This paper studies optimization of dynamic systems described by affine Functional Differential Equations (FDEs) involving a sup-operator. We deal with a class of FDEs-featured Optimal Control Problems (OCPs) in the presence of some additional control constraints. Our aim is to derive the first-order optimality conditions and propose an effective solution algorithm. Moreover, we are interested in applications of the resulting optimal design techniques to the Maximum Power Point Tracking (MPPT) control of solar energy plants. We develop a conceptual computational approach to the specific class of OCPs under consideration and also point possible applications of this new methodology in MPPT control.