Off-Line Identification for a Class of Discrete Event Systems Using Safe Petri Nets

Bekrar, Rebiha; Messai, Nadhir; Essounbouli, Najib; Hamzaoui, Abdelaziz; Riera, Bernard

doi:10.3182/20060926-3-pl-4904.00037

Cited by 13 publications

(14 citation statements)

References 9 publications

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“…For an event e j whose periods are given according to an exponential pdf, the normalized errors δµ i,j k is defined for µ i,j k according to equation (18) …”

Section: Casementioning

confidence: 99%

Design and time parameters identification for non-Markovian Petri net models: application to reliability analysis

Lefebvre

2011

Proceedings of the Institution of Mechanical Engineers, Part O:

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The reliability analysis for dynamic systems is often based on timed stochastic Petri net models. The contribution of this paper concerns the design and identification of non-Markovian timed stochastic Petri net models. In particular, stochastic Petri nets that combine firing periods with normal and exponential probability density functions (pdfs) are considered. A numerical method is proposed for the identification of the parameters that characterize the pdfs of the firing periods. This method is based on a statistical analysis of the collected event sequences that are recorded by supervision systems. The method is applied for the reliability analysis of a single server with variable operation periods.

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“…For an event e j whose periods are given according to an exponential pdf, the normalized errors δµ i,j k is defined for µ i,j k according to equation (18) …”

Section: Casementioning

confidence: 99%

Design and time parameters identification for non-Markovian Petri net models: application to reliability analysis

Lefebvre

2011

Proceedings of the Institution of Mechanical Engineers, Part O:

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“…The concept of influence paths is proposed, from which the feasible transition sequences can be derived such that the observable behavior does not violate the control specifications. Similar work related to the transition firing sequences can be found in [1], where the identified data set, i.e., input and output transition sequences, is used to construct the Petri net model of a system under consideration.…”

Section: Introductionmentioning

confidence: 98%

A monitor solution to enforce legal transition firing sequences problems by using Petri nets

Gao

Wang

et al. 2014

2014 IEEE International Conference on Automation Science and Engineering (CASE)

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This paper focuses on supervisory control of a class of discrete event systems with known initial and desti nation states, whose evolution conforms to a set of specified linear or non-linear constraints. A supervisor is designed, which supervises the considered system to evolve and finally to reach the destination state with minimal costs without violating the specified constraints. A partial structure of the Petri net model of a system is first created by the constraints. Then, we find the destination state under the constraints by a search algorithm with least cost. A legal transition firing sequence can be found by solving integer programming problems with the constraints of the created model and the result of the search algorithm. Otherwise, a more exhaustive model is made under the limit of the constraints. Then, a set of control places is used to implement the transition sequence by introducing a set of complementary transitions. A mental game example is used to demonstrate the proposed approaches.

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“…Given some information on the evolution of a system, several studies discuss the identification problem of DES using Petri nets. Roughly speaking, the existing approaches can be divided into three categories: (a) given a finite language describing the system behavior, it consists in determining the structure and initial marking of a Petri net system whose language coincides with the given one [10][11][12], (b) given an event sequence (transition sequence) as well as the corresponding system states (markings), the goal is to determine a Petri net system such that the given event sequence is firable from its initial marking [13][14][15], and (c) assuming that the net to be identified has special structure (e.g., safe Petri nets) or properties (e.g., exhibiting cyclic behavior), the net is identified from finite data using the customized algorithm [16][17][18][19]. In general, an integer linear programming problem (ILPP) is defined to impose certain 2 Journal of Control Science and Engineering constraints on the structure of the net to be identified in cases (a) and (b).…”

Section: Introductionmentioning

confidence: 99%

“…The approach has polynomial time complexity, but it can only be applied to safe Petri nets. Bekrar et al [19] provide an algorithm that identifies a safe Petri net from the data set of I/O signals of a system. They assume that the considered system is cyclic and all its cycles start from the same initial state.…”

Section: Introductionmentioning

confidence: 99%

“…Meda et al in [17,18] discuss the identification problem by using Interpreted Petri nets, i.e., a Petri net associated with an input function and an output function, assuming that the dependency between transitions is known. All studies in [16][17][18][19] fall into case (c). These approaches are not general and can only be applied to Petri nets with special structure or behavior.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Model Identification of Unobservable Behavior of Discrete Event Systems Using Petri Nets

Zhu

Wang

2019

Journal of Control Science and Engineering

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This paper deals with the problem of identifying a Petri net that models the unobservable behavior of a system from the knowledge of its dynamical evolution. We assume that a partial Petri net model that represents the observable behavior of a system is given in which all the transitions are observable. An identifier monitors the system evolution and records the observed transition sequence (and possible corresponding markings). Some unobservable transitions modeling the unknown system behavior are identified from the transition sequence by formulating and solving integer linear programming problems. These identified unobservable transitions together with the given partial Petri net model characterize the whole system, including observable and unobservable behavior. Two different cases are considered. First, we assume that no place is observable. In such a case, a transition sequence is observed only during the evolution of the system. Second, we assume that a subset of places is observable; i.e., the observation contains not only the transition sequence but the corresponding markings as well. Hence an additional constraint should be imposed on the unobservable transition in the related programming problems according to the observed markings such that a more authentic unobservable transition can be found.

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Off-Line Identification for a Class of Discrete Event Systems Using Safe Petri Nets

Cited by 13 publications

References 9 publications

Design and time parameters identification for non-Markovian Petri net models: application to reliability analysis

Design and time parameters identification for non-Markovian Petri net models: application to reliability analysis

A monitor solution to enforce legal transition firing sequences problems by using Petri nets

Model Identification of Unobservable Behavior of Discrete Event Systems Using Petri Nets

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