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This paper presents a novel approach to synthesize dual controllers forunknown linear time-invariant systems with the tasks of optimizing a quadraticcost while reducing the uncertainty. To this end, a synthesis problem isdefined where the feedback law has to simultaneously gain knowledge of thesystem and robustly optimize the cost. By framing the problem in a finitehorizon setting, the trade-offs arising when the tasks include bothidentification and control are formally captured in the optimization problem.Results show that efficient exploration strategies are achieved when thestructure of the problem is exploited.

Structured exploration in the finite horizon linear quadratic dual control problem