A simple core control model is developed for the control of xenon spatial oscillations in load following operations of a current-design nuclear pressurized water reactor. The model is formulated as a linear-quadratic tracking problem in the context of modern optimal control theory, and the resulting two-point boundary problem is solved directly by the techniques of initial value methods. The system of state equations is composed of the one-group diffusion equation with temperature and xenon feedbacks, the iodine-xenon dynamics equations, and an energy balance relation for the core. Control is via full-length and part-length control rod banks, boron, and coolant inlet temperature. The system equations are linearized around an equilibrium state, which is an eigen-solution of the nonlinear static equations with feedback. The nonlinear eigenvalue problem is shown to have a unique positive solution under certain conditions by using the bifurcation theory, the solution being obtained by an iteration based on the use of monotone operators. A modal expansion reduces the linearized equations to a lumped parameter system. Minimization of an objective functional that expresses tracking the load with small control effort leads to a stiff two-point boundary value problem with boundary layers at both initial and final times, which is solved numerically. In a number of cases, results show that the optimal solution closely follows the desired load demand and maintains the desired power distribution with a small control effort.