Time-Lag Effect on the Capture Capability of Pursuit-Control

The time-lag problem is one of the most important problems in both the fields of mathematics and control. Although many research results have been presented, under the effect of control-lag, there are no any related report on such topics in the pursuit-evasion problem, to the best knowledge of authors. It may be for the reason that the dynamic equations of the pursuit-evasion system are too complex to solve analytically. Therefore, there are only some research reports on the study of its capture capability based on idea assumptions, without consideration of any time lag of pursuit control. A new study method on the capture capability is presented in this paper, under the effect of control-lag. First, the no-time-lag theoretical results of PPN are validated by simulation, which not only demonstrates the correctness of theorem but also indicates the validity of the system modeling and simulation method. Then based on the modeling system with different control lag times, some useful results on pursuit control time-lag are drawn from the simulation of two different aspects, effect on capture probability and pursuit process. The lag effect on short-distance pursuit is greater than long-distance pursuit, if the ratio of the pursuer velocity to target velocity (VROPT) is constant: (1) When the initial relative distance is more than 10 km, the capturability decreases less than 5% compared to that without time lag, even if with a time lag up to 3 seconds during the given pursuit-evasion states. (2) While the initial distance is less than 3 km, if the lag time is up to 3 s it decreases about 50%. (3) The capture capability is almost unchanged if the control-lag is no more than 0.5 second. Simulations also show that the effect on the pursuit-evasion process is similar. Under the constant time lag, VROPT has effect on the capturability. Simulations show that the capturability is improved as the increase of the ratio. Therefore, the pursuit lag time has negative effect on the capturability, especially during short-distance pursuit-evasion phase. The time constant of pursuit control servo system should be less than 0.5 second to maintain the ideal capturability.