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Optimal linear‐quadratic‐Gaussian control for discrete‐time linear systems with white and time‐correlated measurement Noises

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.