  This paper investigates user scheduling and trajectory optimization for a
network supported by an intelligent reflecting surface (IRS) mounted on an
unmanned aerial vehicle (UAV). The IRS is powered via the simultaneous wireless
information and power transfer (SWIPT) technique. The IRS boosts users' uplink
signals to improve the network's longevity and energy efficiency. It
simultaneously harvests energy with a non-linear energy harvesting circuit and
reflects the incident signals by controlling its reflection coefficients and
phase shifts. The trajectory of the UAV impacts the efficiency of these
operations. We minimize the maximum energy consumption of all users by joint
optimization of user scheduling, UAV trajectory/velocity, and IRS phase
shifts/reflection coefficients while guaranteeing each user's minimum required
data rate and harvested energy of the IRS. We first derive a closed-form
solution for the IRS phase shifts and then address the non-convexity of the
critical problem. Finally, we propose an alternating optimization (AO)
algorithm to optimize the remaining variables iteratively. We demonstrate the
gains over several benchmarks. For instance, with a 50-element IRS, min-max
energy consumption can be as low as 0.0404 (Joule), a 7.13% improvement over
the No IRS case (achieving 0.0435 (Joule)). We also show that IRS-UAV without
EH performs best at the cost of circuit power consumption of the IRS (a 20%
improvement over the No IRS case).
