Linear quadratic stochastic optimal control with state- and control-dependent noises: A deterministic data approach

This paper investigates an infinite -horizon linear quadratic stochastic optimal control (LQSOC) problem with state- and control -dependent noises, in which two system matrices are unknown. First, a deterministic system is introduced and a relationship among its system trajectory, its control and the matrices to be solved is formulated. Subsequently, based on the deterministic system, an adaptive dynamic programming (ADP) algorithm is established to tackle the LQSOC problem. Then, the convergence analysis is presented by proving the equivalence between the proposed algorithm and an existing policy iteration algorithm. Finally, the effectiveness of the obtained algorithm is verified by a perturbed turbocharged diesel engine optimal control design example.