BURNS: Backward Underapproximate Reachability for Neural-Feedback-Loop Systems

Learning-enabled planning and control algorithms are increasingly popular, but they often lack rigorous guarantees of performance or safety. Frameworks such as reachability analysis can be used to provide such guarantees. We introduce an algorithm for computing underapproximate backward reachable sets of nonlinear discrete time neural feedback loops. We then use the backward reachable sets to check goal-reaching properties. Our algorithm is based upon ideas from robustness analysis for vision networks, and on overapproximating the system dynamics function. Together these enable computation of underapproximate backward reachable sets through solutions of mixed-integer linear programs. We rigorously analyze the soundness of our algorithm and demonstrate it on a numerical example. Our work expands the class of properties that can be verified for learning-enabled systems.