Differential Game With Constraints And Its Application In Air Combat

Based on the complexity of solving differential game with control constraints and the uncertainty of nonlinear pursuit-evasion differential game models,this paper studies the one to one pursuit-evasion game between an affine nonlinear system and a general nonlinear system.The main summary is as follows:First of all,the research progress,solutions and limitations of differential game are summarized.In order to avoid solving the two-point boundary value problem in the differential game with control constraints,a semi-direct method based on the minimum principle and pseudospectral method is proposed.The minimum principle is used to eliminate the cost function of the affine nonlinear system and the differential game with constraints is transformed into a nonlinear optimal control problem.The nonlinear optimal control problem is further transformed into a nonlinear programming problem by means of Legendre spectral method,and then the final solution of the problem is solved by the SNOPT solver in Matlab.Secondly,considering the minimal principle of optimal control theory only contains the extreme conditions of one player and it can't explain the existence of the optimal strategies of every player in the differential game.That is,the relevant theorem of optimal control theory can't be directly applied into the theory of differential games because of its full lack of mathematical basis.For this theoretical defect,we first give the proof of the minimum principle of differential game with constraints,and it is also the first mention in related articles in the world.Finally,to verify the feasibility and validity of this method,a two-dimensional pursuit-evasion game with control constraints and free time between two nonholonomic systems is built.The simulation result shows that,in the process of the game,the algorithm can not only effectively solve the optimal maneuver control strategy in pursuit of both sides,but also meet the tracking performance and control constraints expected.The method successfully reduces the number of optimization variables and constraints,its higher accuracy and lower computational complexity make it suitable for the rapid optimization of nonlinear control strategies.Based on the theoretical results obtained,it is also possible to extend the semi-direct method to a multi-person differential game with constraints and it can provide some useful references for the choice of maneuver strategy of real-time air combat with control constraints.