Multi-machine joint attack and defense game based on Pareto optimality

The joint attack and defense game involves two parts: cooperative game and non-cooperative game. How to find the optimal solution of joint attack and defense is the key of this paper. A reasonable Pareto optimal differential game model is selected, in which a new type of differentiable state function is created and applied in the countermeasure model. Since the traditional state function is segment-continuous and cannot be used for differential game problems. This paper proposes a new type of continuous differentiable state function. Moreover, the distance advantage function and the angle advantage function that constitute the new state function are constructed based on the relative motion of the people in the game. For the purpose of kinematics description of the two sides of the game, this paper combines the non-holonomic motion with the relative motion and constructs a complete mathematical model of differential game based on the game of air situation. The model's presentation is very concise, reducing the complexity of problem solving. Finally, in order to obtain reasonable Pareto optimal solution, this paper establishes an unconstrained two-to-one aircraft differential confrontation model, and uses the optimal control optimization algorithm and semi-direct method to solve the numerical solution. The simulation results show that the practicability of the Pareto optimal control solution of the joint attack and defense game, as well as the rationality of the state function and its corresponding differential game model. In the environment where the fighter is constantly changing in the offensive and defensive system, it make sure eventually tends to favor the state of its best attack.