State‐Feedback Control for a Class of Timed Petri Nets Subject to Marking Constraints

Abstract

The paper contributes with an original method of designing a control for discrete event systems modeled by a class of timed Petri nets. Precisely, this work deals with the closed loop control of Timed Event Graphs (TEGs) under specifications expressed with linear marking constraints. The objective of the controller is to limit the number of tokens in some places of these TEGs. The behavior of TEGs is represented by a system of difference equations that are linear in Min-Plus algebra and the constraints are described by a set of inequalities, which are also linear in Min-Plus algebra. A formal approach to design control laws that guarantee compliance with these marking constraints is proposed. For this, two sufficient conditions for the existence of control laws are proposed. The computed controls are causal feedbacks, which can be represented by a set of marked and timed places. The proposed method is illustrated in two applications: a manufacturing production line and an assembly system.

Control of a class of discrete event systems with disturbances and capacity constraints: Application to a disassembly problem

“…Proof 1. Assuming a disturbed TEG where ρ is the path under marking constraint defined by inequality (6), the control laws are determined by:…”

“…Their purpose was to meet the temporal constraints imposed on system behavior. Others have examined requirements related to capabilities, which were expressed in Petri nets by marking constraints or forbidden states [4][5][6]. In our work, we are interested in the issue of limited resource capabilities in DESs modeled by timed event graphs (TEGs).…”

“…In this paper, we are interested in solving the problem of synthesizing feedback control laws for partially controllable TEGs subject to marking constraints using Min-Plus algebra. Among recent research in control design for TEGs with forbidden states, the authors in [5] provided an extension of their previous work in [6]. They introduced a new feedback control strategy for observable TEGs, synthesizing laws that would ensure marking constraints on a place or path.…”

Modeling and control of drug assignment for pharmaceutical cabinets using discrete event systems approaches

“…The present contribution extends the existing approaches for controlling TEGs subject to capacity constraints [20,22] by considering a more complex case of TEGs and integrating the phenomena of resource sharing and conflict, these systems are modeled by conflicting timed event graphs (CTEGs). Several works interested in this class use dioid algebra, like in [23], where authors gave their equivalent Max-Plus representation applied to a job shop example.…”