Research On Air Combat Differential Game Based On Differentiable Situation Function

The research on the pursuit evasion of unmanned aerial vehicles(UAVs)is an important research direction in the field of contemporary air combat game.In this paper,based on the new situation function,the problem of air combat differential game is studied deeply and solved numerically by a novel semi-direct method.Firstly,the theoretical basis for solving the differential game problem is introduced.This paper elaborates that the traditional method of analytic method is more difficult to translate the differential game problem into two-point boundary value problem,so the differential game problem is solved by the semi-direct method which combining the direct method and the indirect method.Secondly,a new type of situation function is created.In order to avoid the singularity problem in traditional angle dominance function and traditional distance dominance function,a new angle dominance function,a new situation function and a new situation function of continuously differentiable are reasonably created in this paper.Through a large number of derivation and proof,this function is combined with the air combat differential game problem of aircraft,and is applied to the air combat differential game problem for the first time.Finally,under uncontrolled constraints,terminal time fixed and no terminal constraint,the objective function of both sides is reasonably constructed by using the new situation function,and a set of one-to-one two-dimensional air combat differential game model is established.From the optimal control theory,the differential game problem is transformed into the optimal control problem of a single objective function by the principle of variation.Then the Legendre pseudo-spectral method is used to transform the optimal control problem into the corresponding nonlinear programming problem,and then the SNOPT solver is used to solve the problem quickly and accurately in the MATLAB software environment of computer software.Simulation results show the change curves of the optimal motion trajectory,the state quantity,the relative distance,the angle advantage function,the distance advantage function and the attack probability with the time of differential game.The results show that the application of new situation function in differential game is more successful.At the same time,it is verified that the semi-direct method has the advantages of fastness,accuracy and reliability in solving the air combat differential game.