  We propose a hybridizable discontinuous Galerkin (HDG) method to approximate
the solution of a tangential Dirichlet boundary control problem for the Stokes
equations with an $ L^2 $ penalty on the boundary control. The contribution of
this paper is twofold. First, we obtain well-posedness and regularity results
for the tangential Dirichlet control problem on a convex polygonal domain. The
analysis contains new features not found in similar Dirichlet control problems
for the Poisson equation; an interesting result is that the optimal control has
higher local regularity on the individual edges of the domain compared to the
global regularity on the entire boundary. Second, under certain assumptions on
the domain and the target state, we prove a priori error estimates for the
control for the HDG method. In the 2D case, our theoretical convergence rate
for the control is superlinear and optimal with respect to the global
regularity on the entire boundary. We present numerical experiments to
demonstrate the performance of the HDG method.
