Automated Reachability Analysis of Neural Network-Controlled Systems via Adaptive Polytopes

Taha Entesari, Mahyar Fazlyab
Proceedings of The 5th Annual Learning for Dynamics and Control Conference, PMLR 211:407-419, 2023.

Abstract

Over-approximating the reachable sets of dynamical systems is a fundamental problem for safety verification and robust control synthesis. The representation of these sets is a key factor that affects the computational complexity and the approximation error. In this paper, we develop a new approach for over-approximating the reachable sets of neural network dynamical systems using adaptive template polytopes. We use the singular value decomposition of linear layers along with the shape of the activation functions to adapt the geometry of the polytopes at each time step to the geometry of the true reachable sets. We then propose a branch-and-bound method to compute accurate over-approximations of the reachable sets by the inferred templates. We illustrate the utility of the proposed approach in the reachability analysis of linear systems driven by neural network controllers.

Cite this Paper

BibTeX
@InProceedings{pmlr-v211-entesari23a, title = {Automated Reachability Analysis of Neural Network-Controlled Systems via Adaptive Polytopes}, author = {Entesari, Taha and Fazlyab, Mahyar}, booktitle = {Proceedings of The 5th Annual Learning for Dynamics and Control Conference}, pages = {407--419}, year = {2023}, editor = {Matni, Nikolai and Morari, Manfred and Pappas, George J.}, volume = {211}, series = {Proceedings of Machine Learning Research}, month = {15--16 Jun}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v211/entesari23a/entesari23a.pdf}, url = {https://proceedings.mlr.press/v211/entesari23a.html}, abstract = {Over-approximating the reachable sets of dynamical systems is a fundamental problem for safety verification and robust control synthesis. The representation of these sets is a key factor that affects the computational complexity and the approximation error. In this paper, we develop a new approach for over-approximating the reachable sets of neural network dynamical systems using adaptive template polytopes. We use the singular value decomposition of linear layers along with the shape of the activation functions to adapt the geometry of the polytopes at each time step to the geometry of the true reachable sets. We then propose a branch-and-bound method to compute accurate over-approximations of the reachable sets by the inferred templates. We illustrate the utility of the proposed approach in the reachability analysis of linear systems driven by neural network controllers.} }
Endnote
%0 Conference Paper %T Automated Reachability Analysis of Neural Network-Controlled Systems via Adaptive Polytopes %A Taha Entesari %A Mahyar Fazlyab %B Proceedings of The 5th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2023 %E Nikolai Matni %E Manfred Morari %E George J. Pappas %F pmlr-v211-entesari23a %I PMLR %P 407--419 %U https://proceedings.mlr.press/v211/entesari23a.html %V 211 %X Over-approximating the reachable sets of dynamical systems is a fundamental problem for safety verification and robust control synthesis. The representation of these sets is a key factor that affects the computational complexity and the approximation error. In this paper, we develop a new approach for over-approximating the reachable sets of neural network dynamical systems using adaptive template polytopes. We use the singular value decomposition of linear layers along with the shape of the activation functions to adapt the geometry of the polytopes at each time step to the geometry of the true reachable sets. We then propose a branch-and-bound method to compute accurate over-approximations of the reachable sets by the inferred templates. We illustrate the utility of the proposed approach in the reachability analysis of linear systems driven by neural network controllers.
APA
Entesari, T. & Fazlyab, M.. (2023). Automated Reachability Analysis of Neural Network-Controlled Systems via Adaptive Polytopes. Proceedings of The 5th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 211:407-419 Available from https://proceedings.mlr.press/v211/entesari23a.html.

Related Material