  In this paper, we study cooperative multi-agent systems in which the target
objective and the controls exercised by the agents are dependent on the choices
they made at initial system time. Such systems have been investigated in
several recently published papers, mainly from the perspective of system
analysis on issues such as control communication complexity, control energy
cost and the feasibility of realization of target functions. This paper
continues this line of research by developing optimal control design
methodology for linear systems that are collaboratively manipulated by multiple
agents based on their distributed choices. For target matrices that satisfy
particular structural constraints, we derive control algorithms that can
achieve the specified targets with minimum control cost. We compare
state-feedback as well as open-loop control strategies for target realization
and extend the optimality result to an arbitrary target matrix. The optimal
control solutions are obtained by minimizing the average control cost subject
to the set of specified target-state constraints by means of modern variation
theory and the Lagrange multiplier method.
