(A) gradient-based direct method for a class of quantitative pursuit-evasion games

Abstract

In this thesis, we propose a direct numerical method for quantitative pursuit-evasion games with control variable constraints. The method is a gradient-based one specialized for a class of pursuit-evasion games, for which the payoff of the game is the capture time. The proposed method adopts direct approach that transform the game problem into parameter optimization problem using discretization of control inputs of the players. Linear approximation of final position changes due to small perturbation of control input and final time transforms the pursuit-evasion game problem into a set of parameter optimization problems. The solution of these optimization problems is obtained by an iterative optimization algorithm developed in this thesis. The proposed algorithm is composed of two procedures, update and correction. Derivation of the update and correction algorithms is described in detail. The optimal solution for an example of two-dimensional pursuit-evasion games is calculated to demonstrate the performance of the algorithm. Two evader models, constant-speed evader and realistic evader, are used to investigate the characteristics of the saddle-point trajectory. The solution calculated by the proposed method is also compared with the solution obtained by the indirect approach and analytic approach , which explicitly uses the necessary conditions. Comparison shows that the proposed method accurately computes the optimal capture time and provides a good approximation of the optimal solution. A capture set of the pursuer for the example calculated by the proposed algorithm is presented. The proposed method is extended to the three-dimensional pursuit-evasion problem. 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. In addition to the gradient-based direct method, numerical procedure based on pre-computed optimal trajectories is proposed. In ...