BURNS: Backward Underapproximate Reachability for Neural-Feedback-Loop Systems
This work addresses the lack of rigorous guarantees in learning-enabled systems, expanding the class of verifiable properties, though it appears incremental as it builds on existing reachability methods.
The paper tackles the problem of verifying safety and performance guarantees for learning-enabled control systems by introducing an algorithm to compute underapproximate backward reachable sets for neural feedback loops, using mixed-integer linear programs and demonstrating it on a numerical example.
Learning-enabled planning and control algorithms are increasingly popular, but they often lack rigorous guarantees of performance or safety. 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 on overapproximating the system dynamics function to 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.