Data‐driven policy iteration algorithm for continuous‐time stochastic linear‐quadratic optimal control problems

Abstract This paper studies a continuous‐time stochastic linear‐quadratic (SLQ) optimal control problem on infinite‐horizon. Combining the Kronecker product theory with an existing policy iteration algorithm, a data‐driven policy iteration algorithm is proposed to solve the problem. In contrast to most existing methods that need all information of system coefficients, the proposed algorithm eliminates the requirement of three system matrices by utilizing data of a stochastic system. More specifically, this algorithm uses the collected data to iteratively approximate the optimal control and a solution of the stochastic algebraic Riccati equation (SARE) corresponding to the SLQ optimal control problem. The convergence analysis of the obtained algorithm is given rigorously, and a simulation example is provided to illustrate the effectiveness and applicability of the algorithm.