Feedback control laws to ensure generalized mutual exclusion constraints in a network of partially observable timed event graphs

This paper deals with the control problem of partially-observable Discrete Event Systems (DESs) which are modelled by Networks of Timed Event Graphs (NTEGs) and subject to Generalized Mutual Exclusion Constraints (GMECs). A new mathematical methodology based on the use of Min-Plus formalisms to synthesize control laws that guarantee the concerned constraints is suggested. For this, the dynamic behavior of the NTEGs is described by linear equations in Min-Plus algebra and the GMECs are represented by weighted inequalities in Min-Plus algebra too. Sufficient conditions are supplied to verify the existence of feedback gains guaranteeing the satisfaction of GMECs. Eventually, to verify the analytical results, it is important to examine a real case study of manufacturing systems.