Concurrent, asynchronous and generative interactions for the modeling and control of discrete event systems

Prioritized composition (PC) proposed by Heymann [M. Heymann, 1990] for the control interaction of automata P and Q, each with a priority set of events in whose concurrence the given automation must participate, permits the Boolean interactions of P,Q, AND, and OR. However, it cannot model Boolean interactions which require exclusivity of participation, namely, "exclusively P", "exclusive Q", "exclusive P or exclusive Q", "exclusive P and exclusive Q". To model these asynchronous interactions, we propose a generalization of PC by introducing an exclusivity set. The resulting composition is called prioritized composition with exclusion (PCX). We also introduce a nor set which makes it possible to model the eight new Boolean modes which are generative in their action. The resulting generalized composition (GC) allows for all sixteen Boolean modes of interaction possible when two automata interact. The applicability of these interactions to supervisory control, and in composing the rules based model [V. Chandra and R. Kumar et al., 2002] of systems has been illustrated.