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.