ABSTRACT
In this chapter, we study the quadratic optimal control problem over a finite time horizon in the case where the free dynamics operator A and the control operator B yield a singular estimate for eAtB. Here, eAt is the corresponding s.c. semigroup which, by assumption, is not analytic. The resulting abstract model covers systems of coupled Partial Differential Equations, which possess an analytic component, but which are not themselves analytic. Several applications are given to hyperbolic/parabolic structural acoustic problems, to thermoelastic problems, and to sandwich beam problems. As to structural acoustic problems, we have that a hyperbolic PDE (a wave equation within an acoustic chamber) is coupled with a parabolic PDE (the flexible wall), which is either modeled by an elastic equation with structural damping [1], [5], or else by a thermoelastic equation with no rotational inertia [18-21], [23], [16, Vol. I], or else by a sandwich beam [11], [28].
