Differential Game And Its Application In Pursuit-Evasion Control Of Aircrafts

Differential game refers to a countermeasure using differential equations to describe the phenomena or the law among the players. It is an effective tool to solve continuous and dynamic conflicts, competitions or cooperation problems for two sides or multi-players. According to the characteristics of differential game including the difficulty of solving and the uncertainty of linear differential game, the relevant study is carrying on for pursuit-evasion problem of aircrafts in this article. The main contents of this paper can be summarized as follows:Firstly, according to the complexity of the differential game, a numerical calculation of rolling optimization algorithm named nonlinear model predictive control is proposed for solving differential game under dynamic environment. The predictive control was implemented at each forecast domain based on the gradient descent method, that’s to say, the gradient iteration method was act as optimization technique for process of prediction, and then rolling optimization was executed on-line, thus a feedback control law of closed loop was formed in some sense, and the feedback control laws for both sides of pursuer and evader were obtained.Secondly, because of some certain limitations of the traditional optimization methods, intelligent optimization method is considered to introduce into predictive control, the particle swarm optimization based on simulated annealing(SA-PSO) was used as the optimization strategy, and an improved SA-PSO was acted as the optimization technology of NMPC, SA is exploited to avoid local optimal besides the characteristics of fast, simple and preserving global optimization of PSO, and then though rolling optimization online, the solving of Hamilton-Jacobi-Issacs(HJI) equation is avoided, and the optimal control input of closed-loop for for both sides of pursuer and evader was generated based on the current state.Finally, for a class of uncertain linear differential game LTV and LTI model, a class of robust guidance law was proposed, a nonlinear control item of switch function was combined with a line control item constituted by the solutions of the Riccati equation under the nominal system(which there exist no uncertainties), to ensure the ideal response of the system, with very strong robustness corresponding to structure uncertainties of system, parameter perturbation and external disturbance...