  In this paper, we present a Q-learning algorithm to solve the optimal output
regulation problem for discrete-time LTI systems. This off-policy algorithm
only relies on using persistently exciting input-output data, measured offline.
No model knowledge or state measurements are needed and the obtained optimal
policy only uses past input-output information. Moreover, our formulation of
the proposed algorithm renders it computationally efficient. We provide
conditions that guarantee the convergence of the algorithm to the optimal
solution. Finally, the performance of our method is compared to existing
algorithms in the literature.
