  In this paper, we investigate the problem of optimal supervisory control for
the discrete event systems under energy constraints. We consider that the
execution of events consumes energy and the energy can be replenished at
specific reload states. When the energy level drops below zero, the system will
be crashed. To capture the above scenario, we introduce a new model, called
consumption discrete event system (cDES). Our objective is to find the minimal
initial energy value and synthesize an optimal supervisor ensuring that the
energy will never be exhausted. To solve this problem, we propose a
game-theoretical approach by converting the cDES as a consumption two-player
graph game (cTPG) and reformulate the optimal supervisory control problem in
game theory. In particular, we demonstrate that the converted game can be
decomposed into independent reachability games related to reload vertices,
which can be solved by a fixed point iterative algorithm proposed in this
paper. Through iteratively removing unsafe reload vertices and solving
reachability games for the remaining reload vertices, a solution can be found.
