多星博弈拦截Nash和Pareto策略研究

Nash and Pareto Intercept Strategy in Multi-Satellite Game

针对多星博弈拦截问题,基于微分博弈对策研究了各航天器的博弈策略。分别讨论了多颗拦截器的非合作Nash反馈策略,以及合作Pareto反馈策略。首先针对Nash均衡,各拦截器以终端零控脱靶量为指标设计了博弈策略,而目标的策略以终端脱靶量的加权和进行设计。进一步,考虑各拦截器采取合作方式进行拦截,相应的博弈策略基于单一指标的凸组合进行设计,而目标的策略保持不变。通过比较,Nash反馈策略与Pareto反馈策略相同,使得拦截器可以采取非合作模式实现合作拦截的目的。最后仿真分析了2颗拦截器对同一目标进行拦截的博弈态势,表明了本文提出的博弈策略对多星博弈问题的有效性。

Aiming at the intercept problem of the multi-satellite game,the spacecraft’s strategies are studied on the basis of the differential game theory. The non-cooperative Nash feedback strategy and the cooperative Pareto feedback strategy are discussed,respectively. Firstly,the game strategies of the interceptors are designed by treating the terminal zero effort misses as a cost function,while the target strategy is designed based on the weighted sum of the terminal misses. Furthermore,the cooperative interception is considered.The strategies of the interceptors are derived through the convex combination of single cost function and the target strategy remains unchanged. Through comparison,the Nash feedback strategy is the same as the Pareto strategy,which leads to the achievement of cooperative interception with non-cooperative scheme. Finally,simulations analyze the game situation with two interceptors vs one target and demonstrate the effectiveness of game strategies proposed in this paper for multi-satellite game.