# Precise Mission Process Control Based on a Novel Dual-Code Group Network Plan Diagram
## 5 Mission Process Control Strategy
### Control Strategy Solution
#### 5.2.4 Solving of Control Strategy
Since the maximum anti-disturbance capability can be achieved when the current critical path is unchanged, based on the premise that the critical path is unchanged, if we can obtain the maximum compressible quantity of each validly controllable mission on the critical path, we can assign the control quantity to each valid controllable mission on the current critical path based on the error and realize the solution of the control quantity. Therefore, we design the maximum anti-disturbance capability algorithm for valid controllable missions. The principle of Algorithm 4 is very simple: based on the premise that the critical path is invariant, the maximum compressible quantity of an efficiently controllable mission \(m_{i}^{*}\) at the moment \(t_{c}\,\chi_{m_{i}^{*}}^{\max}(t_{c})\) is equal to the maximum compressible quantity of \(m_{i+1}^{*}\) at the  
Figure 13: Diagram of the critical path conservation theorem. (**a**) shows the dual coding system and the red path is the critical path. (**b**) shows the critical path is not changed. (**c**) shows the critical path is changed. moment \(t_{c}\), minus the quantity contributed by the compression of all previous missions, i.e.,  
\[\chi^{\text{max}}_{m^{*}_{i}}(t_{c})=\text{max}\bigg{(}\Delta T^{m^{*}_{j+1}}_{ PS}(t+\Delta t)\bigg{)}-\sum_{k=1}^{l-1}\chi^{\text{max}}_{m^{*}_{k}}(t_{c}) \tag{58}\]  
With (56), we have obtained the earliest plan start time for the mission \(m^{*}_{i+1}\) at the moment \(t_{c}+\Delta t\), but this could potentially lead to a change in the critical path at the moment \(t_{c}+\Delta t\). Therefore, based on the premise that the critical path is unchanged, the maximum advance in the plan start time of \(m^{*}_{i+1}(t)\) is equal to the minimum of the maximum advance in the plan start time of the subsequent missions on the critical path, namely,  
\[\text{max}\bigg{(}\Delta T^{m^{*}_{j}}_{PS}(t+\Delta t)\bigg{)}=\min_{k\in[j+1,n]}\Big{(}\text{min}\Big{(}T^{m^{*}_{PS}}_{PS}(t+\Delta t)\Big{)}-T^{m^{*}_{k }}_{PS} \tag{59}\]  
To better illustrate the principle of (59), we design a scenario. As shown in Figure 14a, the mission is represented by the single code, and the red path in the figure is the critical path. Assume that the mission \(m_{1}\) is controllable and all other missions are uncontrollable. With the critical path unchanged, now solve for the maximum of the plan start time advance for each mission. Since \(m_{1}\) is the only controllable mission, decreasing \(x_{m_{1}}\) leads to an advancement in the plan start times of \(m_{2}\) and \(m_{5}\). Since \(m_{3}\) and \(m_{4}\) are not controllable, the maximum of the plan start time advance for \(m_{5}\) can be obtained as \(\text{max}(\Delta T^{m_{5}}_{PS}(t))=T^{m_{3}}_{PS}(t)-T^{m_{4}}_{PE}(t)\). As shown in Figure 14b, the threshold state of critical path switching is reached when the compression of \(m_{1}\) is \(\chi^{\text{max}}_{m_{1}}(t_{c})=T^{m_{3}}_{PS}(t)-T^{m_{4}}_{PE}(t)\). At this time, we have \(\text{max}(\Delta T^{m_{5}}_{PS}(t))=\text{max}(\Delta T^{m_{5}}_{PS}(t))\). As shown in Figure 14c, the critical path changes when the compression of \(m_{1}\) is \(\chi^{\text{max}}_{m_{1}}(t_{c})<T^{m_{3}}_{PS}(t)-T^{m_{4}}_{PE}(t)\), when \(\text{max}\big{(}\Delta T^{m_{5}}_{PS}(t)\big{)}>\text{max}\big{(}\Delta T^{ m_{5}}_{PS}(t)\big{)}\). Therefore, provided that the critical path remains unchanged, the plan start time advance of \(m_{2}\) cannot exceed the least upper bound of the plan start time advances of all the missions that come after it, otherwise the critical path changes. Equation (58) is a recursive equation, and it is sufficient to recursively follow the order of the missions in the core path. In addition, based on the conclusions of (53) and (58), it can be obtained that the current maximum anti-disturbance capability of the whole program is equal to the sum of the maximum anti-disturbance capability of each core critical mission, and there is a linear relationship between the two, under the premise that the critical path remains unchanged.