  The conventional Wonham-Ramadge supervisory control framework of discrete
event systems enforces a closed discrete event system to generate correct
behaviors under certain environments, which can be captured by an appropriate
plant model. Nevertheless, such control methods cannot be directly applied for
many practical engineering systems nowadays since they are open systems and
their operation heavily depends on nontrivial interactions between the systems
and the external environments. These open systems should be controlled in such
a way that accomplishment of the control objective can be guaranteed for any
possible environment, which may be dynamic, uncertain and sometimes
unpredictable. In this paper, we aim at extending the conventional supervisory
control theory to open discrete event systems in a reactive manner. Starting
from a novel input-output automaton model of an open system, we consider
control objectives that characterize the desired input-output behaviors of the
system, based on which a game-theoretic approach is carried out to compute a
reactive supervisor that steers the system to fulfill the specifications
regardless of the environment behaviors. We present a necessary and sufficient
conditions for the existence of such a reactive supervisor. Furthermore,
illustrative examples are given throughout this paper to demonstrate the key
definitions and the effectiveness of the proposed reactive supervisor synthesis
framework.
