Demand for unmanned aerial vehicles (UAVs) has been increasing in many applications such as surveillance, reconnaissance, and communication. Through UAV capabilities such as rapid mobility and airborne capability, UAVs can provide a communication network in an area where communication infrastructure is not temporarily available. And UAV-based relay networks can be also used for compensating for cell outage and cell overload in cellular networks, and for enhancing the connectivity of mobile ad-hoc networks. Furthermore, the UAV-based relay networks can be used to extend the communication range or the operational range of ground nodes. In order to construct reliable UAV-based relay networks, we have to solve many technical issues such as positioning, path planning, signal processing, medium access control, and routing. In this dissertation, we investigate energy-aware control problems of UAV-based relays. Communication networks can be constructed within a short time through rapid maneuvering of UAV-based relays. The communication performance can be significantly improved through the efficient maneuvering control of UAV-based relays. However, since the UAV-based relays have a limited energy capacity and the maneuvering power depends on how to control the maneuvering, energy-efficient control and management for seamless networks is required for mission completion. Furthermore, since the maneuvering control needs the location information of ground nodes with time, communication overhead may become another problem.First, we propose an energy-efficient circular maneuvering \& communication scheme for a UAV-based relay connecting two stationary ground nodes. Based on a new energy efficiency metric, which is defined as the ratio of network capacity to the power consumption of both maneuvering and communication, we solve an energy efficiency maximization problem. The proposed maneuvering & communication scheme significantly increases energy efficiency, compared with the...