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.
@article{bwmeta1.element.bwnjournal-article-amcv20i2p349bwm,
author = {Julio Clempner},
title = {A hierarchical decomposition of decision process Petri nets for modeling complex systems},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {20},
year = {2010},
pages = {349-366},
zbl = {1196.93013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv20i2p349bwm}
}
Julio Clempner. A hierarchical decomposition of decision process Petri nets for modeling complex systems. International Journal of Applied Mathematics and Computer Science, Tome 20 (2010) pp. 349-366. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv20i2p349bwm/
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