Data-driven memory-dependent abstractions of dynamical systems via a Cantor-Kantorovich metric

TL;DR

This paper introduces a data-driven method for creating memory-dependent abstractions of dynamical systems using a new metric between Markov models, enabling better system representation through observed outputs and numerical validation.

Contribution

It presents a novel metric-based approach for data-driven, memory-aware abstractions of dynamical systems, enhancing model accuracy with purely observational data.

Findings

Effective in capturing system dynamics from output data

Memory improves abstraction accuracy

Numerical examples demonstrate practical usefulness

Abstract

Abstractions of dynamical systems enable their verification and the design of feedback controllers using simpler, usually discrete, models. In this paper, we propose a data-driven abstraction mechanism based on a novel metric between Markov models. Our approach is based purely on observing output labels of the underlying dynamics, thus opening the road for a fully data-driven approach to construct abstractions. Another feature of the proposed approach is the use of memory to better represent the dynamics in a given region of the state space. We show through numerical examples the usefulness of the proposed methodology.