  This paper presents a novel value iteration (VI) algorithm for finding the
optimal control for a kind of infinite-horizon stochastic linear quadratic
(SLQ) problem with unknown systems. First, an off-line algorithm is
estabilished to obtain the optimal feedback control of our problem. Then, based
on the off-line algorithm, the VI-based model-free algorithm and its
convergence proof is provided. The main feature of the model-free algorithm is
that a stabilizing control is not needed to initiate the algorithm. Finally, we
validate our results with a simulation example.

Optimization and Control