An iterative numerical method for a class of quantitative pursuit-evasion games

In this paper, we introduce a numerical method for a horizontal pursuit-evasion game with control variable constraints. The algorithm is a gradientbased one specialized for a class of pursuit-evasion games, for which the payoff of the game is the capture tune. The terminal constraint is that the pursuer perfectly captures the evader. By applying this method, we calculated the saddle-point solution for an example of pursuit-evasi on game between a coasting pursuer and a realistic evader. Two evader models, constant-speed evader and realistic evader, are used and the solutions calculated for these models are compared. The solution is also compared with the solution obtained by the indirect approach, which explicitly uses the necessary conditions. Comparison shows that the proposed method accurately computes the optimal capture tune, although it is difficult to find the singular arcs precisely. And we applied the proposed method to compute the capture set of the pursuit-evasion games. The distributions of important variables of the solution for initial conditions over the capture set are presented. The merit of the proposed gradient method is that it is computationally efficient and applicable to realistic pursuit-evasion games with complicated missile/target dynamics.