  Finite-time linear-quadratic control of partial differential-algebraic
equations (PDAEs) is considered. The discussion is restricted to those that are
radial with index $0$; this corresponds to a nilpotency degree of 1. We
establish the existence of a unique minimizing optimal control. A projection is
used to derive a system of differential Riccati-like equation coupled with an
algebraic equation, yielding the solution of the optimization problem in a
feedback form. This generalizes the well-known result for PDEs to this class of
PDAEs. These equations and hence the optimal control can be calculated without
construction of the projected PDAE. Finally, we provide numerical simulations
to illustrate application of the theoretical results.
