The regulator problem for parabolic equations with Dirichlet boundary control. I: Riccati's feedback synthesis and regularity of optimal solution (Q1100421)

This is the first part of a two-parts paper devoted to the construction and approximation of the feedback regulator for a quadratic boundary control problem for a second-order parabolic equation. The equation is defined on a bounded domain with finitely many conical points. The control is through the Dirichlet boundary condition. A quadratic cost functional with infinite time horizon is investigated. In the first part of the paper it is shown that the feedback synthesis exists and can be expressed in terms of the solution to a time- independent operator Riccati equation. Regularity of the optimal solution is analyzed.