Static and dynamic partitions of inequalities and their application in supervisor simplification

Although supervisor simplification in the framework of automated manufacturing systems has been studied in many literatures, there is still an intense demand for essential and general techniques. Basically, supervisors can be synthesized by specifications which are expressed by generalized mutual exclusion constraints (GMECs). In this paper, we propose static and dynamic partitions on GMECs to remove redundant ones while retain necessary ones. These two partitions are distinctly different in the utilization of system information. Static partition separates inequalities into independent and dependent ones without doing any structure analysis. While dynamic partition divides inequalities into active and inactive ones necessarily with the aid of system information. Nevertheless, mathematical analysis shows that statically dependent inequalities are essentially dynamically inactive while dynamically active ones are substantially statically independent. Thus, these partitions are contradictory in theory whereas compatible in practice. Since static partition is more general while its dynamic counterpart is more precise, they together complementarily explain many simplification principles. Furthermore, they are applicable to both ordinary and general systems. Experimental results show the effectiveness and efficiency of supervisor simplification based on static and dynamic inequality partitions.