In this paper we consider the distributed linear quadratic control problem
for networks of agents with single integrator dynamics. We first establish a
general formulation of the distributed LQ problem and show that the optimal
control gain depends on global information on the network. Thus, the optimal
protocol can only be computed in a centralized fashion. In order to overcome
this drawback, we propose the design of protocols that are computed in a
decentralized way. We will write the global cost functional as a sum of local
cost functionals, each associated with one of the agents. In order to achieve
'good' performance of the controlled network, each agent then computes its own
local gain, using sampled information of its neighboring agents. This
decentralized computation will only lead to suboptimal global network behavior.
However, we will show that the resulting network will reach consensus. A
simulation example is provided to illustrate the performance of the proposed
protocol.Comment: 7 pages, 2 figure