# CubeSat Mission Scheduling Method Considering Operational Reliability
## 4 CubeSat Scheduling Model  
### Objective Function  
In this paper, the unreliability factors include three aspects: first, low energy power and insufficient energy backup, which will reduce the life of the battery and affect its performance; second, frequent payload start-ups and hidden damages that will reduce the reliability of the system equipment and increase power consumption; and third, the disordered initial start-up sequence of tasks, which will pull down the bus voltage and cause the power supply voltage to be accidentally shut down and may also potentially lead to the problem of system instability or data loss. Aiming at these unreliable factors in the operation process of the CubeSat, this paper defines the total start-up times of tasks and the average state of charge of the lithium battery as the reliability index and combines this with the task priority as a multi-objective optimization model. 1. Objective function \(f_{1}\): maximize the sum of task priorities  
The value and importance of CubeSat missions are expressed by priority. For the CubeSat, the frequency and importance of communication equipment and satellite computers are higher than those of general equipment, so the priority of the antenna and CPU is higher than that of the general equipment. In addition, the attitude control equipment directly affects the satellite's motion state, and the real-time requirement is high, so the momentum wheel has the second highest priority. The lower priority is given to scientific experiment equipment, remote sensing equipment, general loads, and so on. The mission value is positively correlated with the importance of the mission. The more high-priority tasks completed, the greater the sum of task priorities and the higher the value of the tasks that CubeSat can achieve, namely:  
\[maxf_{1}=\sum_{j=1}^{J}\sum_{t=1}^{T}u_{j}x_{j,t} \tag{3}\]  
2. Objective function \(f_{2}\): maximize the average state of charge  
To describe the reliability from the perspective of lithium battery energy backup, the energy level of batteries during the entire operating period can be expressed by the average state of charge. In the pursuit of maximizing the sum of task priorities, if the execution of tasks is not limited, the battery energy will be maximally consumed and the state of charge will be reduced to a lower level, which will reduce the battery lifetime, affect the battery's operating performance, and reduce the reliability of the power system. The average state of charge maintains a high level, which means that the available capacity of the battery is large, the energy reserve is sufficient, and the reliability of the power system is high, namely:  
\[maxf_{2}=\sum_{t=1}^{T}\frac{SOC_{t}}{T} \tag{4}\]
3. Objective function \(f_{3}\): minimize the number of task start-ups  
To describe reliability in terms of the impact of task activation, when the task is powered on, the capacitive components in the circuit charge quickly, resulting in a large surge current that may damage the circuit components and even affect the running instructions of other devices. Although sometimes surge current does not cause obvious damage to equipment, hidden damage can reduce the reliability of system equipment [30]. In addition, frequent start-up of tasks will consume extra time and energy, so reducing the number of task start-ups can improve the reliability of operation, namely:  
\[minf_{3}=\sum_{j=1}^{J}\sum_{t=1}^{T}\phi_{j,t} \tag{5}\]  
Due to the inconsistency of dimensions among multiple objective functions, it is necessary to normalize each objective first and convert each objective into a dimensionless value in the range of [0, 1]. For the normalized objective function, the linear weighting method is used to convert it into a single objective function.