Document Type

Article

Publication Date

2019

Publication Source

Proceedings of The 2019 22nd ACM International Conference on Hybrid Systems: Computation and Control (Hscc '19)

Abstract

We present an approach to construct reachable set overapproxi- mations for continuous-time dynamical systems controlled using neural network feedback systems. Feedforward deep neural net- works are now widely used as a means for learning control laws through techniques such as reinforcement learning and data-driven predictive control. However, the learning algorithms for these net- works do not guarantee correctness properties on the resulting closed-loop systems. Our approach seeks to construct overapproxi- mate reachable sets by integrating a Taylor model-based flowpipe construction scheme for continuous differential equations with an approach that replaces the neural network feedback law for a small subset of inputs by a polynomial mapping. We generate the polynomial mapping using regression from input-output sam- ples. To ensure soundness, we rigorously quantify the gap between the output of the network and that of the polynomial model. We demonstrate the effectiveness of our approach over a suite of bench- mark examples ranging from 2 to 17 state variables, comparing our approach with alternative ideas based on range analysis.

Inclusive pages

157-168

ISBN/ISSN

978-1-4503-6282-5

Document Version

Published Version

Comments

This open-access article is provided for download in compliance with the publisher’s policy on self-archiving. To view the version of record, use the DOI: https://doi.org/10.1145/3302504.3311807

Publisher

ACM

Peer Reviewed

yes

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