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

TL;DR

This paper presents BURNS, an algorithm for computing underapproximate backward reachable sets in neural feedback systems, enabling safety verification and goal-reaching analysis with rigorous guarantees.

Contribution

It introduces a novel mixed-integer linear programming approach for underapproximating backward reachable sets in nonlinear neural feedback systems.

Findings

Algorithm is sound and rigorously verified.

Successfully demonstrated on a numerical example.

Expands verification capabilities for learning-enabled systems.

Abstract

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.