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In this paper we consider the distributed linear quadratic control problemfor networks of agents with single integrator dynamics. We first establish ageneral formulation of the distributed LQ problem and show that the optimalcontrol gain depends on global information on the network. Thus, the optimalprotocol can only be computed in a centralized fashion. In order to overcomethis drawback, we propose the design of protocols that are computed in adecentralized way. We will write the global cost functional as a sum of localcost functionals, each associated with one of the agents. In order to achieve'good' performance of the controlled network, each agent then computes its ownlocal gain, using sampled information of its neighboring agents. Thisdecentralized computation will only lead to suboptimal global network behavior.However, we will show that the resulting network will reach consensus. Asimulation example is provided to illustrate the performance of the proposedprotocol.

Distributed Linear Quadratic Optimal Control: Compute Locally and Act Globally