On the supervisory control of multi-agent product systems

In this paper, we use the formal framework of multiagent (MA) product systems for the analysis of complex systems. The results of this paper constitute a natural extension of the central classical supervisory control results for scalar systems to the more general MA product system case. The notion of MA controllability is introduced and is shown to essentially constitute a necessary and sufficient condition for the synthesis of an MA supervisor. In addition, an algorithm for finding the infimal MA controllable superlanguage of a given vector (language) specification K is presented. It is proven that there is an algorithmic procedure for the recursive construction of an MA supervisor when an additional automaton is added to a system via the MA product. Controllability properties of component structures (such as standard controllability and MA controllability of projections) are considered.