Synthesis and Verification of String Stable Control for Interconnected Systems via Neural sISS Certificate

Large-scale interconnected systems require robust control strategies to ensure string stability, which is crucial for system safety and efficiency. Although learning-based controllers such as reinforcement learning (RL) have demonstrated significant potential in managing complex control scenarios, the lack of interpretability makes it difficult to provide formal string stability guarantees. To address this gap, we propose a novel verification and synthesis framework that integrates scalable input-to-state string stability (sISS) with neural network verification to formally guarantee string stability in interconnected systems. Our contributions are three-fold: (1) we reformulate the string stability analysis as a neural network verification problem by incorporating neural sISS certificates; (2) we develop a counterexample-guided training framework that synthesizes neural network-based controllers satisfying sISS constraints with minimal degradation in control performance; and (3) we validate our approach in an RL-based mixed-autonomy vehicle platooning scenario. Numerical simulations show that the refined RL controller guarantees sISS while preserving the RL policy’s performance.