Green unmanned aerial relaying (UAR) systems, featuring solar-powered unmanned aerial vehicles (UAVs) to provide agile and flexible communication services, have recently gained significant attention for their wide applications. Nonetheless, due to the essential dynamics of wireless channel conditions and solar energy supply, maintaining system stability is a critical concern in practical green UAR systems, as fluctuation in these two factors can significantly affect communication performance. To address this issue, this paper proposes a scheme design for stable communications in a UAR system with dynamic solar energy supply and wireless channel conditions. Specifically, we first formulate an optimization problem, called OFL, to control the power allocation and flow data rate assignment to minimize long-term time-averaged energy consumption while ensuring the demanded data rate and system stability. Considering that solving OFL needs complete prior information about the solar power supply and wireless channel conditions, which is hardly acquired, we then explore the Lyapunov theory to transform OFL as an online optimization problem, called ONL. To find the solution to ONL, we subsequently design a distributed algorithm that enables each UAV to make its own decision locally, thus reducing the computational overhead of each UAV. Particularly, we prove that stability can be guaranteed by employing the designed algorithm. Extensive simulations are conducted to show the performance achieved by the proposed scheme.
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