Synthesis of State Feedback Controllers for Parameterized Discrete Event Systems Under Partial Observation

This paper considers the state feedback control of parameterized discrete event systems consisting of N similar processes for the problem of maintaining a predicate on the state space of the system invariant under partial observation. The basic idea underlying the proposed approach consists in exploiting the symmetry of the system to be controlled, the symmetry of the mask, and the symmetry of the control specification, in order to avoid the exploration of the entire state space. It is shown that it suffices i) to synthesize off-line a controller for a small value (n
0
) of the parameter N; and ii) to infer on-line the control for a larger system, consisting of an arbitrarily large number (n with n
0
≤ n) of processes, from its current state and the small controller.