Research On The Problem Of Air Combat Game Based On The Semi-direct Method

In order to make the air combat decision more scientific, a fast and accurate method is proposed named semi-direct method to solve the air combat game. The method can be used for the games constrained by differential equations with general applicability, and it can be applied to the problem of multi-player differential games. Because it has the characteristics of fast, accuracy, reliability, etc., the method is expected to be applied to the real time control of air defense combat system in the future.The theory basics of the semi-direct method, the variation theory and the Legendre pseudo- spectrum method, are introduced. The traditional analytical method of solving the differential game model is introduced, and the method is to be transformed into a two point boundary value problem. On the basis of this theory, two kinds of methods for solving the optimal control problem, indirect method(variation method and minimum value principle) and direct method(Legendre pseudo-spectral method), are introduced. The feasibility of using semi-direct method to solve the differential game model and the characteristics of high accuracy and low computational complexity are described.With the optimal control problem, the differential game is transformed into the single objective optimal control problem under two kinds of conditions in where the control constrained or non-constrained, which avoids the problem of solving the Hamilton-Jacobi equation with the guarantee of the reliability of the model transformation. When the control is not restricted, the model transformation is based on the variation theory; when the control is restricted, the transformation is based on the minimum principle. Then, the Legendre pseudo-spectral method is used to convert the obtained problem into the nonlinear programming, and solved by SNOPT for numerical solution.The particle model of attack and defense in a two dimensional plane is established, in where the plane coordinates and the heading angle are the states, the heading angular velocity is the control variable. The two-player non-zero-sum differential game and the two-player zero-sum differential game are built with that the controls unbounded and bounded respectively. The optimal states are solved and the trajectory of the two players is simulated respectively under the two kinds of conditions. The different performance of different initial states and the different time of the counter are analyzed. The simulation results show that the numerical solution can converge to a reasonable range at different starting positions, different directions and different end distance. In addition, due to that the whole calculation process only takes a very short time, the algorithm is proved with rapidity and reliability so that the algorithm may be suitable for air combat of real-time control.At last, the algorithm is extended to solve the problem of multi-player differential game. The problems that may be encountered are analyzed, and the corresponding solutions are given.