An algebraic control method to guarantee generalized marking constraints for partially observable timed event graphs

This work deals with the control problem of Discrete Event Systems (DESs) modelled by Timed Event Graphs (TEGs) and subject to Generalized Marking Constraints (GMCs). The aim of this paper is to propose an algebraic methodology for the determination of control laws in the form of state feedback, guaranteeing the satisfaction of marking specifications expressed by weighted inequalities in the Min-Plus algebra. The resultant controller can be represented by marked and timed control places, connected to the initial TEG model. The role of the established feedback is to limit the number of tokens in weighted paths for partially observable TEGs. In order to illustrate and show the interest of these current studies, we applied the suggested control method to a machine of filling bottles with liquid.