The conversion efficiency of the wind turbine in partial load operation can be maximized if it operates at the optimal tip speed ratio and the optimal pitch angle, thus the optimal power coefficient. For this purpose, the wind turbine rotor must track an optimal reference speed. In this work, a nonlinear closed-loop finite horizon optimal tracking via state dependent Riccati equation (SDRE) is applied to track the optimal reference rotor speed of a permanent magnet synchronous generator based wind energy conversion system. The key idea in this technique is to use an approximate analytic approach to convert the state dependent differential Riccati equation (SD-DRE) into the linear differential Lyapunov equation which can be solved in a closed form at each time step of a given time period. In addition, a state dependent vector differential equation is solved simultaneously with SD-DRE at each time step to perform the optimal tracking problem.