Training Neural Network Controllers Using Control Barrier Functions in the Presence of Disturbances

Control Barrier Functions (CBF) have been recently utilized in the design of provably safe feedback control laws for nonlinear systems. These feedback control methods typically compute the next control input by solving an online Quadratic Program (QP). Solving QPs in real-time can be a computationally expensive process for resource-constrained systems. In the presence of disturbances, finding CBF-based safe control inputs can get even more time consuming as finding the worst-case of the disturbance requires solving a nonlinear program in general. In this work, we propose to use imitation learning to learn Neural Network based feedback controllers which will satisfy the CBF constraints. In the process, we also develop a new class of High Order CBF for systems under external disturbances. We demonstrate the framework on a unicycle model subject to external disturbances, e.g., wind or currents.