Language diagnosability captures the capability of the system to detect faults based on observations. When a system is not diagnosable, supervisory control can be used to enforce its diagnosability to prevent the faults from occurring silently, known as the active diagnosis problem. Note that in the context of timed discrete-event systems, an observation contains not only the sequence of the events but also their time information. Therefore, two sequences consisting of the same events but with different occurrence time instants can still reveal the occurrence of faults. This fact motivates us to consider enforcing the diagnosability of a timed discrete-event system by regulating the occurrence time instants of certain controllable events. In this paper, we first construct a verifier for a time-interval automaton to verify its diagnosability. Then, based on the verifier, we enforce the diagnosability of a time-interval automaton by restricting the time intervals of certain controllable events and disabling some controllable events. Note to Practitioners—Fault diagnosis and active diagnosis play a critical role in ensuring the reliability, safety, and efficiency of systems across various industries, ranging from automotive and aerospace to healthcare and smart grids. Discrete-event systems, as general models for complex man-made systems, are well-studied for modeling digital computer systems in the above scenarios. Early detection and correction of faults contribute to improved performance, reduced downtime, and enhanced overall system functionality. This work investigates the active diagnosis problem, i.e., design a supervisor to enforce diagnosability, for discrete-event systems modeled by time-interval automata. The control policy combines the time and logical information of the system, thereby allowing the closed-loop systems to retain more of the original system behavior. Time-interval automata is a model that is not complicated but is closer to actual engineering systems than finite automata, providing new insights for control engineers in modeling and control.

Interval Weighted Automata are a modeling formalism for timed systems that can be viewed as an alternative (more algebraic) to timed automata. We present here a way of deriving a deterministic interval weighted automaton to represent any bounded T-time Petri net subject to strong and single-server semantics. This approach consequently contributes to the characterization of the expressiveness of weighted automata with respect to other formalisms for timed Discrete Event Systems. In addition, the time language of the obtained abstraction has the characteristics of being included or equal to the time language of the T-time Petri net, and, in other words, any accessible state in the obtained Interval Weighted Automaton corresponds to an equally accessible state in the T-time Petri net. This property should allow the future use of this abstraction for the verification of properties that are expressed as an accessibility issue and/or for control.

This paper aims to explore the problem of verifying detectability for unambiguous weighted automata (UWAs) through the utilization of modified self-composition. Specifically, we focus on two types of detectability: strong periodic detectability (SPD) and strong D-detectability (SDD). The problem involves periodically determining the current state or distinguishing certain state-pairs of the system, based on the occurrence of a finite number of observable events. We introduce a new polynomial-time algorithm different from the detector, called self-composition for UWAs, and prove that it can be used to verify the SPD and SDD for UWAs. Ultimately, we propose necessary and sufficient conditions based on modified self-composition techniques to verify the aforementioned detectabilities for the studied UWA.

This article investigates diagnosability and$T$-diagnosability for discrete-event systems modeled by unambiguous max-plus automata (UMPAs). More precisely, diagnosability requires that the occurrence of any fault can be detected within a finite number of events after the fault has occurred.$T$-diagnosability requires that the occurrence of any fault can be detected within a delay of at most$T$time units after its occurrence. First, we propose a polynomial-time algorithm based on the construction of a nondeterministic finite automaton over a weighted alphabet for diagnosability verification of a UMPA. Second, we prove that$T$-diagnosability of a UMPA can be studied by reducing it to the problem of diagnosability. Third, we introduce an approach to calculate the upper on the time needed for detecting fault occurrence for a diagnosable UMPA, and its complexity is of sixth order in the number of states of the UMPA.

In this paper we are interested in a mathematical description of the class of hybrid systems, which can be modelled by hybrid Petri nets (HPN). A state space model using the conventional algebra for the continuous subsystem and the minplus algebra for the discrete subsystem is given, This model is used in the analysis of a special class of HPN.

In this paper we are interested in a mathematical description of the class of hybrid systems, which can be modeled by hybrid Petri nets HPNs . A state space model using conventional algebra for the continuous subsystem and minplus algebra for the discrete subsystem is given. The interface between the discrete and continuous part appears in our model. This model is illustrated through an example. We introduce the concept of discrete control of HPNs.

In this paper, a method for the calculation of the transfer function of timed event graphs is developed. The transfer function has the form of a formal series in one or two formal variables. The knowledge of this formal series plays a crucial role in the max-plus system theory. It is very important in the investigation of the problem of controllability of a system, because it provides us with the input-output relation as an equation in the dioid of formal series. The direct approach to this calculation requires the computation of a star operation of a matrix with entries in this dioid,which seems to be difficult for matrices of large dimensions. For this reason, we propose another approach using only the max-plus modeling of a system, that is, the dater's description. We have considered the multivariable case with several input and output transitions. We can obtain the transfer function as the output corresponding to a special control. This control follows from the dater's description of the zero and identity elements of this dioid. To illustrate this approach we give two examples. The purpose of the first one is to compare different approaches to this problem; the second one may serve as an application. We use our approach to determine the transfer function of a manufacturing system.

In this paper, a method for the calculation of transfer function of timed event graphs is developed. The transfer function has form of a formal series in one or two formal variables. The knowledge of this formal series plays a crucial role in the max-plus system theory. Namely, it is very important in the investigation of the problem of controllability of a system, because it provides the input-output relation as an equation in the dioid of formal series. The direct approach to this calculation requires the computation of a star operation of a matrix with entries in this dioid which seems to be difficult for matrices of large dimensions. This is why the authors propose another approach using only the max-plus modelling of a system. The authors have considered the multivariable case with several input and output transitions. The authors can obtain the transfer function as the output corresponding to a special control. To illustrate this approach the authors give two examples. The purpose of the first one is to compare different approaches to this problem, whereas the second one may serve as an application. The authors use their approach to determine the transfer function of a manufacturing system.