Synthesis of supervisory controls for discrete event systems

Summary form only given. The design of complex control systems often poses problems best captured by means of discrete event system models, such as state machines. Indeed, many complex control systems behave, at a suitable level of abstraction, like collections of interacting, asynchronous, event-driven subsystems. Over the last couple of decades, control scientists have therefore worked at developing comprehensive theories of the control of discrete event systems. One leading approach is supervisory control, founded by Ramadge and Wonham (1989). Like most control theory, supervisory control is aimed at synthesis of controllers from a formal model of the system to be controlled $the ´plant´ - and formal requirements of the behavior of the controlled system - ´specifications.´ It therefore yields techniques for correct-by-construction design of systems that interact with a given ´environment´. The environment (or plant) is typically modelled as a finite state machine, while the requirements (or specifications) may be stated in terms of finite- or infinite-string formal-language inclusions, or the satisfaction of temporal logic or μ-calculus formulas. Monolithic (nonmodular) synthesis techniques typically amount to the evaluation of a fixpoint calculus formula over a finite transition system (Thistle, 1999). Unlike most mainstream control theory, supervisory control seeks to address issues of scale and complexity. It therefore studies useful structural assumptions that simplify synthesis algorithms, and examines modular synthesis procedures and decentralized and hierarchical architectures in Ramadge and Wonham (1989), Thistle (1996), Cassandras and Lafortune (1999), and Wonham. This paper provides a brief overview of supervisory control theory, emphasizing these key features and providing pointers to the literature.