Towards Supervisory Control Theory in Tactical Environments: A Stackelberg Game Approach

In this paper, we propose a new framework for supervisory control of discrete-event systems in tactical environments. In contrast to the standard supervisory control theory, where the environments are considered fully adversarial, we consider the possibility of the presence of attackers who have their own objectives that may not necessarily be in opposition to the specification of the supervisor. We formulate this scenario as a Stakelberg game in the leader-follower setting, where the designer proposes a supervisor, and the attacker takes a best response to the supervisor. We characterize the solution to the Stakelberg supervisory control problem as having both cooperative and antagonistic solutions. Moreover, we provide an effective algorithm for synthesizing a cooperative supervisor that enables both players to achieve their objectives. Our work makes an initial step forward from the traditional zero-sum setting of supervisory control theory to the non-zero-sum setting. Examples are provided to illustrate our results.