Formal Synthesis of Neural Barrier Certificates for Dynamical Systems via DC Programming

Barrier certificate generation is an ingenious and powerful approach for safety verification of cyber-physical systems. This article suggests a new learning and verification framework that helps to achieve the balance between the representation ability and the verification efficiency for neural barrier certificates. In the learning phase, it learns candidate barrier certificates represented as convex difference neural networks (CDiNNs). Since CDiNNs can be rewritten as difference of convex (DC) functions that can express any twice differentiable function, thus have outstanding representation ability and flexibility. In the verification phase, it employs an efficient approach for formally verifying the validity of the neural candidates via DC programming. Due to the convexity-based structure, CDiNNs can significantly facilitate the verification process. We conduct an experimental evaluation over a set of benchmarks, which validates that our method is much more efficient and effective than the state-of-the-art approaches.