The objective of this paper is the development of a randomized Linear Quadratic Regulator (LQR) algorithm via gradient-based methods for Unmanned Aerial Vehicles (UAVs) subject to uncertainty to cope with different operating conditions. A controller gain is synthesized using a Lyapunov approach dealing with a formation of two mini-UAV systems in the classical Leader/Wingman configuration. The advantages of the proposed technique over the existing deterministic methods for control design are as follows: (i) the uncertainty structure is not defined a priori and (ii) one Lyapunov inequality is approximately solved at each iteration of the algorithm, so that the number of inequalities does not grow with the number of uncertain parameters. The main contribution of this paper is to demonstrate that the proposed sequential algorithm provides a randomized controller which stabilizes the uncertain system. This probabilistic technique is then validated with an extensive a posteriori analysis. The final result is to show that the UAV reaches the desired altitude without an additional Proportional-Integral-Derivative (PID) channel, and therefore tuning of the controller gains is avoided.