Approximate Conformance Checking for Closed-Loop Systems With Neural Network Controllers

In this article, we consider the problem of checking approximate conformance of closed-loop systems with the same plant but different neural network (NN) controllers. First, we introduce a notion of approximate conformance on NNs, which allows us to quantify semantically the deviations in closed-loop system behaviors with different NN controllers. Next, we consider the problem of computationally checking this notion of approximate conformance on two NNs. We reduce this problem to that of reachability analysis on a combined NN, thereby, enabling the use of existing NN verification tools for conformance checking. Our experimental results on an autonomous rocket landing system demonstrate the feasibility of checking approximate conformance on different NNs trained for the same dynamics, as well as the practical semantic closeness exhibited by the corresponding closed-loop systems.