Safety control of discrete event systems using finite state machines with parameters

Control theories for discrete event systems modeled as finite state machines have been well developed over the years in addressing various fundamental control issues. However, modeling in finite state machines has long suffered the potential problem of state explosion that renders it (and, hence, the corresponding control techniques) unsuitable for many practical applications. To mitigate the state explosion problem, we proposed, in our previous work, an efficient representation that appends finite sets of parameters to finite state machines in modeling discrete event systems. We follow up in this paper to present the control synthesis techniques operating under this modeling representation. We first propose our notion and means of control under this representation. We then present our algorithms for both offline and online synthesis of safety control policies and illustrate these algorithms with examples.