In the present study, we develop an energetically efficient suboptimal open-loop strategy to control the wake behind a circular cylinder in the laminar regime. The open-loop suboptimal controller is designed to resemble the feedback integral controller with reference to its dynamical behaviour. Energetic efficiency is measured using the power loss coefficient. The Van der Pol model for the evolution of lift force on the cylinder is chosen as the reduced-order model for the development of an open-loop suboptimal controller. The parameter estimation of the low- dimensional model is carried out using the results from the continuum based Navier - Stokes simulations. It is shown that a subspace identification method can be used to model the relationship between the inputs to the reduced-order model and the inputs to the higher-order computational fluid dynamic model. The development of the suboptimal control is realised by means of solving suitably formulated optimal tracking and regulator problems using the Pontryagin's minimum principle. The resultant controller is found to be energetically efficient and also successful in the control of vortex shedding. © 2018 Elsevier Ltd