Abstract
A new approach to the study of discrete event systems (DES), characterized by automata, Petri-Nets or related presentations, is proposed. The Boolean Differential Calculus (BDC) supports modeling, analysis and synthesis of DES. This paper not only demonstrates fundamental properties of the BDC, but also presents a synthesis algorithm for the cat-mouse-example.
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References
Y. C. Ho. Dynamics of discrete event systems. Proceedings of the IEEE, 77 (1): 3–6, January 1989.
R. Scheuring and H. Wehlan. Der Boolesche Differentialkalkül- Eine Methode zur Analyse and Synthese von Petri-Netzen. at - Automatisierungstechnik, 39: 226–233, July 1991.
T. L. Booth. Sequential Machines and Automata Theory. John Wiley, New York, 1967.
P. E. Caines, R. Greiner, and S. Wang. Dynamical Logic Observers for Finite Automata. In Proceedings of the 27th IEEE Conference on Decision and Control, pages 226–233, Austin, Texas, December 1988.
P. E. Caines and S. Wang. Classical and Logic based Regulator Design and its Complexity for Partially Observed Automata. In Proceedings of the 28th IEEE Conference on Decision and Control, pages 132–137, Tampa, Florida, December 1989.
L.E. Holloway and B.H. Krogh. Synthesis of feedback control logic for a class of controlled Petri nets. IEEE Transactions on Automatic Control, 35 (5): 514–523, May 1990.
P.J. Ramadge and W.M. Wonham. Supervisory control of a class of discrete event systems. Siam J. Control and Optimization, 25 (1): 206–230, Jan. 1987.
Randy Cieslak, C. Desclaux, Ayman S. Fawaz, and Pravin Varaiya. Supervisory control of discrete-event processes with partial observations. IEEE Transactions on Automatic Control, 33 (3): 249–260, March 1988.
R.D. Brandt, V. Garg, P. Kumar, F. Lin, S.I. Marcus, and W.M. Wonham. Formulas for Calculating Supremal Controllable and Normal Sublanguages. Systems & Control Letters, 15: 111–117, 1990.
C.H. Golaszewski and P.J. Ramadge. Boolean coordination problems for product discrete event systems. In Proceedings of the 29th IEEE Conference on Decision and Control, pages 3428–3433, Honolulu, Hawaii, December 1990.
Y. Brave and M. Heymann. Stabilization of discrete-event processes. Int. J. Control, 51 (5): 1101–1117, 1990.
S. Balemi. Control of Discrete Event Systems: Theory and Application. PhD thesis, Swiss Federal Institute of Technology (ETH), Zurich, May, 1992.
S. B. Akers. On a theory of Boolean functions. SIAM J., 7: 487–498, 1959.
A. Talantsev. On the analysis and synthesis of certain electrical circuits by, means of special logical operators. Automat. i telemeh., 20: 898–907, 1959.
D. Bochmann and C. Posthoff. Binäre dynamische Systeme. R. Oldenbourg Verlag, München, Wien, 1981.
A. Thayse. Boolean Calculus of Differences, volume 101 of Lecture Notes in Computer Science. Springer Verlag, Berlin, New-York, 1981.
D. Bochmann and B. Steinbach. Logikentwurf mit XBOOLE. Verlag Technik, Berlin, 1991.
R. Scheuring, B. Steinbach, and D. Bochmann. XBMini - User’s Guide. Institut für Systemdynamik und Regelungstechnik, Stuttgart University, Internal report, 1992.
R. Scheuring. Modellierung, Beobachtung und Steuerung ereignisorientierter verfahrenstechnischer Systeme. PhD thesis, Institut für Systemdynamik und Regelungstechnik, Stuttgart University, In preparation, 1993.
P.J. Ramadge and W.M. Wonham. On the supremal controllable sublanguage of a given language. SIAM J. Control and Optimization, 25 (3): 637–659, May 1987.
R. Scheuring and H. Wehlan. On the design of discrete event dynamic systems by means of the boolean differential calculus. In First IFAC Symposium on Design Methods of Control Systems, pages 723–728, Zurich, September 1991.
W.V. Quine. A way to simplify truth functions. American Mathematical Monthly, 62 (9): 627–631, November 1955.
E.J. McCluskey Jr Minimization of boolean functions. Bell System Technical Journal, 35 (6): 1417–1444, November 1956.
P. Kozak, S. Balemi, and R. Smedinga, editors. Preprints of the Joint Workshop on Discrete Event Systems, Prague, August 1992.
J. L. Peterson. Petri Net Theory and the Modeling of Systems. Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1981.
B. Steinbach. Theorie, Algorithmen und Programme für den rechnergestützten logischen Entwurf digitaler Systeme. Dissertation B. Technische Universität Karl-Marx-Stadt, 1984.
B. Steinbach and N. Kuemmling. Effiziente Lösung hochdimensionaler BOOLEscher Probleme mittels XBOOLE auf Transputer. In Grebe R. and C. Ziemann, editors, Parallele Datenverarbeitung mit dem Transputer. Proceedings X (Springerreihe Informatikberichte Band 272), pages 127–434. Springer-Verlag, Berlin, New York, 1991.
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© 1993 Birkhäuser Verlag Basel
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Scheuring, R., Wehlan, H. (1993). Control of Discrete Event Systems by Means of the Boolean Differential Calculus. In: Balemi, S., Kozák, P., Smedinga, R. (eds) Discrete Event Systems: Modeling and Control. Progress in Systems and Control Theory, vol 13. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9120-2_7
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DOI: https://doi.org/10.1007/978-3-0348-9120-2_7
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