## 3 System Model and Problem Formulation
### The Specification of Petri Net
In fact, multi-UAV aided wireless power and information transfer is a dynamic system in which the location of the UAV changes over time. It is necessary to monitor the UAV's energy status in real time and pay attention to the event of arrival or departure from the hovering point. Therefore, this is a hybrid system with continuous and discrete variables, and it is appropriate for HCCPNS to describe its formal specification. Figure 3 shows a representative part of the HCCPNS model for a multi-UAV aided wireless power and information transfer system. Directed arcs with solid black dots and hollow circles at the end of the arrows are the permit arc and the inhibit arc, respectively. The arrow of the read arc and the write arc are both in the middle of directed arc. The explanation of the main places, transitions, and arcs are given in Tables 2 and 3. Figure 2: A simple HCCPNS model. (**a**) Folded model; (**b**) unfolded model: continuous part; (**c**) unfolded model: discrete part. \begin{table}
\begin{tabular}{c c} \hline \hline
**Name** & **Function** \\ \hline \(U_{j}^{i}\) & Place when the \(i\)-th UAV hovers directly over the \(j\)-th SD \\ \(I_{j}\) & Place of the \(j\)-th SD \\ \(T(i)_{j+1}^{j}\) & Transition that the \(i\)-th UAV flies from the \(j\)-th to \((j+1)\)th SD \\ \(Th_{j}^{i}\) & Transition that the \(i\)-th UAV hovers directly over the \(j\)-th SD \\ \(Td_{j}^{i}\) & Transition that the \(i\)-th UAV collects information from the \(j\)-th SD \\ \(T_{sen_{j}}\) & Transition that the \(j\)-th SD consumes energy \\ \(\textit{Teme}(i)\) & Transition that the \(i\)-th UAV returns to the depot emergently \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Description of representative places and transitions. \begin{table}
\begin{tabular}{c c} \hline \hline
**Arc** & **Weight** \\ \hline \(W_{\text{C}}\left(U_{j}^{i},T(i)_{Cj+1}^{j}\right)\) & \(M_{\text{C}}\left(U_{j-j}^{i},T_{j}^{+}\right)\) \\ \(W_{\text{D}}\left(U_{j}^{i},T(i)_{Dj+1}^{j}\right)\) & \(M_{\text{D}}\left(U_{j-j}^{i},T_{j}^{+}\right)\) \\ \(write_{\text{D}}\left(T(i)_{Dj+1}^{j},U_{j+1}^{i}\right)\) & \(M_{\text{D}}\left(U_{j-j}^{i},T_{j}^{+}\right)\) \\ \(write_{\text{C}}\left(T(i)_{Cj+1}^{j},U_{j+1}^{i}\right)\) & \(M_{\text{C}}\left(U_{j-j}^{i},T_{j}^{+}\right)\)-\(P_{mov}\times t_{j+1}\) \\ \(W\left(U_{j}^{i},T_{j}^{i}\right)\) & \(P_{nov}\) \\ \(W\left(U_{j}^{i},T_{j}^{i}\right)\) & \(P_{tra}\) \\ \(W\left(Tc_{j}^{i},I_{j}\right)\) & \(P_{rec}\) \\ \(W\left(I_{j},T_{sen_{j}}\right)\) & \(P_{sen}^{j}\) \\ \(W\left(I_{j},Td_{j}^{i}\right)\) & \(1\) \\ \(write\left(Td_{j}^{i},U_{j}^{i}\right)\) & \(1\) \\ \(inhibit\left(I_{j},Tc_{j}^{i}\right)\), \(permit\left(I_{j},T(i)_{j+1}^{j}\right)\), & \(M_{\text{C}}\left(I_{j}\right)=k_{H}\left(I_{j}\right)\) \\ \(inhibit\left(U_{j}^{i},T_{c}^{i}\right)\), \(inhibit\left(U_{j}^{i},T_{c}^{i}\right)\), \(inhibit\left(U_{j}^{i},T_{j+1}^{i}\right)\) & \(M_{\text{C}}\left(U_{j}^{i}\right)=k_{L}\left(U_{j}^{i}\right)\) \\ \(inhibit\left(U_{j}^{i},T(i)_{j+1}^{j}\right)\) & \(M_{\text{C}}\left(U_{j}^{i}\right)=k_{L}\left(U_{j}^{i}\right)\) \\ \(permit\left(U_{j}^{i},T_{eme}(i)\right)\) & \(M_{\text{C}}\left(U_{j}^{i}\right)=k_{L}\left(U_{j}^{i}\right)\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Description of representative arcs. Figure 3: HCCPNS model of multi-UAV aided wireless power and information transfer.