## 2 Related Work
jointly optimized the UAV hovering location and duration to maximize the minimum energy of sensors after data transmission and energy harvesting under data collection and UAV energy consumption constraints, and a near-optimal UAV route was determined by adjusting the initial feasible UAV route iteratively [27]. [PERSON] et al. proposed a novel multiple-stage dynamic matching to model the charging relationship between energy-constrained devices (ECDs) and UAVs. They maximized the total amount of charging energy by a multiple-period charging process [28]. [PERSON] et al. studied the UAV's trajectory optimization from the viewpoint of UAV's energy utilization efficiency. For this purpose, they presented a polynomial-time randomized approximation scheme (PARS) to obtain the minimal number of hovering locations [29]. Subsequently, to achieve balanced energy consumption among UAVs, they maximized the energy utilization efficiency of UAVs, and they minimized the communication delay by optimizing the trajectory jointly with constraints of the energy capacity and the area of the target region [30]. Taking into account the power consumption of the UAV, the charging process from a base station to the UAV and the conversion loss of the energy harvester, [PERSON] et al. designed two different charging schemes to maximize the sum-energy received by all sensors for a one-dimensional and a two-dimensional wireless power transfer system [31]. [PERSON] et al. formulated an optimization problem to enhance the UAV's sensing performance and power allocation as well as its placement, minimizing the time of transmitting data according to different communication requirements [32]. [PERSON] et al. formulated an optimization problem to minimize the average Age of Information of the data collected from all ground sensor nodes. They used Karush-Kuhn-Tucker (KKT) conditions to find the optimal energy transfer and the data collection time allocation; through this, a UAV's trajectory planning was obtained by dynamic programming and an ant colony heuristic algorithm [33]. Considering the UAV's hovering inaccuracy on received power at ground deployed sensor nodes, [PERSON] et al. proposed a hovering inaccuracy-aware optimal charging system design algorithm to find the optimal transmit power, hovering altitude, and antenna exponent [34]. [PERSON] et al. took into account the realistic nonlinear energy harvesting model for the first time in order to maximize the minimum harvested energy among ground devices under the constraint of a UAV's maximum flight speed limit [35]. [PERSON] et al. made a trade-off between the altitude of a drone and its charging coverage to ensure good harvesting capabilities for industrial scenarios [36]. For the studies in [37; 38; 39], the UAV was used to collect data from sensors, and routing protocols were studied to reduce the data loss as well as energy consumption. Although the above work involves energy consumption, UAV flight trajectory, computational performance, and other aspects, most of them use a single UAV as the energy output source, which actually limits the improvement of UAV performance. In this paper, several UAVs are used to serve SDs, and factors such as the number of UAVs, flight trajectory and communication delay are jointly considered to be applicable to large-scale wireless power and information transfer networks. Petri net has unique advantages in the modeling and analysis of a cyber-physical system (CPS) and also automated manufacturing systems. [PERSON] et al. addressed the problem of scheduling robotic activities in human-robot collaborative contexts based on time Petri nets [40]. Aiming at a kind of CPS containing discrete events, continuous processes, stochastic phenomena, time delay, and decision, [PERSON] et al. proposed the modeling methods of a CPS based on the modified hybrid stochastic timed Petri net with three-tier architecture, and they introduced a decision place to strengthen the decision-making ability of a CPS [41]. [PERSON] et al.