  Recent work by Mania et al. has proved that certainty equivalent control
achieves nearly optimal regret for linear systems with quadratic costs.
However, when parameter uncertainty is large, certainty equivalence cannot be
relied upon to stabilize the true, unknown system. In this paper, we present a
dual control strategy that attempts to combine the performance of certainty
equivalence, with the practical utility of robustness. The formulation
preserves structure in the representation of parametric uncertainty, which
allows the controller to target reduction of uncertainty in the parameters that
`matter most' for the control task, while robustly stabilizing the uncertain
system. Control synthesis proceeds via convex optimization, and the method is
illustrated on a numerical example.
