This article is concerned with the optimal linear-quadratic-Gaussian control problem for discrete-time linear systems corrupted by white and time-correlated measurement noises. First, an optimal predictor for the system under consideration is proposed. Then, an optimal controller is designed, which minimizes an expected loss by a control strategy where the control is a function of measurement sequence. The novelty of this article is that a new sequence instead of the original measurement sequence is used to obtain the optimal control scheme where the element in the new sequence is derived from measurement differencing. A verification example is given to illustrate the effectiveness of the developed new design method.

中文翻译：

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具有白噪声和时间相关测量噪声的离散时间线性系统的最优线性二次高斯控制

本文关注被白噪声和时间相关测量噪声破坏的离散时间线性系统的最优线性二次高斯控制问题。首先，提出了所考虑系统的最佳预测器。然后，设计了一个最优控制器，通过控制是测量序列的函数的控制策略来最小化预期损失。本文的新颖之处在于使用新序列代替原测量序列来获得最优控制方案，其中新序列中的元素来自测量差分。给出了一个验证例子来说明所开发的新设计方法的有效性。