Abstract
This paper considers the linear quadratic Gaussian (LQG) control problem for discrete-time systems subject to multiplicative noises and input delay. When the state variables can be obtained exactly, the necessary and sufficient condition for the existence of a unique solution to the LQG control has been presented and an explicit analytical expression is given for the optimal LQG controller. More specially, the optimal LQG controller is derived which consists of the feedback form of the conditional expectation of the state and one additive deterministic term based on the coupled Riccati equations. Through the completing square approach, the optimal controller is obtained based on the solution to the forward and backward stochastic difference equations (FBSDEs).
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