Differential Game for Satellite Swarm Confrontation System with Strength Supplement

This paper addresses the strength supplement strategies generation problem for satellite swarm confrontation system. First, an attrition forecasting model is established by appling an improved Lanchester equation to forecaste the attrition of satellite swarm confrontation system. Decision-making delay time, reconnaissance information support capacity, and electronic jamming capacity are considered in the model to fit the practice of the satellite swarm confrontation system. Second, the supplement decision-making problem is modelled as a differential game model based on the established attrition forecasting model. In order to better match the practice of the satellite swarm confrontation system, the constraints such as attack rate and engagement rate, confrontation time, supplement number, and sunlight angle are considered in the differential game. The game objective is to maximum the confrontation effectiveness of the satellite swarm confrontation system while using the least amount of supplement possible. Finally, the solution process is derived by multi-interval simultaneous orthogonal collocation decomposition (MISOCD) method. Three collocation methods are compared in the simulation. The results show that Legendre-Gauss-Radau collocation method in MISOCD exhibits a better fit and is more applicable to solve the supplement decision-making problem.