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

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 -