  This paper studies an infinite horizon optimal control problem for
discrete-time linear systems and quadratic criteria, both with random
parameters which are independent and identically distributed with respect to
time. A classical approach is to solve an algebraic Riccati equation that
involves mathematical expectations and requires certain statistical information
of the parameters. In this paper, we propose an online iterative algorithm in
the spirit of Q-learning for the situation where only one random sample of
parameters emerges at each time step. The first theorem proves the equivalence
of three properties: the convergence of the learning sequence, the
well-posedness of the control problem, and the solvability of the algebraic
Riccati equation. The second theorem shows that the adaptive feedback control
in terms of the learning sequence stabilizes the system as long as the control
problem is well-posed. Numerical examples are presented to illustrate our
results.
