  In this paper, for any homogeneous system of agents with linear continuous
time dynamics, we formulate an optimal control problem. In this problem a
convex cost functional of the control signals of the agents shall be minimized,
while the outputs of the agents shall coincide at some given finite time. This
is an instance of the rendezvous or finite time consensus problem. We solve
this problem without any constraints on the communication topology and provide
a solution as an explicit feedback control law for the case when the dynamics
of the agents is output controllable. It turns out that the communication graph
topology induced by the solution is complete. Based on this solution for the
finite time consensus problem, we provide a solution to the case of infinite
time horizon. Furthermore, we investigate under what circumstances it is
possible to express the controller as a feedback control law of the output
instead of the states.
