Robust Boundary Control of the Stokes Fluids with Boundary Point Observations

In this paper, we rst study an optimal boundary control problem governed by the Stokes system with point pressure observations on the boundary. A constrained LQR approach with some hydrostatic potential theory, boundary integral equations and a variational inequality in a Banach space setting is applied to establish a state feedback characterization of the optimal control. Since a hyper-singularity is involved in regularity/singularity analysis and the kernel is only p.v.-integrable, many Lebesgue integral related tools cannot be applied directly. We develop a method to handle such a hyper-singularity in establishing some new regularity results. Robust optimal control problems, i.e., to minimize the velocity at observation points while bringing down the pressure there, are then solved in the last section.