This paper investigates the solution of the optimal linear quadratic Gaussian control (LQG) problem for systems with packet losses over non-acknowledgment networks. The acknowledgment refers to acknowledgment signals, which are sent by the actuator to notify the controller whether the control packets are successfully received or not. Systems without acknowledgment for packet losses are usually called user-diagram-protocol-like (UDP-like) systems. It is known that for general UDP-like systems, there is no analytical solution to the optimal LQG problem and the computational efforts of numerical solutions will exponentially grow with time. By using a moment-preserving Gaussian approximation approach, this paper develops an efficient algorithm to approximately estimate system states. Based on approximate state estimates, an analytical solution to the optimal LQG problem for general UDP-like systems is obtained by using a dynamic programming approach. It is an approximate solution, and it becomes an exact solution under special conditions. Some simulation examples are given to illustrate the effectiveness of the proposed methods.

本文研究了非确认网络上具有分组丢失的系统的最优线性二次高斯控制（LQG）问题的解决方案。确认是指由致动器发送以通知控制器是否成功接收到控制分组的确认信号。通常不将数据包丢失确认的系统称为类用户图协议（UDP）。众所周知，对于一般的类似UDP的系统，没有针对最佳LQG问题的解析解，数值解的计算量将随着时间呈指数增长。通过使用保持矩的高斯近似方法，本文开发了一种有效的算法来近似估计系统状态。根据状态估计值，通过使用动态编程方法，获得了针对通用类UDP系统的最佳LQG问题的解析解。这是一个近似的解决方案，在特殊条件下它将成为精确的解决方案。给出了一些仿真实例来说明所提方法的有效性。