On the supervisory control of multi-agent product systems: Controllability properties

Multi-Agent (MA) product systems were defined in [I. Romanovski, P.E. Caines, On the supervisory control of multi-agent products systems, IEEE Trans. Automated Control 51(5) (2006)] where the notion of an MA controllable vector language specification was introduced and necessary and sufficient conditions for the existence of a supervisor for such a specification were derived. In this paper we present a set of results about the controllability of an MA product system and its components. In particular, we obtain an algorithm for finding the infimal MA-controllable superlanguage  infMA(K)infMA(K) of a given vector (language) specification K w.r.t. an MA product system G   and establish that in fact infMA(K)=L(P1(K)∥MAP2(K)).ΣU*∩L(G). It is proven that there is an algorithmic procedure for the recursive construction of MA supervisors when additional automata are added to a system via the MA product. Controllability properties of component structures (such as standard controllability and MA controllability of projections) are considered. Several examples are given to illustrate the results of the paper.