  This paper addresses the set-point control problem of a heat equation with
in-domain actuation. The proposed scheme is based on the framework of zero
dynamics inverse combined with flat system control. Moreover, the set-point
control is cast into a motion planing problem of a multiple-input, multiple-out
system, which is solved by a Green's function-based reference trajectory
decomposition. The validity of the proposed method is assessed through
convergence and solvability analysis of the control algorithm. The performance
of the developed control scheme and the viability of the proposed approach are
confirmed by numerical simulation of a representative system.
