Robust Recurrence of Discrete-Time Infinite-Horizon Stochastic Optimal Control with Discounted Cost
By: Robert H. Moldenhauer , Dragan Nešić , Mathieu Granzotto and more
Potential Business Impact:
Makes smart systems more reliable with changing rules.
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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