This paper presents the application of inverse optimal control approach to an unmanned quadrotor air vehicle system. Here, the inverse optimal controller is designed to solve the reference tracking problem relying on the use of control Lyapunov function. In the establishment of the control law, the affine-in-input discrete-time nonlinear system model is taken into consideration. A stabilizing feedback control law is constructed such that control Lyapunov function is known a priori. After stability examination and determination of a meaningful cost functional, respective cost functional is optimized. Then, a matrix that minimizes a tracking error function is searched using PSO algorithm. The designed controller has been applied to a nonlinear model of a quadrotor. It is shown that the proposed controller guarantees a fast convergence and makes the quadrotor stabilize itself very fast and follow aggressive trajectories accurately under certain circumstances.