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

Banse, Adrien;Romao, Licio;abate, Alessandro;Jungers, Raphaël
(2025) IEEE Transactions on Automatic Control — Vol. 70, n° 12, p. 8092-8103 (2025)

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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.
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Banse, A., Romao, L., abate, A., & Jungers, R. (2025). Data-driven memory-dependent abstractions of dynamical systems via a Cantor-Kantorovich metric. IEEE Transactions on Automatic Control, 70(12), 8092-8103. https://doi.org/10.48550/arXiv.2405.08353 (Original work published 2025)