Research On Stackelberg Differential Games Based On Adaptive Dynamic Programming

The real world is full of contradictions,confrontations,conflicts or cooperation.Differential games,as an important method that can effectively describe and deal with these complex problems through mathematical methods,has been paid much attention since it was put forward.Most of the existing research results of differential games are concentrated in the same category as decision-making positions of decision makers,such as the well-known Nash equilibrium problem,and in the decision-making position of decision-makers at the same level of this kind of differential games,such as Stackelberg equilibrium problem,although there is a long time to study,but there is still a lot of research space.In the Stackelberg differential games problem,the leader can anticipate all the potential action plans of the follower and,in turn,combine with the predictive information assistance to determine the decision to maximize his or her own benefit.Combined with the adaptive dynamic programming algorithm,this paper focus on the linear and nonlinear two-player Stackelberg differential games,improves the weight update rate of the neural network structure,designs the new Stackelberg differential games control rate,and achieves good control results.Firstly,the birth and development of differential games are reviewed,and compared with the optimal control in the typical control theory,and the current research results of Stackelberg differential games is emphasized.In view of the lack of research on Stackelberg differential games,the ADP method is introduced,and the introduction and development of ADP are briefly introduced.Secondly,this paper introduces the basic concept of differential games and the basic concept of Stackelberg differential games,and introduces the basic knowledge and development of ADP method are introduced in detail,and the Levenberg-Marquardt algorithm is especially introduced.Then,the application of ADP method is studied in relation to linear and nonlinear Stackelberg differential games.The form of Stackelberg equilibrium solution is obtained to solve the Riccati equations and HJI equations,and the equilibrium solution is approximated by neural network,the adaptive iterative algorithm based on policy iteration is summarized,and the convergence of the algorithm is demonstrated.Then,the theoretical results are verified by numerical simulation.Finally,this paper summarizes and points out the direction and prospect of future work for the in-depth study of the Stackelberg differential games problem based on ADP method.