  High-amplitude free stream turbulence and surface roughness elements can
excite a laminar boundary layer flow sufficiently to cause streamwise oriented
vortices to develop. These vortices resemble elongated streaks having alternate
spanwise variations of the streamwise velocity. Downstream, the vortices
`wobble' through an inviscid secondary instability mechanism and, ultimately,
transition to turbulence. We formulate an optimal control algorithm to suppress
the growth rate of the streamwise vortex system. Considering a high Reynolds
number asymptotic framework, we reduce the full compressible Navier-Stokes
equations to the nonlinear compressible boundary region equations (NCBRE). We
then implement the method of Lagrange multipliers via an appropriate
transformation of the original constrained optimization problem into an
unconstrained form to obtain the disturbance equations in the form of the
adjoint compressible boundary region equations (ACBRE) and corresponding
optimality conditions. Numerical solutions of the ACBRE approach for
high-supersonic and hypersonic flows reveal a significant reduction in the
kinetic energy and wall shear stress for all considered configurations. We
present contour plots to demonstrate the qualitative effect of increased
control iterations. Our results indicate that the primary vortex instabilities
gradually flatten in the spanwise direction thanks to the ACBRE algorithm.
