  The optimal adaptive control of a linear system in a signal-plus-noise
setting with infinite horizon LQ regulator cost is studied. The class of
partially observed linear systems for which the certainty equivalence property
holds is identified. It is also shown that a linear system is adaptively
stabilizable if and only if it is uniformly stabilizable, and the class of
partially observed linear systems for which the certainty equivalence value
function is a supersolution of the Bellman equation is identified.

Optimization and Control