This paper is intended to tackle the control problem associated with an
extended phase field system of Cahn-Hilliard type that is related to a tumor
growth model. This system has been investigated in previous contributions from
the viewpoint of well-posedness and asymptotic analyses. Here, we aim to extend
the mathematical studies around this system by introducing a control variable
and handling the corresponding control problem. We try to keep the potential as
general as possible, focusing our investigation towards singular potentials,
such as the logarithmic one. We establish the existence of optimal control, the
Lipschitz continuity of the control-to-state mapping and even its Fr\'echet
differentiability in suitable Banach spaces. Moreover, we derive the
first-order necessary conditions that an optimal control has to satisfy
