# EFFICIENT SYMBOLIC SUPERVISORY SYNTHESIS AND GUARD GENERATION - Evaluating Partitioning Techniques for the State-space Exploration

### Z. Fei, S. Miremadi, K. Åkesson, B. Lennartson

#### Abstract

The supervisory control theory (SCT) is a model-based framework which automatically synthesizes a supervisor that restricts a plant to be controlled based on specifications to be fulfilled. Two main problems typically encountered in industrial applications prevent SCT from having a major breakthrough. First, the supervisor which is synthesized automatically from the given plant and specification models might be incomprehensible to the users. To tackle this problem, in our previous work, an approach was presented to extract compact propositional formulae from the supervisor represented symbolically by binary decision diagrams (BDD) and attach them to the original models. However, this approach, which computes the supervisor symbolically in the conjunctive way, might lead to another problem: the state-space explosion, because of the large number of intermediate BDD nodes during computation. In this paper, we introduce an alternative approach to alleviate this problem, which is based on the disjunctive partitioning technique including a set of selection heuristics. Then this approach is adapted to the guard generation procedure. Finally, the efficiency of the presented approach is demonstrated on a set of benchmark examples.

#### References

- Akers, S. B. (1978). Binary decision diagrams. IEEE Transactions on Computers, 27:509-516.
- A°kesson, K., Fabian, M., Flordal, H., and Malik, R. (2006). Supremica-an integrated environment for verification, synthesis and simulation of discrete event systems. In Proceedings of the 8th international Workshop on Discrete Event Systems WODES08, pages 384-385.
- A°kesson, K., Fabian, M., Flordal, H., and Vahidi, A. (2003). Supremica-a tool for verification and synthesis of discrete event supervisors. In 11th Mediterranean Conference on Control and Automation.
- Aloul, F. A., Markov, I. L., and Sakallah, K. A. (2003). Force: a fast and easy-to-implement variable-ordering heuristic. In in ACM Great Lakes Symposium on VLSI, pages 116-119.
- Balemi, S., Hoffmann, G. J., Gyugyi, P., Wong-Toi, H., and Franklin, G. F. (1993). Supervisory control of a rapid thermal multiprocessor. IEEE Transactions on Automatic Control, 38(7):1040-1059.
- Bollig, B. and Wegener, I. (1996). Improving the variable ordering of OBDDs is NP-complete. IEEE Trans. Comput., 45(9):993-1002.
- Bryant, R. E. (1992). Symbolic manipulation with ordered binary decision diagrams. ACM Computing Surveys 24, 24:293-318.
- Burch, J. R., Clarke, E. M., and Long, D. E. (1991). Symbolic model checking with partitioned transition relations. In Proceedings of the International Conference on Very Large Scale Integration, volume A-1 of IFIP Transactions, pages 49-58. North-Holland.
- Burch, J. R., Clarke, E. M., Long, D. E., Mcmillan, K. L., and Dill, D. L. (1994). Symbolic model checking for sequential circuit verification. IEEE Transactions on ComputerAided Design of Integrated Circuits and Systems, 13(4):401-424.
- Byröd, M., Lennartson, B., Vahidi, A., and A°kesson, K. (2006). Efficient reachability analysis on modular discrete-event systems using binary decision diagrams. In Proceedings of the 8th international Workshop on Discrete Event Systems, WODES'06, pages 288-293.
- Cassandras, C. G. and Lafortune, S. (2008). Introduction to Discrete Event Systems. Springer, 2nd edition.
- Feng, L., Wonham, W. M., and Thiagarajan, P. S. (2007). Designing communicating transaction processes by supervisory control theory. Form. Methods Syst. Des., 30(2):117-141.
- Glover, F. and Laguna, M. (1997). Tabu search. Number 1 in Wiley-Interscience Series in Discrete Mathematics and Optimization. Kluwer Academic Publishers.
- Hoare, C. A. R. (1985). Communicating sequential processes. Communications of the ACM, 21(8):666-677.
- Holloway, L. E. and Krogh, B. H. (1990). Synthesis of feedback control logic for a class of controlled Petri Nets. IEEE Transactions on Automatic Control, 35(5):514- 523.
- JavaBDD (2007). available online.
- Kaelbling, L. P., Littman, M. L., and Moore, A. W. (1996). Reinforcement learning: A survey. Journal of Artificial Intelligence Research, 4:237-285.
- Leduc, R. J. (2002). Hierarchical interface-based supervisory control. PhD thesis, Department of Electrical and Computer Engineering, University of Toronto.
- Miremadi, S. (2010). Symbolic Computation of Control Functions Modeled by Automata with Variables. Licentiate thesis, Chalmers University of Technology, Gothenburg, Sweden.
- Miremadi, S., A°kesson, K., Fabian, M., Vahidi, A., and Lennartson, B. (2008). Solving two supervisory control benchmark problems using supremica. In Discrete Event Systems, 2008. WODES 2008. 9th International Workshop on, pages 131-136.
- Ramadge, P. J. G. and Wonham, W. M. (1987). Supervisory control of a class of discrete event processes. SIAM Journal of Control and Optimization, 25(1):206-230.
- Ramadge, P. J. G. and Wonham, W. M. (1989). The control of discrete event systems. Proceedings of the IEEE, 77(1):81-98.
- Shannon, C. E. and Weaver, W. (1949). The mathematical theory of communication, volume 181. University of Illinois Press.
- Shoaei, M. R., Lennartson, B., and Sajed, M. (2010). Automatic Generation of Controllers for Collision-Free Flexible Manufacturing Systems. In CASE 2010 6th IEEE Conference on Automation Science and Engineering, page 7.
- Vahidi, A., Fabian, M., and Lennartson, B. (2006). Efficient supervisory synthesis of large systems. Control Engineering Practice, 14(10):1157-1167.
- Wonham, W. M. (1999). Notes on control of discrete event systems. Technical report, University of Toronto.

#### Paper Citation

#### in Harvard Style

Fei Z., Miremadi S., Åkesson K. and Lennartson B. (2011). **EFFICIENT SYMBOLIC SUPERVISORY SYNTHESIS AND GUARD GENERATION
- Evaluating Partitioning Techniques for the State-space Exploration** . In *Proceedings of the 3rd International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,* ISBN 978-989-8425-40-9, pages 106-115. DOI: 10.5220/0003178801060115

#### in Bibtex Style

@conference{icaart11,

author={Z. Fei and S. Miremadi and K. Åkesson and B. Lennartson},

title={EFFICIENT SYMBOLIC SUPERVISORY SYNTHESIS AND GUARD GENERATION
- Evaluating Partitioning Techniques for the State-space Exploration},

booktitle={Proceedings of the 3rd International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,},

year={2011},

pages={106-115},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003178801060115},

isbn={978-989-8425-40-9},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 3rd International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,

TI - EFFICIENT SYMBOLIC SUPERVISORY SYNTHESIS AND GUARD GENERATION
- Evaluating Partitioning Techniques for the State-space Exploration

SN - 978-989-8425-40-9

AU - Fei Z.

AU - Miremadi S.

AU - Åkesson K.

AU - Lennartson B.

PY - 2011

SP - 106

EP - 115

DO - 10.5220/0003178801060115