Exploiting symmetry in the synthesis of supervisors for discrete event systems

In this paper we investigate a method to exploit the symmetry inherent to many systems in order to reduce the computational complexity of the supervisory control problem (SCP). We characterize symmetry using notions of group theory and show that under the condition of existence of a special group of permutations acting on the alphabet of a (regular) language we can define a quotient automaton representation for the language which has, in general, a much smaller state space than its original deterministic, trim and minimal (in number of states) automaton representation. We then propose an algorithm to synthesize a solution to the SCP which is similar to the classical one but performed on reduced automata. Special attention is given to the particular case of systems whose models contain similar components. The approach is illustrated by an example of control of a small production line.