Supervisory Control of Time-Interval Discrete Event Systems

Brandin and Wonham introduced a timed supervisory control framework in 1994. The key innovations arguably were the introduction of tick events to model the passing of time, and the introduction of event forcing. The framework enriches the Ramadge-Wonham framework, albeit with the cost to deal with high modeling and synthesis complexities due to explicit enumeration of ticks. To address these challenges, the framework presented forgoes the explicit enumeration of tick events and instead relies on time-interval automata whose transitions are labeled by events equipped with discrete time-intervals. In contrast to the time-interval resetting mechanism of the Brandin-Wonham framework, where the time-interval of each event is reset either straight after the event occurs or when the event is not defined at a destination state, in the present framework, the time-interval of each event is reset after a new state is reached, where this event is defined. This new framework contains the Brandin-Wonham framework as a special case. After introducing the plant modeled as a free (time-interval) language, and considering the impact of event forcing on plant behaviors with the concept of time-coerced languages, the supervisory control problem is introduced, whose requirements also are time-interval languages. After presenting the concept of controllability in the time-interval framework and demonstrating the surprising existence of supremal time-coerced controllable sublanguages for a given plant and requirements, even though time-coerced languages are typically not closed under union in contrast to free languages, a new supremal controllable sublanguage synthesis algorithm is presented.