Lmst

#finiteAbstractions

Data-driven memory-dependent abstractions of dynamical systems

by Adrien Banse, Licio Romao, Alessandro Abate, Raphaël M. Jungers
arXiv:2212.01926. https://arxiv.org/pdf/2212.01926.pdf

#dynamicalSystems #memory #abstraction #markovChains #sampling #finiteAbstractions #ergodicity #dynamicalModels

Abstract

We propose a sample-based, sequential method to abstract a (potentially black-box) dynamical system with a sequence of memory-dependent Markov chains of increasing size. We show that this approximation allows to alleviating a correlation bias that has been observed in sample-based abstractions. We further propose a methodology to detect on the fly the memory length resulting in an abstraction with sufficient accuracy. We prove that under reasonable assumptions, the method converges to a sound abstraction in some precise sense, and we showcase it on two case studies. Keywords: dynamical models, switched systems, finite abstractions, memory, ergodicity, observability.

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