Hydrogen production from water electrolysis has the potential to mitigate the intermittency associated with power generated from variable renewable energy. In addition, proton exchange membrane water electrolyzer (PEMWE) has gained attention within the last decade because of its relative advantage over other water electrolysis technologies. However, the high cost of operation that is due to its energy intensity has been a major setback. In this work, we develop an optimal operating strategy for the PEMWE process using the parametric optimization and control framework. First, we present a dynamic mathematical model of the PEMWE that captures the detailed electrochemical interaction, transport phenomenon, bubble coverage, and other interactions associated with energy losses in the system. Secondly, we design a model predictive control (MPC), which is then reformulated into a multiparametric model predictive control (mp-MPC). Unlike the MPC, the mp-MPC avoids the online optimization procedure at every time step because the optimization is done once and offline. The control action is an explicit function of parameters that are realized during the process. The controller is tested on the original dynamic model in a closed loop validation scheme.