  This paper studies a discrete-time stochastic control problem with linear
quadratic criteria over an infinite-time horizon. We focus on a class of
control systems whose system matrices are associated with random parameters
involving unknown statistical properties. In particular, we design a
distributed Q-learning algorithm to tackle the Riccati equation and derive the
optimal controller stabilizing the system. The key technique is that we convert
the problem of solving the Riccati equation into deriving the zero point of a
matrix equation and devise a distributed stochastic approximation method to
compute the estimates of the zero point. The convergence analysis proves that
the distributed Q-learning algorithm converges to the correct value eventually.
A numerical example sheds light on that the distributed Q-learning algorithm
converges asymptotically.
