A new formal method of control for Min-Plus linear systems subject to time constraints

Abstract

In this paper, we are interested in the problem of the control of Discrete Event Systems modeled basically by Timed Event Graphs (TEGs) subject to strict specific time constraints. For this type of systems with critical-time, whose correctness depends not only on the logic correctness but also on the respect of temporal constraints. To ensure these time specifications, it seems to be necessary to develop an efficient formal method to Figure out this problem. In this paper, a closed loop feedback control method is proposed to deal with the control problem of TEGs. The behavior of these systems is described by a linear Min-Plus equation and the temporal constraints are represented by linear inequalities in Min-Plus algebra. An analytical approach for computing state feedback controllers is proposed. Sufficient conditions, which are essential for the existence of control laws, are also given. Its function is to ensure the respect of a maximal bound of time in some paths of the TEGs through the relaxing of some previous hypothesis.