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

• Autorzy: Julio Clempner
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2010
• Tom: 20
• Numer: 2
• Strony: 349-366

Daty

wydano

2010

otrzymano

2008-12-22

poprawiono

2009-07-08

Twórcy

autor

Julio Clempner

• Center for Computing Research, National Polytechnic Institute (CIC-IPN), Av. Juan de Dios Batiz s/n, Edificio CIC, Col. Nueva Industrial Vallejo, 07738 Mexico City, Mexico

Bibliografia

• Bellman, R.E. (1957). Dynamic Programming, Princeton University Press, Princeton, NJ.
• Bouyakoub, S. and Belkhir, A. (2008). H-SMIL-Net: A hierarchical Petri net model for SMIL documents, 10-th International Conference on Computer Modeling and Simulation, Cambridge, UK, pp. 106-111.
• Buchholz, P. (1994). Hierarchical high level Petri nets for complex system analysis, in R. Valette(Ed.) Application and Theory of Petri Nets, Lecture Notes in Computer Science, Vol. 815, Springer, Zaragoza, pp. 119-138.
• Clempner, J., Medel, J. and Cârsteanu, A. (2005a). Extending games with local and robust Lyapunov equilibrium and stability condition, International Journal of Pure and Applied Mathematics 19(4): 441-454.
• Clempner, J. (2005b). Optimizing the decision process on Petri nets via a Lyapunov-like function, International Journal of Pure and Applied Mathematics 19(4): 477-494.
• Clempner, J. (2005c). Colored decision process Petri nets: Modeling, analysis and stability, International Journal of Applied Mathematics and Computer Science 15(3): 405-420.
• Dai, X., Li, A.J. and Meng, Z. (2009). Hierarchical Petri net modelling of reconfigurable manufacturing systems with improved net rewriting systems, International Journal of Computer Integrated Manufacturing 22(2): 158-177.
• Gomes, L. and Barros, J.P. (2005). Structuring and composability issues in Petri nets modeling, IEEE Transactions on Industrial Informatics 1(2): 112-123.
• Hammer, M. and Champy, J. (1993). Reengineering the Corporation: A Manifesto for Business Revolution, HarperBusiness, New York, NY.
• Howard, R.A. (1960). Dynamic Programming and Markov Processes, MIT Press, Cambridge, MA.
• Huber, P., Jensen, K. and Shapiro, R. (1990). Hierarchies in colored Petri nets, Lecture Notes in Computer Science Vol. 483, Springer-Verlag, pp. 313-341.
• Jensen, K. (1992). Coloured Petri Nets. Basic Concepts, Analysis Methods and Practical Use, Vol. 1: Basic Concepts, EATCS Monographs in Theoretical Computer Science, Springer-Verlag, New York, NY.
• Kalman, R.E. and Bertram, J.E. (1960). Control system analysis and design via the second method of Lyapunov, Journal of Basic Engineering 82: 371-393.
• Lakshmikantham, V., Leela, S. and Martynyuk, A.A. (1990). Practical Stability of Nonlinear Systems, World Scientific, Singapore.
• Lakshmikantham, V., Matrosov, V.M. and Sivasundaram, S. (1991). Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems, Kluwer Academic Publishers, Dordrecht.
• Murata, T. (1989). Petri nets: Properties, analysis and applications, Proceedings of the IEEE 77(4): 541-580.
• Passino, K.M., Burguess, K.L. and Michel, A.N. (1995). Lagrange stability and boundedness of discrete event systems, Journal of Discrete Event Systems: Theory and Applications 5(5): 383-403.
• Puterman, M.L. (1994). Markov Decision Processes: Discrete Stochastic Dynamic Programming, Wiley, New York, NY.

Identyfikatory

DOI

10.2478/v10006-010-0026-2