Modelling and Control of Timed Event Graphs with Shared Resource in Dioids

The purpose of this work is modelling and control of a timed discrete event system with shared resources under dioids algebraic structures, i.e, $\mathbb{Z}_{max}$ or $\mathbb{Z}_{min}$ (also denoted as (max,+) or (min,+)). Conflicting Timed Event Graphs (CTEG) considered in this paper is a class of timed Petri net, which can exhibit phenomena such as parallelism, synchronization, and resources sharing, whose behavior can be breezily described in the form of dioids algebraic by using a switching model method. By using the residuation theory and open-loop control laws, control methods that can achieve a desired system performance are proposed. And in the open-loop control strategy, two kinds of constraints are considered respectively. An example is utilized to verify the efficiency of the proposed method.