Safety and Stability Guarantees for Control Loops With Deep Learning Perception

Deep learning is currently used in the perception pipeline of autonomous systems, such as when estimating the system state from camera and LiDAR measurements. While this practice is typical, hard guarantees on the worst-case behavior of the closed-loop system are rare. In this letter, however, we leverage recent results on neural network approximation, combined with classical input-to-state stability (ISS) properties, and show how to design deep neural networks for state estimation that guarantee the safety and stability of the resulting closed-loop system.