  This paper presents a novel approach to synthesize dual controllers for
unknown linear time-invariant systems with the tasks of optimizing a quadratic
cost while reducing the uncertainty. To this end, a synthesis problem is
defined where the feedback law has to simultaneously gain knowledge of the
system and robustly optimize the cost. By framing the problem in a finite
horizon setting, the trade-offs arising when the tasks include both
identification and control are formally captured in the optimization problem.
Results show that efficient exploration strategies are achieved when the
structure of the problem is exploited.
