Data-Driven Memory-Dependent Abstractions of Dynamical Systems via a Cantor–Kantorovich Metric
Adrien Banse, Licio B. R. R. Romao, Alessandro Abate, Raphaël M. Jungers · IEEE Transactions on Automatic Control · 2025
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.