Algebraic approaches for designing control laws of time‐constrained networked conflicting timed event graphs

This paper outlines a new control synthesis procedure for Networked Conflicting Timed Event Graphs (NCTEGs) to satisfy upper time bounds imposed on certain critical paths. Switching Max-Plus models are used to describe the NCTEGs behaviour and temporal constraints are expressed by linear Max-Plus inequalities. Sufficient conditions for the existence of control laws to guarantee these strict time constraints are established for both cases of NCTEGs; fully observable and partially observable NCTEGs. The computed control laws are feedback gains that can be represented by control places which supervise the system to prevent from violating of temporal constraints. Finally, a case study is given to illustrate the proposed approach and to show the efficiency of the developed control laws.