图注意力网络的微分博弈追逃问题最优策略

Optimal Strategy of Differential Game Pursuit Problem in Graph Attention Network

微分博弈追逃问题的最优策略,是建立在追逃双方的轨迹预测模型基础上,通过双方轨迹进行预判,从而做出更有预见性的动态策略。因此为了获得博弈双方最优策略,提出并设计双方随机运动算法,建立了追逃双方的状态方程,并在此基础上通过改进图注意力网络(graph attention network,GAT),对其网络中邻接矩阵和特征数据连接方式进行重新设计,构建了攻击方与目标方轨迹预测模型并进行数值验证。此外采用将双方随机运动的轨迹由圆环覆盖的方法,建立轨迹连接图。结果表明,GAT网络在MAE、MAPE、RMSE等预测指标上均优于图卷积网络和契比雪夫频谱卷积网络,可用于微分博弈追逃问题的最优策略研究。

The optimal strategy for the pursuit of fugitives in differential game is based on the trajectory prediction model of the pursuit of fugitives,and the prediction is made through the trajectory of both parties,so as to make a more predictable dynamic strategy.Therefore,in order to obtain the optimal strategy of both sides in the game,the algorithm of random motion of both sides is proposed and designed,and the state equation of chasing both sides is established.On this basis,the adjacency matrix and the connection mode of feature data in the network are redesigned by improving the graph attention network(GAT).The trajectory prediction model of attacker and target is constructed and verified numerically.In addition,the method of covering the trajectories of random motion by ring is used to establish the trajectory connection graph.The results show that GAT network is superior to graph convolution network and Chebshev spectrum convolution network in MAE,MAPE and RMSE,and can be used to study the optimal strategy of differential game pursuit problem.