A language measure for partially observed discrete event systems

Recent literature has introduced and validated a signed real measure of regular languages for quantitative analysis and synthesis of discrete-event supervisory (DES) control systems, where all events are assumed to be observable. This paper presents a modification of the language measure for supervisory control under partial observation and shows how to generalize the analysis when some of the events may not be observable at the supervisory level. In the context of DES control synthesis, the language measure of partially observable discrete-event processes is expressed in a closed form which is structurally similar to that of completely observable discrete-event processes. Examples are provided to elucidate the concept of DES control under partial observation.