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arXiv · 2407.04988

The Reachability Problem for Neural-Network Control Systems

Christian Schilling·Martin Zimmermann
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Abstract

A control system consists of a plant component and a controller which periodically computes a control input for the plant. We consider systems where the controller is implemented by a feedforward neural network with ReLU activations. The reachability problem asks, given a set of initial states, whether a set of target states can be reached. We show that this problem is undecidable even for trivial plants and fixed-depth neural networks with three inputs and outputs. We also show that the problem becomes semi-decidable when the plant as well as the input and target sets are given by automata over infinite words.

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BibTeXRIS

Christian Schilling, Martin Zimmermann. 2024-07-06. The Reachability Problem for Neural-Network Control Systems. https://doi.org/10.1007/978-3-031-73741-1_27

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