Decentralized LQG Control With $d$-Step Delayed Information Sharing Pattern

In this article, we study a class of discrete-time decentralized linear-quadratic-Gaussian (LQG) control problems with two controllers and $d$-step delayed information sharing pattern. An explicit form of the pair of optimal linear controllers is obtained in terms of backward Riccati equations and forward equations of estimation error covariance. To overcome the difficulty that arises due to the coupling of the backward–forward equations, we propose a forward iteration approach to derive a steady-state solution. This accordingly leads to an asymptotically optimal linear controller where the feedback gains are designed by using the convergent steady-state solutions.