  We model the cooling of open optical and optomechanical resonators via
optical feedback in the Linear Quadratic Gaussian setting of stochastic control
theory. We show that coherent feedback control schemes, in which the resonator
is embedded in an interferometer to achieve all-optical feedback, can
outperform the best possible measurement-based schemes in the quantum regime of
low steady-state excitation number. Such performance gains are attributed to
the coherent controller's ability to process non-commuting output field
quadratures simultaneously without loss of fidelity, and may provide important
clues for the design of coherent feedback schemes for more general problems of
nonlinear and robust control.
