Optimal LQG control for discrete time-varying system with multiplicative noise and multiple state delays

• 作者: Xiao Lu Qiyan Zhang Xiao Liang Haixia Wang Chunyang Sheng Zhiguo Zhang
• 来源期刊: 控制理论与技术（英文版）
• 年，卷（期）: 2021,（3）
• 所属期刊栏目: RESEARCH ARTICLES
• 页码范围: 328-338
• 页数: 11页
• 语种: 英文

摘要

This paper is concerned with the optimal linear quadratic Gaussian (LQG) control problem for discrete time-varying system with multiplicative noise and multiple state delays. The main contributions are twofolds. First, in virtue of Pontryagin's maximum principle, we solve the forward and backward stochastic difference equations (FBSDEs) and show the relationship between the state and the costate. Second, based on the solution to the FBSDEs and the coupled difference Riccati equations, the necessary and sufficient condition for the optimal problem is obtained. Meanwhile, an explicit analytical expression is given for the optimal LQG controller. Numerical examples are shown to illustrate the effectiveness of the proposed algorithm.