# SYNTHESIZING DETERMINISTIC CONTROLLERS IN SUPERVISORY CONTROL

### Andreas Morgenstern, Klaus Schneider

#### Abstract

Supervisory control theory for discrete event systems is based on finite state automata whose inputs are partitioned into controllable and uncontrollable events. Well-known algorithms used in the Ramadge-Wonham framework disable or enable controllable events such that it is finally possible to reach designated final states from every reachable state. However, as these algorithms compute the least restriction on controllable events, their result is usually a nondeterministic automaton that can not be directly implemented. For this reason, one distinguishes between supervisors (directly generated by supervisory control) and controllers that are further restrictions of supervisors to achieve determinism. Unfortunately, controllers that are generated from a supervisor may be blocking, even if the underlying discrete event system is nonblocking. In this paper, we give a modification of a supervisor synthesis algorithm that enables us to derive deterministic controllers. Moreover, we show that the algorithm is both correct and complete, i.e., that it generates a deterministic controller whenever one exists.

#### References

- Accellera (2004). PSL/Sugar. http://www.haifa.il.ibm.com/projects/verification/sugar.
- Averest (2005). www.averest.org.
- B üchi, J. (1960a). On a decision method in restricted second order arithmetic. In Nagel, E., editor, International Congress on Logic, Methodology and Philosophy of Science, pages 1-12, Stanford, CA. Stanford University Press.
- B üchi, J. (1960b). Weak second order arithmetic and finite automata. Z. Math. Logik Grundlagen Math., 6:66- 92.
- Dietrich, P., Malik, R., Wonham, W., and Brandin, B. (2002). Implementation considerations in supervisory control. In B. Caillaud, P. Darondeau, L. Lavagno, and X. Xie, editors, Synthesis and control of discrete event systems, pages 185-201. Kluwer Academic Publishers.
- Emerson, E. (1990). Temporal and modal logic. In Handbook of Theoretical Computer Science, volume B, chapter Temporal and Modal Logics, pages 996-1072. Elsevier.
- Emerson, E. and Clarke, E. (1982). Using branching-time temporal logic to synthesize synchronization skeletons. Science of Computer Programming, 2(3):241- 266.
- Kozen, D. (1983). Results on the propositional µ-calculus. Theoretical Computer Science, 27:333-354.
- Malik, P. (2003). From Supervisory Control to Nonblocking Controllers for Discrete Event Systems. PhD thesis, University of Kaiserslautern, Kaiserslautern, Germany.
- Pnueli, A. (1977). The temporal logic of programs. In Symposium on Foundations of Computer Science (FOCS), volume 18, pages 46-57, New York. IEEE Computer Society.
- Ramadge, P. and Wonham, W. (1987). Supervisory control of a class of discrete event processes. SIAM Journal of Control and Optimization, 25(1):206-230.
- Schneider, K. (2003). Verification of Reactive Systems - Formal Methods and Algorithms. Texts in Theoretical Computer Science (EATCS Series). Springer.
- Thomas, W. (1990). Automata on infinite objects. In Handbook of Theoretical Computer Science, volume B, chapter Automata on Infinite Objects, pages 133-191. Elsevier.
- Wonham, W. (2001). Notes on control of discrete-event systems. Technical Report ECE 1636F/1637S 2001-02, Department of Electrical and Computer Engineering, University of Toronto.
- Ziller, R. and Schneider, K. (2003). A generalized approach to supervisor synthesis. In Formal Methods and Models for Codesign (MEMOCODE), pages 217- 226, Mont Saint-Michel, France. IEEE Computer Society.

#### Paper Citation

#### in Harvard Style

Morgenstern A. and Schneider K. (2005). **SYNTHESIZING DETERMINISTIC CONTROLLERS IN SUPERVISORY CONTROL** . In *Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,* ISBN 972-8865-30-9, pages 24-31. DOI: 10.5220/0001164500240031

#### in Bibtex Style

@conference{icinco05,

author={Andreas Morgenstern and Klaus Schneider},

title={SYNTHESIZING DETERMINISTIC CONTROLLERS IN SUPERVISORY CONTROL},

booktitle={Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,},

year={2005},

pages={24-31},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001164500240031},

isbn={972-8865-30-9},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,

TI - SYNTHESIZING DETERMINISTIC CONTROLLERS IN SUPERVISORY CONTROL

SN - 972-8865-30-9

AU - Morgenstern A.

AU - Schneider K.

PY - 2005

SP - 24

EP - 31

DO - 10.5220/0001164500240031