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The study of optimal control techniques is of interest in various types application which required the control of complex dynamical systems, one of this cases are Unmanned Aerial Vehicles (UAV). UAV have been used in diverse fields such as: civil engineering, agriculture, disaster management, etc. Such UAV require control strategies that guarantee their stability, reject external disturbances and measurement noise. The results obtained when applying optimal control techniques to a stationary platform, powered by four motors, are presented. A comparative analysis of the results for the different controls obtained is made. For this comparison, performance specifications of the time response were used and the performance index was calculated for each implemented strategy. The analysis includes the development of the steady state platform dynamic model by means of Euler-Lagrange equations of motion, obtaining a MIMO system described by six state equations and four inputs. The first optimal control technique studied was the linear quadratic regulator (LQR) with a state-observer. This implementation required the evaluation of different performance index weight matrices Q and R until a satisfactory response of the system was obtained. The next technique studied was the implementation of the LQ controller with Kalman filter (linear quadratic Gaussian regulator, LQG) and the use of Loop Transfer Recovery (LTR) to recover the robustness characteristics of LQR. Results obtained show the viability of applying such optimal control techniques to unmanned aerial vehicles, obtaining the best results with the LQG/ LTR technique. [ABSTRACT FROM AUTHOR]