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2010 | 20 | 2 | 349-366
Tytuł artykułu

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

Autorzy
Treść / Zawartość
Warianty tytułu
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.
Rocznik
Tom
20
Numer
2
Strony
349-366
Opis fizyczny
Daty
wydano
2010
otrzymano
2008-12-22
poprawiono
2009-07-08
Twórcy
  • 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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv20i2p349bwm
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