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

Model-free Value Iteration Algorithm for Continuous-time Stochastic Linear Quadratic Optimal Control Problems