Control theories for discrete event systems modeled as finite state machines have been well developed to address various fundamental control issues. However, finite state machine model has long suffered from the problem of state explosion that renders it unsuitable for some practical applications. In an attempt to mitigate the state explosion problem, we propose an efficient representation that appends finite sets of variables to finite state machines in modeling discrete event systems. We also present the control synthesis techniques for such finite state machines with variables (FSMwV). We first present our notion and means of control under this representation. We next present our algorithms for both offline and online synthesis of safety control policies. We then apply these results to the control of electric power grids
