  We consider estimation and control of the cylinder wake at low Reynolds
numbers. A particular focus is on the development of efficient numerical
algorithms to design optimal linear feedback controllers when there are many
inputs (disturbances applied everywhere) and many outputs (perturbations
measured everywhere). We propose a resolvent-based iterative algorithm to
perform i) optimal estimation of the flow using a limited number of sensors;
and ii) optimal control of the flow when the entire flow is known but only a
limited number of actuators are available for control. The method uses
resolvent analysis to take advantage of the low-rank characteristics of the
cylinder wake and solutions are obtained without any model-order reduction.
Optimal feedback controllers are also obtained by combining the solutions of
the estimation and control problems. We show that the performance of the
estimators and controllers converges to the true global optima, indicating that
the important physical mechanisms for estimation and control are of low rank.
