Abstract
This paper is concerned with the linear quadratic regulation (LQR) problem for discrete-time systems involving input delay and colored multiplicative noise. Due to the correlation of the adjoining state, this problem will be more complicated than the case of white noise. In this paper, the necessary and sufficient condition for the solvability of optimal control problem is presented by solving the forward and backward stochastic difference equations (FBSDEs). Moreover, the optimal LQR controller is given in terms of the coupled difference equations developed in this paper.
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