Abstract: Compared to single-agent systems, multi-agent systems exhibit advantages such as high efficiency and strong survivability in task execution. However, an increase in distance increases the difficulty for agents to communicate with each other and also severely limits the task-performance range of multi-agent systems. A potential solution to this problem is the use of communication relays between agent nodes. Given their small size, low cost, and flexibility compared to traditional satellites or ground stations, unmanned aerial vehicles (UAVs) are gradually playing an increasingly important role in the field of communication relay. This study focuses on aerial multi-agent systems. Specifically, fixed-wing UAVs are used to enhance the network communication performance among multiple agents. These agents operate in the air, and their motion trajectories are determined by their respective tasks. This study proposes a model-based adaptive motion control method for UAV communication relay, which solves the relay motion control problem by simultaneously considering unknown radio frequency (RF) channel parameters, unknown multi-agent mobility, and unavailable angle of arrival (AoA) information of received signals. We first model and mathematically express the problem of using relay UAV to enhance communication between airborne multi-agent systems and select the received signal strength as the communication optimization indicator. Based on this, we subsequently consider two aspects: unknown channel parameter estimation and optimal relay position search. For the former, we propose an estimation algorithm based on Gaussian process learning and online data measurement to estimate the wireless channel parameters between the UAV and each agent. For the latter, we consider two different relay applications: end-to-end communication and multi-node communication. For the optimal relay position search under end-to-end communication, we propose a line search algorithm and demonstrate its stability and convergence. Regarding the optimal relay position search under multi-node communication, we propose a general gradient-based algorithm, which provides a target relay position at each decision time step, reducing two-dimensional search to a one-dimensional search. We analyze and provide the computational complexity of these two different optimal relay position search methods. Notably, the gradient-based optimal relay position search algorithm under multi-node communication is also applicable to end-to-end communication scenarios. However, given the smaller computational complexity of the line search-based optimal relay position search method compared to the gradient-based method under end-to-end communication, we recommend using the line search-based algorithm in end-to-end communication. Additionally, while solving the aforementioned two important problems, solving the problem of predicting the positions of multi-agents and guiding the relay UAV to the optimal relay position searched in real-time is necessary. This study uses a position estimation algorithm based on Kalman filtering and a guidance law based on the Lyapunov guidance vector field to solve these two problems. Finally, the simulation experiments are designed to support communication from stationary to moving nodes and from end-to-end to multi-node communication. Meanwhile, to compare the impact of different channel models and wireless channel parameter estimation algorithms on the relay implementation performance of the network, simulation experiments are conducted. We compare the relay network performance achieved by the proposed channel model with that of the distance channel model, as well as the performance of the proposed Gaussian process learning algorithm with the maximum likelihood estimation algorithm. Simulation results show that the proposed relay motion control algorithm can drive the UAV to reach or track the motion of the optimal relay position and improve the network performance, and the improvement is better than the methods based on the distance channel model and the maximum likelihood estimation.