Stability Verification in Stochastic Control Systems via Neural Network Supermartingales


  • Mathias Lechner IST Austria
  • Đorđe Žikelić IST Austria
  • Krishnendu Chatterjee IST Austria
  • Thomas A. Henzinger IST Austria



Machine Learning (ML), Reasoning Under Uncertainty (RU)


We consider the problem of formally verifying almost-sure (a.s.) asymptotic stability in discrete-time nonlinear stochastic control systems. While verifying stability in deterministic control systems is extensively studied in the literature, verifying stability in stochastic control systems is an open problem. The few existing works on this topic either consider only specialized forms of stochasticity or make restrictive assumptions on the system, rendering them inapplicable to learning algorithms with neural network policies. In this work, we present an approach for general nonlinear stochastic control problems with two novel aspects: (a) instead of classical stochastic extensions of Lyapunov functions, we use ranking supermartingales (RSMs) to certify a.s. asymptotic stability, and (b) we present a method for learning neural network RSMs. We prove that our approach guarantees a.s. asymptotic stability of the system and provides the first method to obtain bounds on the stabilization time, which stochastic Lyapunov functions do not. Finally, we validate our approach experimentally on a set of nonlinear stochastic reinforcement learning environments with neural network policies.




How to Cite

Lechner, M., Žikelić, Đorđe, Chatterjee, K., & Henzinger, T. A. (2022). Stability Verification in Stochastic Control Systems via Neural Network Supermartingales. Proceedings of the AAAI Conference on Artificial Intelligence, 36(7), 7326-7336.



AAAI Technical Track on Machine Learning II