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
Publisher
ACM
Peer Reviewed
yes
Sponsoring Agency
United States Department of Defense US Air Force Research Laboratory; National Science Foundation (NSF)
eCommons Citation
Dutta, Souradeep; Chen, Xin; and Sankaranarayanan, Sriram, "Reachability Analysis for Neural Feedback Systems Using Regressive Polynomial Rule Inference" (2019). Computer Science Faculty Publications. 186.
https://ecommons.udayton.edu/cps_fac_pub/186
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