Supervisory control of partially observed weighted discrete-event systems

When the Ramadge-Wonham supervisory control paradigm is applied to practical problems,\nit is desirable to require a closed-loop system be finitely coreachable in the sense\nthat a marker state can be reached within a finite number of transitions regardless of\nthe current state. Furthermore, considering that actions in a real system usually carry\ncosts, it is desirable to synthesize a supervisor that incurs only a minimum cost. Pursuing\nfinite coreachability with a minimum cost is the main motivation for developing a theory\nabout optimal supervisory control of weighted discrete-event systems in the literature. In\nthis paper we follow the same line of optimal supervisory control but with a new focus\non partial observation, which is common in practical applications. We first define three\nfinitely-weighted supervisory control problems, namely (1) to decide the existence of a\nfinitely-weighted controllable and normal sublanguage; (2) to compute a finitely-weighted\ncontrollable and normal sublanguage, when the answer to Problem (1) is affirmative; (3)\nto compute the supremal minimum-weighted controllable and normal sublanguage, when\nthe answer to Problem (1) is affirmative. Then we provide concrete algorithms to solve\nthem.