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We consider the problem of controlling a set of dynamically decoupled plantswhere the plants' subcontrollers communicate with each other according to afixed and known network topology. We assume the communication to beinstantaneous but there is a fixed processing delay associated with incomingtransmissions. We provide explicit closed-form expressions for the optimaldecentralized controller under these communication constraints and usingstandard LQG assumptions for the plants and cost function. Although thisproblem is convex, it is challenging due to the irrationality ofcontinuous-time delays and the decentralized information-sharing pattern. Weshow that the optimal subcontrollers each have an observer-regulatorarchitecture containing LTI and FIR blocks and we characterize the signals thatsubcontrollers should transmit to each other across the network.

Agent-level optimal LQG control of dynamically decoupled systems with processing delays