Capturability distinction analysis of continuous and pulsed guidance laws

The capture zones of the continuous and pulsed guidance laws in the pursuit-evasion game are analytically discussed in this paper to provide deep insights into the capturability distinction between the continuous guidance law and the pulsed guidance law. Specifically, first, in the pursuit-evasion game, various capture cases are defined regarding the Zero-Effort Miss distance (ZEM) to facilitate the capturability analysis. Then, for both the evader and the pursuer, the Linear-Quadratic Differential Game (LQDG) guidance laws concerning the continuous acceleration and the pulsed acceleration are converted into a unified form. In each capture case, the optimal solution existence conditions are derived, and the corresponding capture zones are formulated. The discussion on the capture zones shows that if the optimal solution exists, the distinction between the pulsed guidance law and the continuous guidance law can be neglected under small guidance effort weight. However, the capture zone of the continuous guidance law is larger than that of the pulsed guidance law with large pursuer guidance effort weight, but smaller with large evader guidance effort weight. Finally, various simulations are conducted to illustrate the distinction of the continuous and pulsed guidance laws, as well as the impact of the acceleration ratio and the time constant ratio on the capturability.