracy

Enables control design without full model knowledge

Abstract

At the intersection of dynamical systems, control theory, and formal methods lies the construction of symbolic abstractions: these typically represent simpler, finite-state models whose behavior mimics that of an underlying concrete system but are easier to analyse. Building an abstraction usually requires an accurate knowledge of the underlying model: this knowledge may be costly to gather, especially in real-life applications. We aim to bridge this gap by building abstractions based on sampling finite length trajectories. To refine a controller built for the abstraction to one for the concrete system, we newly define a notion of probabilistic alternating simulation, and provide Probably Approximately Correct (PAC) guarantees that the constructed abstraction includes all behaviors of the concrete system and that it is suitable for control design, for arbitrarily long time horizons, leveraging scenario theory. Our method is then tested on several numerical benchmarks.