  In this paper we study optimal control problem for non local
Cahn-Hilliard-Brinkman system which models phase separation of binary fluids in
porous media. We consider the system in two dimensional bounded domain with
regular potential. We extend recently proved existence of weak solution results
for such a system and prove the existence of strong solution under certain
assumptions on the forcing term and initial datum. Further using our regularity
results, we study the tracking type optimal control problem. We prove the
existence of an optimal control and establish the first order optimality
condition. Lastly, we characterize optimal control in terms of the solution of
corresponding adjoint system. The existence of solution for the adjoint system
is also established.
