A self-powered scheme is explored for achieving long-endurance operation, with the use of solar power and buoyancy lift. The end goal is the capability of "infinite" endurance while complying with the UAV dynamics and the required control performance, maneuvering, and duty cycles. Nondimensional power terms related to the UAV power demand and solar energy input are determined in a framework of Optimal Uncertainty Quantification (OUQ). OUQ takes uncertainties and incomplete information in the dynamics and control, available solar energy, and the electric power demand of a solar UAV model into account, and provides an optimal solution for achieving a self-sustained system in terms of energy. Self-powered trajectory tracking, speed and control are discussed. Aerial vehicles of this class can overcome the flight time limitations of current electric UAVs, thereby meeting the needs of many applications. This paper serves as a reference in providing a generalized approach in design of self-powered solar electric multirotor UAVs.