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

A Q-learning algorithm for discrete-time linear-quadratic control with random parameters of unknown distribution: convergence and stabilization