## 2 System Model and Problem Formulation  
In this work, we propose a UAV-enabled wireless-powered MEC system in a post-disaster area, as shown in Figure 1. The terrestrial wireless infrastructures were damaged in the disaster. In order to get the situation of the disaster area and prepare for further rescue, a UAV, which is equipped with an RF transmitter and an MEC device, providescharging and computing services for a set \(\mathcal{N}\triangleq\{1,\ldots,N\}\) of ground users, which has certain computation tasks \(R_{n}\) to complete, trapped in the disaster area. Without loss of generality, we adopt a three-dimensional Euclidean coordinate system to represent the locations, and measure all dimensions in meters. Affected by the destruction of terrestrial wireless infrastructures, the UAV only knows the approximate location of \(n\)th users, denoted by \(\mathbf{q}_{n}=(x_{n},y_{n},0)\), with limited location information, while the exact location of \(n\)th users is \(\bar{\mathbf{q}}_{n}=(\bar{x}_{n},\bar{y}_{n},0)\), with a estimation error \(\Delta\mathbf{q}_{n}\). The relation between the exact and approximate location of \(n\)th users is given by  
\[\bar{\mathbf{q}}_{n} =\mathbf{q}_{n}+\Delta\mathbf{q}_{n}, \tag{1}\] \[\Delta\mathbf{q}_{n} \in\Omega_{n} \triangleq\{\|\Delta\mathbf{q}_{n}\|\leq\varepsilon_{n}\},\]  
where \(\Omega_{n}\) is a continuous set of possible location estimation errors for the \(n\)th users, and \(\varepsilon_{n}\) denotes the radius of the uncertainly region \(\Omega_{n}\). We assume that the UAV takes off and lands at a safe location \(\mathbf{q}_{s}=(x_{s},y_{s},0)\) within finite flight duration \(\mathcal{T}\). The flight duration \(\mathcal{T}\) is discretized into \(T\) sufficiently small time slots with equal length \(\delta=\mathcal{T}/\mathcal{T}\). Thus, the UAV can be seen as fixed in a certain position in each time slot, and its horizontal plane coordinate at \(t\)th slot is \(\mathbf{q}_{u}[t]=(x_{t},y_{t})\). Similar to [29], we assume that the UAV flies at a constant altitude \(H\) to avoid the flight energy consumption caused by frequent ascend or descend. Correspondingly, the distance between UAV and user \(n\) is  
\[d_{n}[t]=\sqrt{H^{2}+\ \|\ \mathbf{q}_{u}[t]-\mathbf{q}_{n}\ \|^{2}}, \tag{2}\]  
where \(\|\cdot\|\) denotes the Euclidean norm. Similar to [18], we assume the wireless channel between the UAV and users is LoS link. Then, the channel power gain between UAV and users is  
\[g_{n}[t]=\beta_{0}d_{n}[t]^{-2}, \tag{3}\]  
where \(\beta_{0}\) is the channel power gain at \(d_{0}=1\) m.  
In downlink WPT mode, we consider that the UAV uses constant transmission power \(P_{u}\) for wireless power transmission. The energy harvested by \(n\)th user is given as  
\[E_{h}[t]=\eta g_{n}[t]P_{u}\delta, \tag{4}\]  
Figure 1: The UAV-enabled wireless-powered MEC system in post-disaster area. where \(0<\eta\leq 1\) denotes the energy conversion efficiency of each user, while in uplink WIT mode, for given offloading power \(P_{o,n}[t]\), the offloading rate \(r_{tr,n}[t]\) of \(n\)th user in the \(t\)th slot is given as  
\[r_{tr,n}[t]=Blog_{2}(1+\frac{P_{o,n}[t]g_{n}[t]}{\sigma^{2}}), \tag{5}\]  
where \(B\) is the communication bandwidth, and \(\sigma^{2}\) is the variance of additive white Gaussian noise with zero mean. To utilize the energy in an efficient way, we assume that both UAV and users can adaptively adjust the CPU frequency [29]. The computation task amounts \(R_{c,n}\) and the computation energy consumption \(E_{c,n}\) of \(n\)th user in the \(t\)th slot are given as  
\[R_{c,n} =\frac{f_{n}[t]\delta}{C_{n}}, \tag{6}\] \[E_{c,n} =\theta_{n}f_{n}[t]^{3}\delta,\]  
where \(f_{n}[t]\) represents the CPU frequency of users, \(C_{n}\) denotes the number of CPU cycles to complete the computation, and \(\theta_{n}\) is the effective capacitance coefficient of the CPU. The expressions of computation amounts \(R_{c,n}\) and computation energy consumption \(E_{c,n}\) of UAV are consistent with users, which are not listed here.