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

Julio Clempner

International Journal of Applied Mathematics and Computer Science (2010)

  • Volume: 20, Issue: 2, page 349-366
  • ISSN: 1641-876X

Abstract

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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 properties, we show that the HDPPN theoretic notions of (local and global) equilibrium and stability are those of the DPPN. As a result in the trajectory-dynamic properties framework, we obtain equivalent characterizations of that of the DPPN for final decision points and stability. We show that the HDPPN mark-dynamic and trajectory-dynamic properties of equilibrium, stability and final decision points coincide under some restrictions. We propose an algorithm for optimum hierarchical trajectory planning. The hierarchical decomposition process is presented under a formal treatment and is illustrated with application examples.

How to cite

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Julio Clempner. "A hierarchical decomposition of decision process Petri nets for modeling complex systems." International Journal of Applied Mathematics and Computer Science 20.2 (2010): 349-366. <http://eudml.org/doc/207992>.

@article{JulioClempner2010,
abstract = {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 properties, we show that the HDPPN theoretic notions of (local and global) equilibrium and stability are those of the DPPN. As a result in the trajectory-dynamic properties framework, we obtain equivalent characterizations of that of the DPPN for final decision points and stability. We show that the HDPPN mark-dynamic and trajectory-dynamic properties of equilibrium, stability and final decision points coincide under some restrictions. We propose an algorithm for optimum hierarchical trajectory planning. The hierarchical decomposition process is presented under a formal treatment and is illustrated with application examples.},
author = {Julio Clempner},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {hierarchy; decomposition; structuring mechanisms; re-usable components; decision process; DPPN; stability; Lyapunov methods; optimization},
language = {eng},
number = {2},
pages = {349-366},
title = {A hierarchical decomposition of decision process Petri nets for modeling complex systems},
url = {http://eudml.org/doc/207992},
volume = {20},
year = {2010},
}

TY - JOUR
AU - Julio Clempner
TI - A hierarchical decomposition of decision process Petri nets for modeling complex systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2010
VL - 20
IS - 2
SP - 349
EP - 366
AB - 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 properties, we show that the HDPPN theoretic notions of (local and global) equilibrium and stability are those of the DPPN. As a result in the trajectory-dynamic properties framework, we obtain equivalent characterizations of that of the DPPN for final decision points and stability. We show that the HDPPN mark-dynamic and trajectory-dynamic properties of equilibrium, stability and final decision points coincide under some restrictions. We propose an algorithm for optimum hierarchical trajectory planning. The hierarchical decomposition process is presented under a formal treatment and is illustrated with application examples.
LA - eng
KW - hierarchy; decomposition; structuring mechanisms; re-usable components; decision process; DPPN; stability; Lyapunov methods; optimization
UR - http://eudml.org/doc/207992
ER -

References

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