This paper develops two-dimensional linear quadratic (2DLQ) optimal control schemes that can be applied for iterative learning control (ILC) design. For a class of repetitive 2D processes, based on control objectives defined over a single cycle or multiple cycles, two different 2DLQ optimal control schemes, single-cycle 2DLQ (SC-2DLQ) and multicycle 2DLQ (MC-2DLQ), are derived. Furthermore, to balance control performance and computational load of MC-2DLQ optimal control, a cyclewise receding horizon 2DLQ (CWRH-2DLQ) optimal control strategy is introduced based on a quadratic performance index with a cyclewise receding horizon. The cyclewise stability and robustness analysis are conducted based on the cyclewise dynamics of the closed-loop system. The simulation shows that the proposed algorithms are effective. On the basis of the results of this paper, new ILC schemes for batch processes will be presented as a sequel to this paper.