This paper presents a model predictive approach to the energy-aware control of tasks’ execution in an assembly line. The proposed algorithm takes into account both the need for optimizing the assembly line operations (in terms of the minimization of the total cycle time) and that of optimizing the energy consumption deriving from the operations, by exploiting the flexibility added by the presence of a local source of renewable energy (a common scenario of industries that are often equipped, e.g., with photovoltaic plants) and, possibly, also exploiting an energy storage plant. The energy-related objectives we take into account refer to the minimization of the energy bill and the minimization of the peaks in the power injected and absorbed from the grid (which is desirable also from the perspective of the network operator). We propose a mixed-integer linear formulation of the optimization problem, through the use of H-infinite norms, instead of the quadratic ones. Simulation results show the effectiveness of the proposed algorithm in finding a trade-off that allows keeping at a minimum the cycle time, while saving on the energy bill and reducing peak powers.