Advanced topics in supervisory control

The signed real measure of regular languages, introduced in Chapter 1, has been the driving force for quantitative analysis and synthesis of discrete-event supervisory (DES) control systems dealing with finite state automata (equivalently, regular languages). However, this approach relies on memoryless state-based tools for supervisory control synthesis and may become inadequate if the transitions in the plant dynamics cannot be captured by finitely many states. From this perspective, the measure of regular languages needs to be extended to that of non-regular languages, such as Petri nets or other higher level languages in the Chomsky hierarchy [9]. The development of measures for non-regular languages is a topic of future research that has not apparently been reported in open literature. This chapter introduces two research topics in the field of language-measure-based supervisory control. One topic is complex measure of non-regular languages, dealing with linear context free grammars (LCFG). The proposed complex measure reduces to the signed real measure [16] [12] [15], as presented in Chapter 1, if the LCFG is degenerated to a regular grammar. The other topic is modification of the (regular) language measure for supervisory control under partial observation. This chapter shows how to generalize the analysis to situations where some of the events may not be observable at the supervisory level.