作为现代控制理论的重要组成部分，随机Stackelberg博弈控制近年来受到学者的广泛关注。而对于具有输入时滞的随机Stackelberg博弈控制问题的研究进展缓慢，许多问题尚未得到解决。申请人前期针对确定性系统的Stackelberg博弈控制问题做了相关研究，并且取得了一定的成果。本项目在前期工作的基础上研究具有输入时滞的随机Stackelberg博弈控制问题，并将其应用到混合H2/H∞控制问题。本项目拟利用建立随机极大值原理并求解时滞正倒向随机微分(差分)方程(D-FBSDEs)的方法解决相关控制问题，得到最优解存在且唯一的充分必要条件以及最优Stackelberg策略。这一研究将为时滞随机系统Stackelberg博弈控制及应用提供新方法、新工具，拟解决时滞随机博弈控制诸多悬而未决的问题、完善随机系统LQ最优控制理论。

As an important part of modern control theory, the stochastic Stackelberg game control has attracted much attention of scholars in recent years. However, the research progress of stochastic Stackelberg game control with input delay is slow, and many problems have not yet been fully resolved. The applicant has studied the Stackelberg game control problem of deterministic system and obtained some results. Based on the previous work, the project will study the stochastic Stackelberg game control problem with input delay and apply it to the mixed H2/H∞ control problem. The project will solve the correlation control problem by establishing the stochastic maximum principle and solving the delayed forward-backward stochastic differential(difference) equations, and the necessary and sufficient conditions for the existence and uniqueness of the optimal solution and the optimal Stackelberg strategy will be obtained. This study will provide a new method and a new tool for control and application of stochastic Stackelberg game with input delay, so as to solve many outstanding problems which are concerned with stochastic systems with time delays and bring the stochastic LQ optimal control theory to completion.