Supervisory Control of Networked Discrete Event Systems With Observation Losses

Networks have now been widely used in everyday life. Many engineering systems are networked systems that can be modeled as discrete event systems (DES). To control such systems, supervisory control of networked DES has been developed. Because of nondeterminism, the behavior of a controlled/supervised system is described by the upper bound (large) language and the lower bound (small) language. Therefore, three types of controls are needed: (1) control for the large language to ensure safety, (2) deterministic control (when the large and small languages are equal) to ensure nonblocking, and (3) control for the small language to ensure minimum requirements. Network observability, DL-observability, and network S-observability are needed to characterize the existences of three types of controls, respectively. In this paper, algorithm to check network observability is developed for systems with observation losses. DL-observability is then defined. Algorithm to check DL-observability is also developed for systems with observation losses. The algorithm is of polynomial complexity. Finally, the relationship among three types of controls are investigated and proved.