On Compositional Supervisor Synthesis for Discrete Event Systems

Licentiate thesis, 2012

Over the past decades, human dependability on technical devices has rapidly increased. Many activities of such devices can be described by sequences of events, where the occurrence of an event causes the system to go from one state to another. This is elegantly modeled by automata. Systems that are modeled in this way are referred to as discrete event systems. Many of these systems appear in settings that are safety critical, and small failures may result in huge financial and/or human losses. Having a control function is one way to guarantee system correctness. Supervisory control theory, proposed by Ramadge and Wonham, provides a general framework to automatically calculate control functions for discrete event systems. Given a model of the system, the plant, to be controlled, and a specification of the desired behaviour, it is possible to automatically compute, i.e. synthesise, a supervisor that ensures that the specification is satisfied. Usually, systems are modular and consist of several components interacting with each other. Calculating a supervisor for such a system in the standard way involves constructing the complete model of the considered system which may lead to the inherent complexity problem known as the state-space explosion problem. This problem occurs when composition of the components results in a model with a huge number of states, as the number of states grows exponentially with the number of components. This problem makes it intractable to examine the states of a system due to lack of memory and time. This thesis uses a compositional approach to alleviate the state-space explosion problem. A compositional approach exploits the modular structure of a system to reduce the size of the model of the system. The thesis mainly focuses on developing the methodology for abstracting a system in a way that the final synthesis result is the same as it would have been for the nonabstracted system. The algorithms have been implemented in the discrete event system software tool Supremica and have been applied to compute modular supervisors for several large industrial models.