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arXiv · 2504.20705

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

Robert H. Moldenhauer·Dragan Nešić·Mathieu Granzotto·Romain Postoyan·Andrew R. Teel
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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.

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Robert H. Moldenhauer, Dragan Nešić, Mathieu Granzotto, Romain Postoyan, Andrew R. Teel. 2025-04-29. Robust Recurrence of Discrete-Time Infinite-Horizon Stochastic Optimal Control with Discounted Cost. https://arxiv.org/abs/2504.20705

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