Observer design for weighted timed event graphs in a dioid framework

Abstract

An observer is used in a feedback control system to compensate for the fact that not all states can be measured. This work refers to systems that can be modeled by timed Petri nets, more precisely, Weighted Timed Event Graphs (WTEGs). The WTEG allows modeling of problems without conflicts of resources. In the context of manufacturing systems, WTEGs are appropriate to design complex assembly lines, where dynamic behavior is described by the synchronization and saturation effects. We propose the design of an observer for WTEGs that, which consists of: (i) an Optimal Observer that is based on the conversion of the WTEG to the Timed Event Graph(TEG), which has a linear representation in the mathematical structure of the dioids; (ii) a Simulator, which is a copy of the system without disturbances; (iii) and an Interface that is used to connect the WTEG to the Optimal Observer and to the Simulator.