Neural Vector Lyapunov–Razumikhin Certificates for Delayed Interconnected Systems

Jingyuan Zhou, Yuexuan Wang, Kaidi Yang
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:165935-165956, 2026.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-zhou26au, title = {Neural Vector {L}yapunov–Razumikhin Certificates for Delayed Interconnected Systems}, author = {Zhou, Jingyuan and Wang, Yuexuan and Yang, Kaidi}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {165935--165956}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/zhou26au/zhou26au.pdf}, url = {https://proceedings.mlr.press/v306/zhou26au.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Neural Vector Lyapunov–Razumikhin Certificates for Delayed Interconnected Systems %A Jingyuan Zhou %A Yuexuan Wang %A Kaidi Yang %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-zhou26au %I PMLR %P 165935--165956 %U https://proceedings.mlr.press/v306/zhou26au.html %V 306 %X 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.
APA
Zhou, J., Wang, Y. & Yang, K.. (2026). Neural Vector Lyapunov–Razumikhin Certificates for Delayed Interconnected Systems. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:165935-165956 Available from https://proceedings.mlr.press/v306/zhou26au.html.

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