This chapter presents an optimal control framework tailored for space power satellites (SPS) subject to multi-source uncertainties and periodic disturbances. Addressing the limitations of probabilistic methods in data-sparse space environments, the dynamic modeling is grounded in non-probabilistic interval analysis, treating initial states and uncertain inertia as unknown-but-bounded (UBB) parameters. A hybrid control architecture is developed, integrating feedforward compensation for periodic disturbances with an interval Linear-Quadratic Regulator (LQR). A key theoretical contribution discussed is the formulation and solution of the interval algebraic Riccati equation (IARE), which allows for the direct computation of uncertain feedback gain bounds. Furthermore, to assess the system's safety over time, an interval-based time-dependent reliability (ITDR) model is constructed utilizing interval process theory and first passage concepts. The control parameters are refined through a constrained multi-objective optimization strategy. Numerical simulations on a classical Abacus architecture SPS demonstrate that this interval-based methodology achieves control precision comparable to Monte Carlo simulations (MCSs) but with significantly higher computational efficiency.