Necessary conditions for control consistency in hierarchical control of discrete-event systems

Hierarchical consistency is an important concept in control theory of hierarchical discrete-event systems (DESs). In order to establish corresponding control structure in high level, Wong introduced (1990, 1994) the concept of control consistency, which implies hierarchical consistency. However, to check whether a hierarchical DES is control consistent is computationally expensive. In this note, we try to reduce the computational complexity. At first, the kernel condition of control consistency is divided into three simpler parts and computational complexity is analyzed. Further discussion is made to obtain some new necessary conditions for control consistency, by which one can easily verify whether a hierarchical DES is not control consistent.