Modeling and Control of Hybrid Timed Event Graphs with Multipliers Using (Min, +) Algebra

Abstract

We study a subclass of Petri nets, called hybrid timed event graphs with multipliers, or equivalently, hybrid timed weighted marked graphs, composed of continuous and discrete graphs interconnected among themselves. Such graphs can be modeled by using a particular algebra, called dioid, defined on a set of operators and endowed with the pointwise minimum operation as addition and the composition operation as multiplication. A just in time control method of these graphs based on residuation theory is proposed.