A Comparison of Verification Methods for Neural-Network Controllers Using Mixed-Integer Programs

This paper addresses the problem of formal verification of neural networks (NNs) for control. This work focuses on NNs with piece-wise linear activation functions, which can be represented in a mixed-integer linear program (MILP). This paper explains different methods to certify stability using MILP formulations for discrete-time linear systems controlled in closed-loop. The proposed methods are applied to a numerical example and compared against each other. The work concludes that, for the studied linear system, sufficiently big regions of attraction can be certified to be stable using reachable set analysis or by learning a Lyapunov function for the feedback system.