This chapter establishes an optimal control framework tailored for periodic satellites operating under bounded parameter uncertainties. Addressing the limitations of conventional design methods, the methodology adopts a set-theoretical perspective to extend the periodic linear quadratic regulator (PLQR) into the interval domain. By leveraging the Chebyshev interval method, the governing periodic Riccati differential equation is reconstructed to explicitly account for parameter variations, enabling the analytical computation of interval bounds for both the periodic feedback gain and the control cost function. The aforementioned interval-based time-dependent reliability (ITDR) index is used for reliability assessment. To solve this complex constrained problem, a novel set-based iterative optimization algorithm is developed. Numerical validations demonstrate that this approach effectively mitigates the impact of periodic disturbances and uncertainties, achieving a superior balance between control precision and system reliability compared to Monte Carlo simulations (MCSs).