  This paper investigates the output feedback setpoint regulation control of a
reaction-diffusion equation by means of boundary control. The considered
reaction-diffusion plant may be open-loop unstable. The proposed control
strategy consists of the coupling of a finite-dimensional observer and a PI
controller in order to achieve the boundary setpoint regulation control of
various system outputs such as the Dirichlet and Neumann traces. In this
context, it is shown that the order of the finite-dimensional observer can
always be selected large enough, with explicit criterion, to achieve both the
stabilization of the plant and the setpoint regulation of the system output.
