Piecewise deterministic Markov processes represented by dynamically coloured Petri nets

Everdij, M.H.C.; Blom, H.A.P.

doi:10.1080/17442500512331341040

Cited by 35 publications

(25 citation statements)

References 11 publications

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“…In this paper, one way to avoid this problem is investigated. The idea is to represent the interconnection of the recovery logic and linear system using a type of Petri net called a Dynamically Colored Petri Net (DCPN) [4]. A Petri net (cf.…”

Section: Introductionmentioning

confidence: 99%

Dynamically colored petri net representation of nonlinear sampled-data systems with embedded recovery algorithms

Herencia-Zapana

González

Gray

2007

2007 46th IEEE Conference on Decision and Control

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Safety critical control systems are being implemented with computers that include error recovery capabilities to reduce the effect of common mode faults triggered by harsh environments. To study the effect of the error recovery algorithms on the stability and tracking performance of the closed-loop system, this paper models the interconnection of a stochastic exosystem, error recovery logic, and nonlinear sampleddata system using a Dynamically Colored Petri Net. This representation is then mapped into a Piecewise Deterministic Markov Process representation, generalizing a recent result that did not include an error recovery algorithm. The special case of a discrete-time plant is also considered. In this case, the representation becomes simply a Markovian jump linear system.

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Section: Introductionmentioning

confidence: 99%

Dynamically colored petri net representation of nonlinear sampled-data systems with embedded recovery algorithms

Herencia-Zapana

González

Gray

2007

2007 46th IEEE Conference on Decision and Control

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show abstract

“…In using the (S)DCPN formalism [26], [27], [28] in modelling more and more complex multi-agent hybrid systems, it was found that the compositional specification power of Petri nets reaches its limitations. More specifically, the following problems were identified:…”

Section: Specification Of Petri Net Modelmentioning

confidence: 99%

“…In [36], [42] a colour does not change as long as the token to which it is attached remains at its place. Everdij and Blom [26], [27] defined a Dynamically Coloured Petri Net (DCPN) by incorporating the following extensions: (1) a colour assumes values from a Euclidean state space, its value evolves as solution of a differential equation and influences the time period between enabling and firing; (2) the new tokens and attached colours are produced as random functions of the removed tokens and colours. An SDCPN extends an DCPN in the sense that colours evolve as solutions of a stochastic differential equation [28].…”

Section: Development Of MC Simulation Modelmentioning

confidence: 99%

Free Flight Collision Risk Estimation by Sequential MC Simulation

Blom¹,

Krystul²,

Bakker³

2006

Automation and Control Engineering

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“…We alsoa pply thea lgorithmo fS ection 4t os howt hatt his value-passing CPDP can be converted to aPDP.The ATM-examplew as first modelled as aD ynamically Coloured Petri Net (DCPN) (see the chaptera t pp. 325-350 of this book).DCPN is aPetri net formalism, whichhas alsobeen designed forc ompositional specification of PDP-type systems (see [6]a nd [7] fort he DCPN model).…”

Section: Communicatingp Iecewise Deterministic Markov Processesmentioning

confidence: 99%