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This paper addresses the set-point control problem of a heat equation within-domain actuation. The proposed scheme is based on the framework of zerodynamics inverse combined with flat system control. Moreover, the set-pointcontrol is cast into a motion planing problem of a multiple-input, multiple-outsystem, which is solved by a Green's function-based reference trajectorydecomposition. The validity of the proposed method is assessed throughconvergence and solvability analysis of the control algorithm. The performanceof the developed control scheme and the viability of the proposed approach areconfirmed by numerical simulation of a representative system.

In-domain control of a heat equation: an approach combining zero-dynamics inverse and differential flatness