# Compensation Control Strategy for Orbital Pursuit-Evasion Problem with Imperfect Information
## 6 Results and Discussion
### Examples of Compensation Control Strategy
#### 4.2.2 Terminal Time is Fixed  
The terminal time is set as 212 s.  
Figure 11 shows the average ZEM distance of 100 Monte Carlo runs in three fixed-time scenarios: the pursuer plays without time delay, without compensation for time delay, and with compensation for time delay. When the pursuer plays without time delay, the average terminal distance between the two players reaches 0.00003202 m, which is less than the safe distance. When the pursuer plays without compensation for time delay, the average terminal distance between the two players is 25.6273 m, which means the pursuer failed to intercept the evader. When the pursuer plays with compensation for time delay, the average terminal distance between the two players reaches 0.1064 m, which is less than the safe distance. According to Figure 11b, when the pursuer has delayed information, the zero-effort miss distance at the beginning of the confrontation shows an upward trend. The reason is that the pursuer adopts no control at the beginning of the confrontation due to lack of information. According to Figure 11c, when the pursuer plays without time delay, the average zero-effort miss distance reaches below the safe distance at 180.43 s. When the pursuer plays with compensation for time delay, the average zero-effort miss distance reaches below the safe distance at 202.59 s. However, when the pursuer plays without compensation for time delay, the zero-effort miss distance converges to a large value, which means the pursuer cannot intercept the evader. Figure 10: The average control variable of 100 Monte Carlo runs in the scenario that the pursuer plays (**a**) without time delay; (**b**) without compensation for time delay; and (**c**) with compensation for time delay. **Example 3**. : _The pursuer's information has no time delay, and the evader plays under three scenarios: no time delay, with compensation for time delay, and without compensation for time delay. The delay time is 1 s._  
_Terminal Time is Free_  
Figure 12 shows the average relative distance of 100 Monte Carlo runs between the players in three scenarios: the evader plays without time delay, without compensation for time delay, and with compensation for time delay. When the evader plays without time delay, the average interception time is 209.56 s. The average terminal distance between the two players is 0.9013 m, which is less than the safe distance. When the evader plays without compensation for time delay, the average interception time is 204.39 s. The average terminal distance between the two players is 0.7960 m, which is less than the safe distance. When the evader plays with compensation for time delay, the average interception time is 208.48 s. The average terminal distance between the two spacecraft is 0.9904 m, which is less than the safe distance. By comparison, we can see that the pursuer can successfully intercept the evader in all scenarios. In the time delay scenarios, the interception time is shorter than that in the no-delay scenario. The reason is that the pursuer takes advantage of the evader's control based on delay information to shorten the interception time in the time delay scenarios. The interception time in the scenario that the evader plays without compensation for time delay is shorter than that in the scenario the evader plays with compensation for time delay, which means the compensation control strategy can help the evader prolong the interception time. Figure 11: The average ZEM distance of 100 Monte Carlo runs: (**a**) the ZEM distance changing with time; zoom in on the curve at (**b**) the beginning of the confrontation and (**c**) the end of the confrontation. Figure 13 shows the average \(t_{go}\) and \(\Delta t_{go}\) of 100 Monte Carlo runs between the players in three scenarios: the evader plays without time delay, without compensation for time delay, and with compensation for time delay. When the evader plays without time delay, \(t_{go}\) decreases linearly with time, and \(\Delta t_{go}\) is a non-negative value during the confrontation.