Data-driven memory-dependent abstractions of dynamical systems

TL;DR

This paper introduces a sample-based, sequential approach to create memory-dependent Markov chain abstractions of dynamical systems, improving accuracy and convergence, with practical detection of optimal memory length demonstrated on case studies.

Contribution

It presents a novel method for constructing memory-dependent abstractions that reduces correlation bias and adaptively determines the necessary memory length for accuracy.

Findings

Method converges to a sound abstraction under certain conditions.

Detects optimal memory length on the fly.

Validated on two case studies.

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.