Keywords
Discrete events
control theory
dynamic systems
controllable language
How to Cite
Abstract
In this work are exposed the solution steps of the cat and mouse problem published in the article from 1984, using Petri networks models and the Hiearchical Petri Net Simulator Software (HiPS). The objective is to show familiarity and the methodology of applying controllable language in discrete events using the previous tools, since the article was written almost 39 years ago without the advantages of information technologies where discrete events can be simulated. Besides showing the control schematics of Petri networks that allows the problem solution under fulfillment of certain conditions, the simulation software is used in advantage to get the model’s coverage and reachability table, an incidence matrix, the identification of out-of-conflict states and transitions to execute those states without restrictions. In symbolic terms, the behavior of the cat and the mouse can represent equipment, sensors, actuators, robots, machinery, or dynamic production systems. The results were optimal, and conclusions are discussed.
References
Kuntsevich, V. M., Gubarev, V. F., Kondratenko, Y. P., Lebedev, D. V. y Lysenko, V. P. (2018). Control Systems: Theory and Applications. River Publishers.
Balemi, S. (1992). Control of Discrete Event Systems: Theory and application. ADAG Administration & Druck AG.
Gunardi, Y. y Hanafi, D. (2022, julio 20-21). Petri net modeling for mobile robot in sharp turning cases. International Seminar of Intelligent Technology and its Applications (ISITIA). Surabaya, Indonesia. doi: https://doi.org/10.1109/ISITIA56226.2022.9855287
Murata, T. (1989). Petri nets: Properties, analysis and applications. Proceedings of the IEEE, 77(4), 541-580. doi: https://doi.org/10.1109/5.24143
Wang, J. (2007). Petri Nets for Dynamic Event-Driven System Modeling. En P. A. Fishwick (Ed.), Handbook of Dynamic System Modeling. Monmouth University. doi: https://doi.org/10.1201/9781420010855
Zurawski, R. y Zhou, M. (1994). Petri nets and industrial applications: A tutorial. IEEE Transactions on Industrial Electronics, 41(6), 567-583. doi: https://doi.org/10.1109/41.334574
Restrepo, P. L. A. (2011). Un método computacional para la detección y caracterización de conflictos en redes de Petri. Revista Ingenierías Universidad de Medellín, 10(19), 189-199. https://repository.udem.edu.co/handle/11407/931
Ramadge, P. J. (1983). Control and Supervision of Discrete Event Processes. Department of Electrical Engineering, University of Toronto.
Ramadge, P. J. y Wonham, W. M. (1982, diciembre 8-10). Supervision of discrete event processes. 21st IEEE Conference on Decision and Control. Orlando, FL, EE.UU. doi: https://doi.org/10.1109/CDC.1982.268351
Ramadge, P. J. y Wonham, W. M. (1987). Supervisory control of a class of discrete event processes. SIAM Journal on Control and Optimization, 25(1), 206-230. doi: https://doi.org/10.1137/0325013
Wonham, W. M. y Ramadge, P. J. (1987). On the Supremal Controllable Sublanguage of a given Language. SIAM Journal on Control and Optimization, 25(3), 637-659. doi: https://doi.org/10.1137/0325036
Wonham, W. M. y Ramadge, P. J. (1984, diciembre 12-14). On the supremal controllable sublanguage of a given language. 23rd Conference on Decision and Control. Las Vegas, NV, EE.UU. doi: https://doi.org/10.1109/CDC.1984.272178
Čapkovič, F. (1993). A Petri Nets-Based Approach to the Maze Problem Solving. En S. Balemi, P. Kozák y S. Smendiga (Eds.), Discrete Event Systems: Modeling and Control (pp. 173-179). Birkhäuser Basel. doi: https://doi.org/10.1007/978-3-0348-9120-2_15
Uzam, M. (2004). Synthesis of feedback control elements for discrete event systems using Petri net models and theory of regions. International Journal of Advance Technology, 24, 48-69. doi: https://doi.org/10.1007/s00170-003-1715-x
Harie, Y., Mitsui, Y., Fujimori, K., Batajoo, A. y Wasaki, K. (2017, octubre 24-27). HiPS: Hierarchical Petri Net design, simulation, verification and model checking tool. IEEE 6th Global Conference on Consumer Electronics (GCCE). Nagoya, Japón. doi: https://doi.org/10.1109/GCCE.2017.8229199
KWasaki1967. (2017, junio 4). HiPS: Hierarchical Petri net Simulator [video]. YouTube. https://www.youtube.com/watch?v=usF1JrQegOE
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