OPTIMAL BOUNDARY CONTROL OF THE STOKES FLUIDS WITH POINT VELOCITY OBSERVATIONS

This paper studies constrained linear-quadratic regulator (LQR) proble ms in distributed boundary control systems governed by the Stokes equa tion with point velocity observations. Although the objective function is not well defined, we are able to use hydrostatic potential theory and a variational inequality in a Banach space setting to derive a fir st-order optimality condition and then a characterization formula of t he optimal control. Since matrix-valued singularities appear in the op timal control, a singularity decomposition formula is also established , with which the nature of the singularities is clearly exhibited. It is found that in general, the optimal control is not defined at observ ation points. A necessary and sufficient condition that the optimal co ntrol is defined at observation points is then proved.