Extremal trajectories in P-time Event Graphs: application to control synthesis with specifications

This paper presents a modelling and an analysis of P-time Event Graphs in the field of topical algebra. A particular serie of matrices is introduced whose evolution determines the system behavior and the existence of a trajectory without token deaths. The extremal trajectories obeying to an interval of desired output are deduced. If every event is controllable, the Just-In-Time control of Timed Event Graph is solved when additional specifications are given by a P-time Event Graph.