Neural networks in closed-loop systems: Verification using interval arithmetic and formal prover

Machine Learning approaches have been successfully used for the creation of high-performance control components of cyber-physical systems, where the control dynamics result from the combination of many subsystems. However, these approaches may lack the trustworthiness required to guarantee their reliable application in a safety-critical context. In this paper, we propose a combination of interval arithmetic and theorem-proving verification techniques to analyze safety properties in closed-loop systems that embed neural network components. We show the application of the proposed approach to a model-predictive controller for autonomous driving comparing the neural network verification performance with other existing tools. The results show that open-loop neural network verification through interval arithmetic can outperform existing approaches proving properties with a smaller time overhead. Furthermore, we demonstrate the capability of combining the two approaches to construct a formal model of the network in higher-order logic of the controlled system in a closed-loop.