Performance evaluation of nonlinear weighted T-system

In this paper, two approaches for diagnosability analysis of discrete event systems are discussed and experimentally evaluated. The considered approaches are the diagnoser-based approach proposed in [1, 2] and the model-checking reformulation approach proposed in [3, 4]. Experiments are performed on a level crossing benchmark, using the software tools integrating the considered approaches. These two approaches show different features in terms of state-space building and procedure for analyzing diagnosability. Based on the obtained results through the benchmark, a comparative discussion is provided particularly regarding the generated state-spaces and the time consumption for analyzing diagnosability.

Secret inference and attacktability analysis of discrete event systems

Petrinets are the suitable tool for modeling and analysis of discrete event systems. The effective methods of analyzing the discrete event systems (DES) are exhibited by Petri nets. The entire structure of the system is mathematically expressed using Petrinets and also all the properties are analysed by different methods. The properties of Petrinets are different in various systems, a Flexible Manufacturing System (FMS) requires production activities in which raw materials, energy, labour, and equipment are combined together in the modification process for the production of good quality goods.” The word “flexible” explains the capability of the system to relate productively to make changes in the system. These changes can be internal failure of the system or classification problems such as a sample or external changes in the structure of the model as well as demand for the process. The inherent limitations such as undecidable properties, complexity in checking, automatic verification of the modeled system are existing in FMS. This paper explains a study on FMS using Petri net reduction. A PN underlies event structures with casuality and compatibility relations. Partial order methods and reduction methods reduce the complexity of constructing the reachability graph. The determination of PN system through reduction methods in recent years focused by many researchers. The significance of reduction methods are highlighted to execute the faster analysis of a system. Instead of coverability trees and the graphical representation the incidence matrix of the PNs are used for the reduction methods. Reduction methods are used to simplify large scale PNs into “equivalent” smaller nets. Boundedness, liveness, simplification of implicit places, shared resources and elimination of self-loops are checked though equivalent smaller nets. The structure of FMS is preserved.

For over twenty years, hybrid systems, involving both a discrete-valued state component and a continuous-valued state component (evolving in either discrete or continuous time), have challenged control engineers interested in expanding the applications of control theory. In particular, the hybrid system representation has motivated the formulation of "fault-tolerant" optimal control problems for systems subject to abrupt changes in their structure, parameters or operating environment. One approach has been the development of optimal controllers for jump linear systems. Strong theoretical results are currently limited, however, to Markov and semi-Markov jump processes, when change in the system structure are perfectly observed. During the same two decades, theory and methods for the analysis of discrete event systems have been developed. Recently the control of discrete event systems has received significant attention. This paper is directed toward the application of jump systems control theory to the control of continuous variable processes driven by discrete event systems.

A GSPN-Based automatic analysis tool for discrete event systems

This paper aims at defining a model-driven approach for the diagnosability analysis of discrete event systems (DES). The proposed approach can be adopted during the design of modern control systems, in which many sensors and actuators are employed and the diagnosability of faults within a certain delay could be an issue. The proposal represents a first step towards an automatic model-driven process which derive formal models from a complete high-level specification of DESs. The specification activity of our approach relies on the Dynamic STate Machine (DSTM) formalism, a new language that extends state machines with dynamic instantiation, interrupts and asynchronous communication. The paper will describe how we can automatically derive Petri net and Promela models from the high-level DSTM specification. The former model can be used to apply diagnosability analysis approaches proposed in the DES community, while the latter can be used to apply model checking techniques. An application of the proposed model-driven approach is described by deriving both a PN and a Promela model for the well-known railway level crossing benchmark.

Min-max functions are dynamic programming operators of zero-sum deterministic games with finite state and action spaces. The problem of computing the linear growth rate of the orbits (cycle-time) of a min-max function, which is equivalent to computing the value of a deterministic game with mean payoff, arises in the performance analysis of discrete event systems. We present here an improved version of the policy iteration algorithm given by Gaubert and Gunawardena in 1998 to compute the cycle-time of a min-max functions. The improvement consists of a fast evaluation of the spectral projector which is adapted to the case of large sparse graphs. We present detailed numerical experiments, both on randomly generated instances, and on concrete examples, indicating that the algorithm is experimentally fast.

Companies have been forced to collaborate with each other, sharing knowledge, adopting and applying better practices of product design and manufacturing, and exploring internet-based applications. This collaborative activity is established in the context of productive processes, properly described. In other words, the steps of the productive process should be described in a language that could be interpreted by the production equipment of different collaborators (companies that are part of this new organization). However, the available languages for describing the processes today do not consider heterogeneous environments with heterogeneous productive resources (equipment, tools, devices and others from different manufacturers, for example). On the other hand, there are formal methods that allow extensions that make them able to describe and interpret the productive operations sequence. One of such tools is the Petri net, which is used in the modeling and analysis of discrete event systems. Thus, a notation is proposed, based on Petri net, for the description of productive processes in a collaborative environment.

The class of Discrete Event Systems which can be modelled as timed event graphs may be described by linear equations in a non-traditional algebraic systems called a dioid or max-algebra. This paper extends the dioid algebra approach to a broader class of systems including both timed and untimed models, time-varying systems, and decision-making systems. We introduce an algebraic structure called a dioid vector space which allows any number of continuous functions to be included in the system description.

The paper deals with the definition of procedure that enables one to determine, for a given plant, if all faults can be detected and located after a finite sequence of observable events. More formally, the diagnosability is the property that every fault can be correctly detected from the observable events of the system after its occurrence no later than a bounded number of events. In this paper, the diagnosability problem of Discrete Event Systems (DESs) is studied. As modeling tool, finite-state automaton in an event-based framework is used. A necessary and sufficient condition of diagnosability of such systems is proposed. The results proposed in this paper allow checking the diagnosability of discrete event systems in an efficient way, i.e. in polynomial time.

We deal with timed event graphs whose holding times associated with places are variable. Defining a first-in-first-out functioning rule, we show that such graphs can be linearly described in (max,+) algebra. Moreover, this linear representation allows extending the just-in-time control synthesis existing for timed event graphs with constant holding times. An example is proposed in order to illustrate how the approach can be applied as a just-in-time strategy for production lines.

Modeling and analysis of discrete-event dynamic systems representing manufacturing processes are considered. The manufacturing processes considered represent the repetitive production of a given number of products by means of a fixed set of machines. It is necessary to introduce a certain number of simplifying assumptions to make the system representable by timed event graphs, a special class of Petri nets, for which tools capable of providing an analytical performance evaluation exist. In this framework, some analysis and optimization problems can be considered. >

Localization of time shift failures in (max,+)-linear systems

Timed event graphs (TEGs) are a subclass of timed Petri nets suitable to model decision-free timed discrete event systems. In classical TEGs, exact synchronization of two transitions T1 and T2 is available by requiring that transitions T1 and T2 fire simultaneously. In this paper, a new sort of synchronization, namely partial synchronization, is introduced: transition T2 has to fire when transition T1 fires, but transition T1 is not influenced by transition T2. Under some assumptions, optimal control, already available for classical TEGs, is extended to TEGs under partial synchronization.

This chapter discusses the timed event graphs (TEGs) a suitable tool for the modelling of manufacturing systems characterized by synchronization and delay phenomena but devoid of choices. Furthermore, TEGs have a linear representation in an algebraic structure called idempotent semirings. The chapter introduces several idempotent semirings, for example, max-plus algebra min-plus algebra and minax and demonstrates with several examples. As many manufacturing systems and the operation are subject to additional constraints, the standard notion of linear systems in dioids has been extended. Using the approach, it is possible to model minimal and maximal operation times, that is, time window constraints, as well as minimal and maximal numbers of work in progress, for example, in systems operating with a nested schedule. The chapter shows that the approach is relatively robust to mistakes in the modelling procedure. More precisely, if unfeasible constraints are requested, the resulting system will indicate that some transitions are blocked from the beginning.