On multi-agent product systems: Graph MA Products and partially observed MA products

In this paper we explore the notion of the graph MA product that constitutes a formal framework for the analysis of complex systems and their associated vector languages defined on graphs. This product is a generalization of the notion of an MA product which was introduced and developed in [P. Hubbard and P. E. Caines, 1999] and [P. Hubbard, December 1999]. It is shown that a necessary and sufficient condition for the existence of graph MA supervisors is the same as for the case when the MA product model is used. Next, we consider MA product systems under partial observation, introduce the notions of MA observability and MA co-observability, and show that these notions play a crucial role for the existence of vector supervisors.