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We consider the problem of optimal distributed control with delayed information sharing over chain structures motivated by applications of heavy duty vehicle platooning. We introduce a novel approach to find distributed controllers that take into account communication delays and correlation between the dynamic interconnection. The design decomposes the solution into separate optimization problems. The results show that a tight control is achieved, even in the presence of delays, and behaves well with respect to the imposed disturbances. The computed theoretical cost of the proposed optimal controller is significantly better than the theoretical cost for the centralized control with a global delay and close to the cost for a fully centralized control with full state information at all times.