An Application for the Control of Stochastic Petri nets via Fluidification Approach

Year 2012, Volume: 25 Issue: 4, 901 - 908, 29.03.2012

Hanife Apaydın Özkan

Abstract

Petri nets are frequently used for modeling and analysis of discrete event systems. Similar to other modeling formalisms for discrete systems,  it suffers from state explosion. Fluidification can be used to overcome this difficulty yielding  fluid approximation of original Petri nets  in the sense of behaviours and  properties. This models are called  continuous Petri nets. In this work, stochastic Petri nets and their fluid approximation timed continuous Petri nets is considered. One of the main advantages of timed continuous Petri nets is to be able to design a controller by using more analytical techniques. But it is important to come back to a reasonable design or control in the original discrete setting.  In this work, a target state control strategy of timed continuous Petri nets will be interpreted for the control of underlying Stochastic Petri nets.  The efficiency of this interpretation  will be studied  on  a table factory system.

Petri nets are frequently used for modeling and analysis of discrete event systems. Similar to other modeling formalisms for discrete systems,  it suffers from state explosion. Fluidification can be used to overcome this difficulty yielding  fluid approximation of original Petri nets  in the sense of behaviours and  properties. This models are called  continuous Petri nets. In this work, stochastic Petri nets and their fluid approximation timed continuous Petri nets is considered. One of the main advantages of timed continuous Petri nets is to be able to design a controller by using more analytical techniques. But it is important to come back to a reasonable design or control in the original discrete setting.  In this work, a target state control strategy of timed continuous Petri nets will be interpreted for the control of underlying Stochastic Petri nets.  The efficiency of this interpretation  will be studied  on  a table factory system.

Keywords

Timed continuous Petri nets, Stochastic Petri nets, control

References

• D. Mandrioli, A. Morzenti, M. Pezze, P. Pietro S.,and S. Silva. A Petri net and logic approach to the specification and verification of real time systems. In Formal Methods for Real Time Computing. John Wiley &Sons Ltd.
• T. Murata. Petri nets: properties, analysis and applications. Proceedings of the IEEE, 77:541– 580, 1989.
• R. David and H.Alla. Continuous Petri nets. In 8th European Workshop on Application and Theory of Petri Nets, Zaragoza, Spain, 1987.
• M. Silva and L. Recalde. Petri nets and integrality relaxations a view of continuous Petri nets. IEEE Trans on Systems Man and Cybernetics, 32(4):314-327, 2002.
• C. Mahulea, A. Ramirez, L. Recalde, M.Silva. Steady state control reference and token conservation laws in continuous Petri net systems. IEEE Transactions on Automation Science and Engineering, 2008, 5(2): 307–320.
• C. Mahulea, A. Giua, L. Recalde, C. Seatzu, M. Silva. Optimal model predictive control of timed continuous Petri nets. IEEE Transactions on Automatic Control, 2008, 53(7): 1731 – 1735.
• J. Xu, L. Recalde, M. Silva. Tracking control of join-free timed continuous Petri net systems under infinite servers semantics. Discrete Event Dynamic Systems, 2008, 18(2): 263–288.
• H. Apaydın - Özkan, J. Julvez, C. Mahulea, M. Silva. Approaching minimum time control of Timed continuous petri nets. Nonlinear Analysis: Hybrid Systems, 2011, 5(2): 136 – 148.
• C.R. Vázquez, M. Silva, "Performance Control of Markovian Petri Nets via Fluid Models: A Stock- Level Control Example", In 5th IEEE Conference on Automation Science and Engineering (IEEE CASE). (Session In Memoriam of prof. Laura Recalde: Advances in Petri Net theory.), Bangalore, India, aug 2009.
• L. Recalde, E. Teruel, and M. Silva. On linear systems. Journal of Circuits Systems and Computers, 8(1):223–265, 1998.
• L. Recalde, E. Teruel, and M. Silva. Autonomous continuous P/T systems. In S. Donatelli and J. Kleijn, editors, Application and Theory of Petri Nets, 1639:107–126. Springer, 1999.
• L. Recalde and M. Silva. Petri nets fluidification revisited semantics and steady state. Eoropean Journal of Automation APII JESA, 35(4):435–449, 2001.
• H.Alla and R.David, A modeling and Analysis tool for discrete event systems-Continuous Petri net. Performance Evaluation, 1998, 33(1),175- 199.
• M. Silva, L. Recalde. On fluidification of Petri net models: from discrete to hybrid and continuous models.
• J. Julvez, L. Recalde, and M. Silva. On reachability in autonomous continuous Petri net systems. In 24th International Conference on Application and Theory of Petri Nets, pages 221– 240, Eindhoven, Netherlands, June2003. Springer
• C.R. Vazquez, L. Recalde, and M. Silva. Stochastic–continuous state approximation of markovian petri net systems. In CDC 2008: 47th
• IEEE Conference on Decision and Control,
• Cancun, Mexico, December 2008.
• E. Teruel, J. M. Colom, M. Silva. Choice-free Petri nets: A model for deterministic concurrent systems with bulk services and arrivals. IEEE Transactions on Systems, Man, and Cybernetics, 1997, 1(27): 73–83.