English

Robust Recurrence of Discrete-Time Infinite-Horizon Stochastic Optimal Control with Discounted Cost

Optimization and Control 2025-04-30 v1 Systems and Control Systems and Control

Abstract

We analyze the stability of general nonlinear discrete-time stochastic systems controlled by optimal inputs that minimize an infinite-horizon discounted cost. Under a novel stochastic formulation of cost-controllability and detectability assumptions inspired by the related literature on deterministic systems, we prove that uniform semi-global practical recurrence holds for the closed-loop system, where the adjustable parameter is the discount factor. Under additional continuity assumptions, we further prove that this property is robust.

Keywords

Cite

@article{arxiv.2504.20705,
  title  = {Robust Recurrence of Discrete-Time Infinite-Horizon Stochastic Optimal Control with Discounted Cost},
  author = {Robert H. Moldenhauer and Dragan Nešić and Mathieu Granzotto and Romain Postoyan and Andrew R. Teel},
  journal= {arXiv preprint arXiv:2504.20705},
  year   = {2025}
}

Comments

Accepted for 13th IFAC Symposium on Nonlinear Control Systems