Abstract: In this talk we study the Dirichlet boundary control of Stokes flows in energy space. The motivation to study the problem in energy space lies in the fact that the choice of control space in ${\bf L}^2(\Gamma)$ yields discontinuous solutions which is in contrast to that of elliptic equation constrained case and is usually not desirable in real applications. We prove the well-posedness for the energy space setting and derive the first order optimality conditions, and show that the solutions of the  control problem are much regular than that of the ${\bf L}^2(\Gamma)$ setting. We present the finite element approximations of control problems in two different formulations and prove optimal a priori error estimates for control problems in energy space. Several numerical experiments are carried out for the comparison of different formulations.