The application of situation function in differential game problem of the air combat

Abstract

The issue of air combat can be attributed to the problem of air combat situation game. Due to the complexity of the expression of aerial situation, it is more difficult to model and solve than the pursuit problem. In essence, it is a differential game problem based on the situation function. Because the traditional situational function is piecewise continuous and cannot be used in the differential game problem. This paper presents a new continuously differentiable situational function. Because the distance advantage function and the angle advantage function that constitute the new situation function are constructed based on the relative motion of players in the game, this paper combines the non-integrated movement with the relative movement when the two sides of the game are described by kinematics. A complete differential game mathematical model based on the air situation game problem was constructed. The representation of the model is very simple, reducing the complexity of problem solving. Finally, a semi-direct simulation method is used to solve the problem. The simulation results verify the rationality of the created situation function and its corresponding differential game model to ensure that the fighter in the offense and defense system in the time-varying environment, eventually tend to favor their own attack state.