Research The Problem Of Differential Games Based On The Optimal Control

In recent years,the two person differential games become the important part of the field of optimal control studying,with the optimal control methods joined,to promote the new upsurge in the study of games theory。In this context,this article with the aid of the research method of optimal control, classification was studied under different conditions of games problem:one is that the non-autonomous two-person zero-sum differential games under the case of deterministic;the other is that the problem of stochastic linear non-quadratic two-person zero-sum differential game。This paper is divided into four parts:First of all,The author has a brief introduction of the background of choosing the thesis and research progress;Secondly,for the non-autonomous two-person zero-sum differential games under the case of deterministic,mainly through the use of Minimax Principle to give the display expression of optimal control strategies,and proposed it combined with the solution for quasi-Riccati differential equation,therefore gives that the relation between the solution of differential games and the solution of quasi-Riccati differential equation,and for the study of stochastic linear two-person differential game problems and pave the way;Then,for the problem of stochastic linear non-quadratic two-person zero-sum differential games,mainly through the introduction of the proposed Riccati differential equations,proved that the solvability of quasi-Riccati differential equation is sufficient conditions of the stochastic linear nonquadratic two-person zero-sum differential games the saddle strategy exists,and also gives that the display expression of optimal control strategies and the optimal performance function value;Finally, is conclusion and prospect,based on the conclusion of the full paper,the author discussed that the future research directions of stochastic linear two-person zero-sum differential games。...