非对称信息最优LQ控制及其在当地和远程控制器网络控制系统中的应用

非对称信息的存在，使得最优LQ控制变得非常复杂，其研究面临巨大的挑战。本项目拟针对带有非对称信息的当地和远程控制器网络控制系统展开研究。首先研究带有单时滞的非对称信息当地和远程控制器网络控制系统有限时间最优LQ控制问题，拟通过求解正倒向随机差分方程得到最优控制器存在的充分必要条件，同时给出最优控制器的显式表达式；其次，基于有限时间最优LQ控制结果，推导无限时间最优LQ控制结果，利用无限时间最优性能指标定义Lyapunov泛函，给出闭环系统反馈镇定的充分必要条件，并得到网络系统可镇定所允许的最大丢包概率和时滞界；最后，基于单时滞最优LQ控制结果，研究带有多个不同时滞的非对称信息有限时间最优LQ控制，给出最优控制器存在的充分必要条件以及最优控制器的解析解。该研究的目的是完善最优LQ控制理论，实现非对称信息最优LQ控制在网络控制系统中的应用。

The existence of asymmetric information makes the study of LQ control more complicated and brings in huge challenge. This project plans to study the networked control systems with local and remote controllers as well as asymmetric information. Firstly, the finite horizon optimal LQ control problem for networked control systems with local and remote controllers as well as single delay is considered. This project plans to obtain the necessary and sufficient condition for the existence of optimal controllers by solving the forward and backward stochastic difference equations and present the expressions of the optimal controllers. Secondly, this project plans to derive the infinite horizon results based on the finite horizon results and give the necessary and sufficient condition for the stabilization of systems by using the Lyapunov function. Then this project shall give the maximum packet-dropout probability and delay-boundary. Finally, this project plans to investigate the finite horizon optimal LQ control with asymmetric information as well as multiple different delays based on the results of single delay. Then this project plans to show the necessary and sufficient condition for the existence of the optimal controllers as well as the expression of the optimal controllers. The aim of this project is to improve the optimal LQ control theory and make the optimal LQ control with asymmetric information applicable in networked control systems.