Solving The Problem Of Uav Air Combat Game Based On Differential Variational Inequality And D-GAP Function

In this paper, an effective method is proposed to solve the problem of unmanned aerial vehicle air combat differential game. With two unmanned aerial vehicles pursuit-evasion model as the research object, the two unmanned aerial vehicles air optimal situation are modeled and solved. Considering the factors of two-dimensional movement, position, velocity and angle advantage of unmanned aerial vehicle ad, nonzero-sum differential game model is established reference to dynamic nature of differential game.The problem of unmanned aerial vehicle air combat can be described as a differential game problem. For general differential game problem, the analytical solutions are usually difficult to obtain. Only in most cases can we get its numerical solutions. Solving the problem of differential game can be seen as solving the problem of bilateral optimal differential Nash equilibrium. By converting Nash differential game problem to the corresponding differential variational inequality problem, and then the differential game is converted into nonlinear continuous optimal control problem via D-gap function. Solving the differential variational inequality is converted into solving the optimal control problem.The specific steps are as follows. At first, according to the cosine law and angle function monotonicity, the bearing angle and angle-off of unmanned aerial vehicle are written. Second, by constructing Hamilton function and adjoint equation, the derivative of bearing angle and angle-off about state variable are obtained. Finally, according to the necessary and sufficient condition of minimum principle, the differential Nash equilibrium problem is transformed into differential variational inequality problem, and by constructing a bounded differentiable D-gap function differential variational inequality problem is transformed into the optimal control problem. The optimal control model of unmanned aerial vehicle air combat is gotten, which is conducive to getting its numerical solutions.Compared with other solving methods, the specific implementation process of this method is more simple, and complex differential game problem can be solved by this method, so it has certain validity and feasibility.