A HIERARCHICAL DECOMPOSITION OF DECISION PROCESS PETRI NETS FOR MODELING COMPLEX SYSTEMS

作者：Clempner Julio^*

来源：International Journal of Applied Mathematics and Computer Science, 2010, 20(2): 349-366.

DOI：10.2478/v10006-010-0026-2

• hierarchy
• decomposition
• structuring mechanisms
• re-usable components
• decision process
• DPPN
• stability
• Lyapunov methods
• optimization

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.

• 出版日期2010-6