Safety Certification for Stochastic Systems via Neural Barrier Functions

Safety Certification for Stochastic Systems via Neural Barrier Functions

Mathiesen, Frederik Baymler (TU Delft Team Luca Laurenti)
Calvert, S.C. (TU Delft Transport and Planning)
Laurenti, L. (TU Delft Team Luca Laurenti)

2023

Providing non-trivial certificates of safety for non-linear stochastic systems is an important open problem. One promising solution to address this problem is the use of barrier functions. Barrier functions are functions whose composition with the system forms a Martingale and enable the computation of the probability that the system stays within a safe set over a finite time horizon. However, existing approaches to find barrier functions generally restrict the search to a small class of functions, often leading to conservatism. To address this problem, in this letter, we parameterize barrier functions as neural networks and show that bound propagation techniques and linear programming can be successfully employed to find Neural Barrier Functions. Further, we develop a branch-and-bound scheme based on linear relaxations that improves the scalability of the proposed framework. On several case studies we show that our approach scales to neural networks of hundreds of neurons and multiple hidden layers and often produces certificates of safety that are tighter than state-of-the-art methods.

Neural networks
system verification
stochastic systems
linear programming

http://resolver.tudelft.nl/uuid:871349c2-ca36-46db-a382-199e594cb8c0

https://doi.org/10.1109/LCSYS.2022.3229865

2023-07-01

2475-1456

IEEE Control Systems Letters, 7, 973-978

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

journal article

© 2023 Frederik Baymler Mathiesen, S.C. Calvert, L. Laurenti