Background/Objectives: Design and development of an optimal control system for a quadcopter unmanned aerial vehicle (UAV). Methods/Statistical Analysis: The 6DOF quad copter state-space models was used for Linear Quadratic Regulator (LQR) and Linear Quadratic Gaussian (LQG) simulations in MATLAB/Simulink. The simulations produced satisfactory results, which have been presented. Findings: A comparison between Low Pass Filter (LPF) and Kalman filter is also shown which shows that LQR is useless in presence of noise hence LQG was employed in such a situation. Application/Improvements: The optimal control system for quadcopter was successfully developed, which can be practically implemented on an actual quadcopter for stable unmanned flight of the aerial vehicle.