  Recent papers have treated {\em control communication complexity} in the
context of information-based, multiple agent control systems including
nonlinear systems of the type that have been studied in connection with quantum
information processing. The present paper continues this line of investigation
into a class of two-agent distributed control systems in which the agents
cooperate in order to realize common goals that are determined via independent
actions undertaken individually by the agents. A basic assumption is that the
actions taken are unknown in advance to the other agent. These goals can be
conveniently summarized in the form of a {\em target matrix}, whose entries are
computed by the control system responding to the choices of inputs made by the
two agents. We show how to realize such target matrices for a broad class of
systems that possess an input-output mapping that is bilinear. One can classify
control-communication strategies, known as {\em control protocols}, according
to the amount of information sharing occurring between the two agents.
Protocols that assume no information sharing on the inputs that each agent
selects and protocols that allow sufficient information sharing for identifying
the common goals are the two extreme cases. Control protocols will also be
evaluated and compared in terms of cost functionals given by integrated
quadratic functions of the control inputs. The minimal control cost of the two
classes of control protocols are analyzed and compared. The difference in the
control costs between the two classes reflects an inherent trade-off between
communication complexity and control cost.
