Real-world applications, including supply chains, flexible industrial systems, networked control, and urban transport, frequently exhibit the structure of Discrete Event Systems (DES). This study focuses on controlling DES subject to disturbances while ensuring strict time constraints, specifically addressing partially controllable and observable timed event graphs. The behavior of these graphs is modeled using Min-Plus algebra and linear inequalities, which are then used to formalize the constraints to be satisfied. An algebraic approach for designing control laws to meet these restrictions is proposed. Sufficient conditions for the existence of causal state feedback that guarantees specification satisfaction are established. The approach is validated through a disturbed supply chain application, where controllers are implemented as timed and marked places, acting as supervisors to prevent constraint violations.

This paper addresses the control problem related to marking and strict timing constraints in Timed Event Graphs (TEGs). An analytic approach is developed to design state feedback control laws using Min-Plus formalism. In this approach, the dynamic behavior of TEGs and the mixed constraints are represented by linear equations and inequalities within the Min-Plus algebra dioid. Utilizing these mathematical frameworks, control laws are formulated to enforce the required constraints on TEG paths, provided certain sufficient conditions are met. The proposed controllers are implemented through a set of monitor places that oversee the initial TEGs, ensuring all mixed constraints are satisfied. Finally, a manufacturing system case study is presented to demonstrate the theoretical results and validate the effectiveness of the proposed methods.

This paper provides an algebraic control strategy for solving the problem of generalized mutual exclusion constraints in a network of timed event graphs with disturbance transitions. To this end, linear Min-Plus equations are used to describe the behavior of this class of timed Petri nets, and weighted Min-Plus inequalities translate the constraints to be satisfied. By combining these mathematical formalisms, sufficient conditions for the existence of control laws guaranteeing these mutual exclusion constraints are proposed. The theoretical results presented in this study are applied to accommodate supply disruptions from two suppliers to reconfigured manufacturing line.

In this paper, we present a new framework for modeling supply chains (SC) using a class of uncertain timed Discrete Event Systems (DESs) modeled by Timed Automata with Guards (TAGs). We also introduce an analytical approach based on dioidalgebra for the temporal performance evaluation of these systems.Specifically, by using the representation of extremal behaviors of TAGs with Min-Plus algebra, we determine the optimal completion intervals for the logistic chain.

In the field of automation systems, networked control systems in critical context must be temporally assess. To this end, the evaluation can be based on a reliable and well-defined graphical formalism. In this paper we propose the use of Timed Coloured Petri Nets to compute the maximal delay of a control network with switches. We introduce coloured formal series, an extension of formal series in the tropical algebra, to handle coloured models description by means of algebraic representations. These new representations are powerful as they can express linear coloured models behaviour as well as conflict resolution in the tropical algebra. They also yield functions to achieve automated temporal assessment.

Cyber-Physical Systems (CPS) brought connectivity to factories, and with connectivity comes a risk of cyber attack. CPSs are vulnerable to malicious attacks in which an attacker is inserted between a process and its control unit. Some papers have proposed to model attacked CPSs with discrete event systems (DES), have successfully modeled attacked systems and characterised different types of attacks. Nevertheless, these papers tend to treat attacks after they have become problematic. The objective of this paper is to extend previous works on cyber attack in DES to build models for diagnosis of attacks. We will design a model using Labeled Petri Nets and construct a reachability graph of an attacked net in order to enrich a diagnosis model which will allow the detection of attacks before they completely destabilise the system. This construction is illustrated by an industrial example.

This paper discusses the modelling and time performance evaluation of Distributed Control Systems (DCS). More precisely, we focus on the estimation of the response time and reactivity for these automation architectures using dioid algebra. We use Timed Automata with Guards (TAGs) to model system components and adopt an analytical approach to determine the response time formula as a function of temporal parameters for DCS. The main interest of this contribution is to introduce a algebraic tool capable of providing crucial validation elements concerning the temporal performances and sizing for an industrial scale DCS.

In this paper, two approaches of Fault-Tolerant Control for Discrete Event Systems are compared: the Fault-Hiding approach [4] and the control reconfiguration approach [5]. They are applied on a single case study in order to be compared. Then, a discussion on processing capacities, model sizes and limitations of the two methods is proposed.

In this paper, we present an analytic approach to evaluate the reactivity of client-server networked automation systems (NASs). Both deterministic and probabilistic analyses are provided while modeling the NAS using Timed Event Graphs (TEG). Since many results with regard to the deterministic approach have already been published, we recall only its main steps that prove useful, while exposing the probabilistic method. Thereby, we provide the density of probability distribution of the response time (or reactivity) using the probability densities of the local delays, experienced at the different stages of the NAS. Furthermore, a case study is presented to compare the results of the study to measures taken from a real platform.

This paper presents a novel approach to evaluate the response time in networked automation systems (NAS) that use a client/server protocol. The developments introduced are derived from modeling the entire architecture in the form of timed event graphs (TEGs), as well as from the resulting state representation in Max-Plus algebra. The various architectural stages are actually modeled in a very abstract pattern, which yields just those TEG models where local delays are sufficient to perform the overall evaluation. In this manner, linear Max-Plus equations are obtained. A thorough analysis of these equations has led to analytical formulas for direct calculus of NAS response time. As a final step, experimental measurements taken on a laboratory facility have been used to verify the validity of the results. In conclusion, the benefit and effectiveness of this novel method have been demonstrated.