不完全信息Epsilon纳什均衡的航天器末端追逃博弈策略

Epsilon Nash Equilibrium Differential Game Strategy for Spacecraft Terminal Pursuit-Evasion under Incomplete Information

针对不完全信息下的航天器末端追逃问题,提出了一种满足Epsilon纳什均衡的微分博弈控制策略。首先,建立了完全信息下的有限时间追逃纳什均衡策略对,并将其作为目标航天器实际采取的控制策略,使目标航天器掌握博弈进程的完全信息,进而获得更好的逃逸性能。在此基础上,考虑拦截航天器不能获取目标控制矩阵信息的态势,设计了基于广义卡尔曼滤波的行为学习信息估计算法,使拦截器能够对目标的不完全信息进行估计,并提出了不完全信息下的末端追逃博弈控制策略。经过理论分析,证明了所设计的不完全信息下微分博弈策略对满足Epsilon纳什均衡。最后,仿真结果表明该算法可以有效估计目标的不完全信息,确保拦截器能够在有限时间内快速拦截目标。

A differential game control strategy with Epsilon Nash equilibrium is proposed for spacecraft terminal pursuit-evasion problems under incomplete information.Firstly,finite time pursuit-evasion Nash equilibrium strategy pairs under complete information are established.This strategy is taken as the maneuver strategy of the target spacecraft,it means that the target spacecraft can obtain complete information of the whole game process,and then will have better evasion performance.On this basis,considering the situation that the interceptor cannot get the information of the target control matrix.A behavior learning information estimation algorithm is designed based on the generalized Kalman filter to make the interceptor estimate the incomplete information of the target.Furthermore,the game control strategy under incomplete information is designed.Through theoretical analysis,it is proved that the designed differential game strategy pairs under incomplete information satisfy Epsilon Nash equilibrium.Finally,the simulation results show that the algorithm can estimate the target information effectively,and the interceptor can pursue the target rapidly in a limited time.