System transformation and model-free value iteration algorithms for continuous-time linear quadratic stochastic optimal control problems

In this paper, we investigate a continuous-time linear quadratic stochastic optimal control (LQSOC) problem in an infinite horizon, where diffusion and drift terms of the corresponding stochastic system depend on both state and control variables. In light of the stochastic control theory, this LQSOC problem is reduced to solving a generalised algebraic Riccati equation (GARE). With the help of an existing model-based value iteration (VI) algorithm, we propose two data-driven VI algorithms to solve the GARE. The first one relies on transforming the stochastic system into a deterministic control system first and then solving the LQSOC problem by the data of the deterministic system. Consequently, this algorithm does not need the information of two system coefficients and has a lower algorithm complexity. The second algorithm directly uses the data generated by the stochastic system, and thus it circumvents the requirement of all system coefficients. We also provide convergence proofs of these two data-driven algorithms and validate these algorithms through two simulation examples.