Publication Type

Conference Proceeding Article

Version

publishedVersion

Publication Date

3-2024

Abstract

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 frst 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.

Discipline

OS and Networks

Research Areas

Intelligent Systems and Optimization

Areas of Excellence

Digital transformation

Publication

Proceedings of the 36th AAAI Conference on Artificial Intelligence (AAAI-22), Virtual Conference, February 22 - March 1,

Volume

36

Issue

7

First Page

7326

Last Page

7336

Identifier

10.1609/aaai.v36i7.20695

Publisher

ACM

City or Country

New York

Copyright Owner and License

Authors

Additional URL

https://doi.org/10.1609/aaai.v36i7.20695

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