  In this paper we propose an original distributed control framework for DC
mcirogrids. We first formulate the (optimal) control objectives as an
aggregative game suitable for the energy trading market. Then, based on the
dual theory, we analyze the equivalent distributed optimal condition for the
proposed aggregative game and design a distributed control scheme to solve it.
By interconnecting the DC mcirogrid and the designed distributed control system
in a power preserving way, we steer the DC microgrid's state to the desired
optimal equilibrium, satisfying a predefined set of local and coupling
constraints. Finally, based on the singular perturbation system theory, we
analyze the convergence of the closed-loop system. The simulation results show
excellent performance of the proposed control framework.
