Language convergence in controlled discrete-event systems

Discrete-event systems modeled as state machines in the framework of Ramadge and Wonham are considered. In this paper, convergence of the language generated or marked by the system to a specified legal language is investigated. The convergence property is studied both with respect to open-loop (uncontrolled) systems and with respect to controlled systems. In the latter case, both questions of existence and synthesis of supervisors that force convergence are examined. Algorithms for verification of convergence and for synthesis of stabilizing supervisors are provided. Finally, the concept of asymptotic behavior of systems is defined, and questions related to this concept are investigated