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This paper considers an unmanned aerial vehicle (UAV) that is used in industrial Internet of things (IIoT) networks to execute one or more {\em pre-loaded} computation tasks. A key novelty is that these tasks support imprecise computation, where each task has a mandatory and optional part. Another novelty is that both parts of a task require data from one or more solar-powered ground devices. The mandatory part of each task must be computed by the UAV before the end of its trajectory. If there are sufficient resources and time, the UAV can download more data from devices and execute the optional part of tasks to improve results quality.
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To schedule tasks on a UAV, this paper outlines a novel mixed integer linear program (MILP) to optimize the execution of tasks and data collection. Further, it outlines the first model predictive control (MPC) based solution, called MPC-$S$, for the problem at hand that uses current and past energy arrivals information of devices.
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Our results show that MPC-$S$ achieves approximately 89.9\% of the optimal results quality.
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