Improvement with Look-ahead on Cooperative Pursuit Games

The multi-player pursuit-evasion (PE) game problem has recently received a lot of attention. Hierarchical decomposition is previously proposed for multi-player differential game for a suboptimal solution in Li, D. et al, (2005). Furthermore, optimization based on limited look-ahead is used to improve such a suboptimal solution in Li, D. and Cruz, J.B. (2006), However, it requires intensive computation. In this paper, through the further study on the properties of the suboptimal value function of a cooperative pursuit game, it becomes evident that the performance improvement by limited look-ahead results from the structure relaxation on pursuers' strategies when optimization is conducted. Based on a problem with certain objective and dynamics, we prove a linear structure of the improving strategies in terms of the structured controls associated with the suboptimal solution, and then optimization is parameterized by the linear weights. The problem is further transformed into a nonlinear programming problem. It is shown that computation can be reduced the decentralized implementation is possible