This article focuses on the problem of optimal linear quadratic Gaussian control for networked control systems with multiple delays and packet dropouts. The main contributions are twofold. Firstly, based on the introduced maximum principle for linear quadratic Gaussian system with multiple input delays and packet dropouts, a nonhomogeneous relationship between the state and costate is obtained, which is the key technical tool to solve the problem. Secondly, a necessary and sufficient condition for the optimal networked control problem is given in virtue of the coupled Riccati equations, and the explicit expression of the optimal controller is presented. Numerical examples are shown to illustrate the proposed algorithm.

中文翻译：

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具有多个延迟和数据包丢失的网络控制系统的最佳控制

本文重点研究具有多个延迟和丢包的网络控制系统的最优线性二次高斯控制问题。主要贡献是双重的。首先，基于引入具有多个输入延迟和丢包的线性二次高斯系统的最大值原理，得到状态和costate之间的非齐次关系，这是解决该问题的关键技术工具。其次，利用耦合Riccati方程给出了最优网络控制问题的充要条件，并给出了最优控制器的显式表达式。显示了数值例子来说明所提出的算法。