基于微分对策的多飞行器协同最优分配方法

Multi-aircraft Cooperative Optimal Allocation Method Based on Differential Games

研究了N个拦截飞行器与M个进攻飞行器之间的攻防对抗博弈问题。考虑双方均采用最优博弈策略的情况,通过设计鞍点策略,解决了在多飞行器追逐-逃避场景下的最优武器分配问题。采用终端位置误差价值评价方法得到博弈对抗的价值函数,并证明了价值函数满足Hamilton-JacobiIsaacs方程,采用新颖的阿波罗尼乌斯圆不仅可以实现对最优分配策略的快速求解,还可以有效克服多飞行器对抗过程中维数问题。分析N=M和N>M的情况下,攻防对抗双方均可以获得协同最优分配和最优制导律解析解,最终进行多飞行器对抗仿真分析,验证了本文提出的算法的有效性。

The game problem of offensive and defensive confrontation between N intercepting aircraft and M attacking aircraft is studied.The situation where both parties adopt the optimal game strategy is considered,and by designing a saddle point strategy,the problem of optimal weapon allocation in the chase-evasion scenario of multi-aircraft is solved.The terminal position error value evaluation method is used to obtain the value function of the game confrontation,and it is proved that the value function satisfies the Hamilton-JacobiIsaacs equation.Using the novel Apollonius circle can not only realize the rapid solution of the optimal allocation strategy,but also effectively overcome the dimensionality problem in the process of multi-aircraft confrontation.When N=M and N>M are analyzed,both offensive and defensive opponents can obtain coordinated optimal allocation and optimal guidance law analytical solutions.Finally,multi-aircraft confrontation simulation analysis is performed to verify the effectiveness of the proposed algorithm.