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A hierarchical decomposition of decision process Petri nets for modeling complex systems

Julio Clempner (2010)

International Journal of Applied Mathematics and Computer Science

We provide a framework for hierarchical specification called Hierarchical Decision Process Petri Nets (HDPPNs). It is an extension of Decision Process Petri Nets (DPPNs) including a hierarchical decomposition process that generates less complex nets with equivalent behavior. As a result, the complexity of the analysis for a sophisticated system is drastically reduced. In the HDPPN, we represent the mark-dynamic and trajectory-dynamic properties of a DPPN. Within the framework of the mark-dynamic...

A novel continuous model to approximate time Petri nets: modelling and analysis

Tianlong Gu, Rongsheng Dong (2005)

International Journal of Applied Mathematics and Computer Science

In order to approximate discrete-event systems in which there exist considerable states and events, David and Alla define a continuous Petri net (CPN). So far, CPNs have been a useful tool not only for approximating discrete-event systems but also for modelling continuous processes. Due to different ways of calculating instantaneous firing speeds of transitions, various continuous Petri net models, such as the CCPN (constant speed CPN), VCPN (variable speed CPN) and the ACPN (asymptotic CPN), have...

A quadratic optimal control problem for a class of linear discrete distributed systems

Mostafa Rachik, Mustapha Lhous, Ouafa El Kahlaoui (2006)

International Journal of Applied Mathematics and Computer Science

A linear quadratic optimal control problem for a class of discrete distributed systems is analyzed. To solve this problem, we introduce an adequate topology and establish that optimal control can be determined though an inversion of the appropriate isomorphism. An example and a numerical approach are given.

Algebraic approach for model decomposition: Application to fault detection and isolation in discrete-event systems

Denis Berdjag, Vincent Cocquempot, Cyrille Christophe, Alexey Shumsky, Alexey Zhirabok (2011)

International Journal of Applied Mathematics and Computer Science

This paper presents a constrained decomposition methodology with output injection to obtain decoupled partial models. Measured process outputs and decoupled partial model outputs are used to generate structured residuals for Fault Detection and Isolation (FDI). An algebraic framework is chosen to describe the decomposition method. The constraints of the decomposition ensure that the resulting partial model is decoupled from a given subset of inputs. Set theoretical notions are used to describe the...

An analytical method for well-formed workflow/Petri net verification of classical soundness

Julio Clempner (2014)

International Journal of Applied Mathematics and Computer Science

In this paper we consider workflow nets as dynamical systems governed by ordinary difference equations described by a particular class of Petri nets. Workflow nets are a formal model of business processes. Well-formed business processes correspond to sound workflow nets. Even if it seems necessary to require the soundness of workflow nets, there exist business processes with conditional behavior that will not necessarily satisfy the soundness property. In this sense, we propose an analytical method...

Analysis of structural properties of Petri nets based on product incidence matrix

Guangyou Ji, Mingzhe Wang (2013)


This paper presents some structural properties of a generalized Petri net (PN) with an algorithm to determine the (partial) conservativeness and (partial) consistency of the net. A product incidence matrix A = C C T or A ˜ = C T C is defined and used to further improve the relations among PNs, linear inequalities and matrix analysis. Thus, based on Cramer’s Rule, a new approach for the study of the solution of a linear system is given in terms of certain sub-determinants of the coefficient matrix and an efficient...

Boolean Biology: Introducing Boolean Networks and Finite Dynamical Systems Models to Biology and Mathematics Courses

R. Robeva, B. Kirkwood, R. Davies (2011)

Mathematical Modelling of Natural Phenomena

Since the release of the Bio 2010 report in 2003, significant emphasis has been placed on initiating changes in the way undergraduate biology and mathematics courses are taught and on creating new educational materials to facilitate those changes. Quantitative approaches, including mathematical models, are now considered critical for the education of the next generation of biologists. In response, mathematics departments across the country have initiated changes to their introductory calculus sequence,...

Continuous extension of order-preserving homogeneous maps

Andrew D. Burbanks, Colin T. Sparrow, Roger D. Nussbaum (2003)


Maps f defined on the interior of the standard non-negative cone K in N which are both homogeneous of degree 1 and order-preserving arise naturally in the study of certain classes of Discrete Event Systems. Such maps are non-expanding in Thompson’s part metric and continuous on the interior of the cone. It follows from more general results presented here that all such maps have a homogeneous order-preserving continuous extension to the whole cone. It follows that the extension must have at least...

Controllability in the max-algebra

Jean-Michel Prou, Edouard Wagneur (1999)


We are interested here in the reachability and controllability problems for DEDS in the max-algebra. Contrary to the situation in linear systems theory, where controllability (resp observability) refers to a (linear) subspace, these properties are essentially discrete in the max -linear dynamic system. We show that these problems, which consist in solving a max -linear equation lead to an eigenvector problem in the min -algebra. More precisely, we show that, given a max -linear system, then, for every natural...

Decentralized structural controller design for large-scale discrete-event systems modelled by Petri nets

Aydın Aybar, Altuğ İftar (2009)


A decentralized structural controller design approach for discrete-event systems modelled by Petri nets is presented. The approach makes use of overlapping decompositions. The given Petri net model is first overlappingly decomposed into a number of Petri subnets and is expanded to obtain disjoint Petri subnets. A structural controller is then designed for each Petri subnet to avoid deadlock. The obtained controllers are finally applied to the original Petri net. The proposed approach significantly...

Eigenspace of a three-dimensional max-Łukasiewicz fuzzy matrix

Imran Rashid, Martin Gavalec, Sergeĭ Sergeev (2012)


Eigenvectors of a fuzzy matrix correspond to stable states of a complex discrete-events system, characterized by a given transition matrix and fuzzy state vectors. Description of the eigenspace (set of all eigenvectors) for matrices in max-min or max-drast fuzzy algebra was presented in previous papers. In this paper the eigenspace of a three-dimensional fuzzy matrix in max-Łukasiewicz algebra is investigated. Necessary and sufficient conditions are shown under which the eigenspace restricted to...

Equation with residuated functions

Ray A. Cuninghame-Green, Karel Zimmermann (2001)

Commentationes Mathematicae Universitatis Carolinae

The structure of solution-sets for the equation F ( x ) = G ( y ) is discussed, where F , G are given residuated functions mapping between partially-ordered sets. An algorithm is proposed which produces a solution in the event of finite termination: this solution is maximal relative to initial trial values of x , y . Properties are defined which are sufficient for finite termination. The particular case of max-based linear algebra is discussed, with application to the synchronisation problem for discrete-event systems;...

Event monitoring of parallel computations

Alexander M. Gruzlikov, Nikolai V. Kolesov, Marina V. Tolmacheva (2015)

International Journal of Applied Mathematics and Computer Science

The paper considers the monitoring of parallel computations for detection of abnormal events. It is assumed that computations are organized according to an event model, and monitoring is based on specific test sequences.

FDI(R) for satellites: How to deal with high availability and robustness in the space domain?

Xavier Olive (2012)

International Journal of Applied Mathematics and Computer Science

The European leader for satellite systems and at the forefront of orbital infrastructures, Thales Alenia Space, is a joint venture between Thales (67%) and Finmeccanica (33%) and forms with Telespazio a Space Alliance. Thales Alenia Space is a worldwide reference in telecoms, radar and optical Earth observation, defence and security, navigation and science. It has 11 industrial sites in 4 European countries (France, Italy, Spain and Belgium) with over 7200 employees worldwide. Satellite evolution...

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