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

• Published in: European journal of control Vol. 71; p. 100809
• Main Authors: Rajah, Jihene, Amari, Said, Tebani, Karima, Barkallah, Maher, Haddar, Mohamed
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.05.2023
• Subjects: Control laws; Discrete event systems; Generalized mutual exclusion constraints; Min-Plus algebra; Networks of timed event graphs; Discrete event systems; Min-Plus algebra; Generalized mutual exclusion constraints; Networks of timed event graphs; Control laws
• ISSN: 0947-3580; 1435-5671
• DOI: 10.1016/j.ejcon.2023.100809

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.