Neural Vector Lyapunov–Razumikhin Certificates for Delayed Interconnected Systems

Ensuring scalable input-to-state stability (sISS) is critical for the safety and reliability of large-scale interconnected systems, especially in the presence of communication delays. While learning-based controllers can achieve strong empirical performance, their black-box nature makes it difficult to provide formal and scalable stability guarantees. To address this gap, we propose a framework to synthesize and verify neural vector Lyapunov-Razumikhin certificates for discrete-time delayed interconnected systems. Our contributions are three-fold. First, we establish a sufficient condition for discrete-time sISS via vector Lyapunov-Razumikhin functions, which enables certification for large-scale delayed interconnected systems. Second, we develop a scalable synthesis and verification framework that learns the neural certificates and verifies the certificates on reachability-constrained delay domains with scalability analysis. Third, we validate our approach on mixed-autonomy platoons, drone formations, and microgrids against multiple baselines, showing improved verification efficiency with competitive control performance.

Large-scale AI-controlled systems, such as connected vehicles, drone teams, and smart grids, often rely on many agents working together. In practice, these agents may receive delayed information because of sensing, computation, or communication limits. Such delays can make the overall system unstable, especially when the system becomes large. This paper develops a method to check whether learning-based controllers can keep these delayed interconnected systems stable. Instead of analyzing the whole large system at once, our method learns local neural certificates for individual agents and verifies how these certificates interact with each other. It also reduces the verification burden by focusing on delay states that the system can actually reach and by reusing certificates for agents with similar structures. We test the method on vehicle platoons, drone formations, and microgrids. The results show that the proposed approach can verify stability more efficiently while maintaining competitive control performance. Overall, this work provides a practical step toward making learning-based controllers more reliable in large networked systems where communication delays are unavoidable.