Partial Observation in Distributed Supervisory Control of Discrete-Event Systems

Saeidi, V.; Afzalian, A.; Gharavian, D.

doi:10.22060/miscj.2017.12041.4997

Partial Observation in Distributed Supervisory Control of Discrete-Event Systems

Document Type : Research Article

Authors

Dept. of Electrical Engineering, Abbaspour School of Engineering, Shahid Beheshti University, Tehran, Iran

10.22060/miscj.2017.12041.4997

Abstract

Distributed supervisory control is a method to synthesize local controllers in discrete-event
systems with a systematic observation of the plant. Some works were reported on extending this method
by which local controllers are constructed so that observation properties are preserved from monolithic to
distributed supervisory control, in an up-down approach. In this paper, we find circumstances in which
observation properties are preserved from monolithic to distributed supervisory control. Local observation
properties, i.e. local normality and local relative observability are employed for investigating observation
properties of each local controller, which are constructed by any localization algorithm that preserves control
equivalency to the monolithic supervisor with respect to the plant. These properties enable us to investigate
the observation properties from monolithic to distributed supervisory control. Moreover, observation
equivalence property is defined according to the control equivalence in a distributed supervisory control
with partial observation. It is proved that with preserving observation equivalence of the local controllers to
the monolithic supervisor, the control equivalence is satisfied, if and only if the intersection of local event
sets is a subset of or equal to the global observable event set.

Highlights

[1] P.J. Ramadge, W.M. Wonham, Supervisory control of a class of discrete event processes, SIAM journal on control and optimization, 25(1) (1987) 206-230.

[2] F. Lin, W.M. Wonham, Decentralized control and coordination of discrete-event systems with partial observation, IEEE Transactions on automatic control, 35(12) (1990) 1330-1337.

[3] J. Komenda, J.H. van Schuppen, Modular control of discrete-event systems with coalgebra, IEEE Transactions on Automatic Control, 53(2) (2008) 447-460.

[4] H. Zhong, W.M. Wonham, On the consistency of hierarchical supervision in discrete-event systems, IEEE Transactions on automatic Control, 35(10) (1990) 1125-1134.

[5] K.C. Wong, W.M. Wonham, Hierarchical control of discrete-event systems, Discrete Event Dynamic Systems, 6(3) (1996) 241-273.

[6] K.C. Wong, W.M. Wonham, Modular control and coordination of discrete-event systems, Discrete Event Dynamic Systems, 8(3) (1998) 247-297.

[7] K. Schmidt, T. Moor, S. Perk, Nonblocking hierarchical control of decentralized discrete event systems, IEEE Transactions on Automatic Control, 53(10) (2008) 2252-2265.

[8] K. Schmidt, C. Breindl, Maximally permissive hierarchical control of decentralized discrete event systems, IEEE Transactions on Automatic Control, 56(4) (2011) 723-737.

[9] L. Feng, W.M. Wonham, Supervisory control architecture for discrete-event systems, IEEE Transactions on Automatic Control, 53(6) (2008) 1449-1461.

[10] T.-S. Yoo, S. Lafortune, A general architecture for decentralized supervisory control of discrete-event systems, Discrete Event Dynamic Systems, 12(3) (2002) 335-377.

[11] K. Rudie, W.M. Wonham, Think globally, act locally: Decentralized supervisory control, IEEE transactions on automatic control, 37(11) (1992) 1692-1708.

[12] K. Cai, R. Zhang, W.M. Wonham, On relative observability of discrete-event systems, in: Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on, IEEE, 2013, pp. 7285-7290.

[13] J. Komenda, T. Masopust, J.H. van Schuppen, Coordination control of discrete-event systems revisited, Discrete Event Dynamic Systems, 25(1-2) (2015) 65-94.

[14] J. Komenda, T. Masopust, J.H. van Schuppen, On conditional decomposability, Systems & Control Letters, 61(12) (2012) 1260-1268.

[15] K. Cai, W.M. Wonham, Supervisor localization: a top-down approach to distributed control of discrete-event systems, IEEE Transactions on Automatic Control, 55(3) (2010) 605-618.

[16] F. Lin, W.M. Wonham, On observability of discrete-event systems, Information sciences, 44(3) (1988) 173-198.

[17] K. Cai, R. Zhang, W.M. Wonham, Relative observability of discrete-event systems and its supremal sublanguages, IEEE Transactions on Automatic Control, 60(3) (2015) 659-670.

[18] E. José, N. Patrícia, L. Stéphane, Verification of Nonconflict of Supervisors Using Abstractions, (2009).

[19] R. Zhang, K. Cai, W.M. Wonham, Supervisor localization of discrete-event systems under partial observation, Automatica, 81 (2017) 142-147.

[20] V. Saeidi, A.A. Afzalian, D. Gharavian, Distributed supervisory control with partial observation, in: Control, Instrumentation, and Automation (ICCIA), 2016 4th International Conference on, IEEE, 2016, pp. 136-141.

[21] S. Mohajerani, R. Malik, M. Fabian, An algorithm for weak synthesis observation equivalence for compositional supervisor synthesis, IFAC Proceedings Volumes, 45(29) (2012) 239-244.

[22] M. Noorbakshsh, A. Afzalian, Design and PLC based implementation of supervisory control for under-load tap-changing transformers, in: Control, Automation and Systems, 2007. ICCAS'07. International Conference on, IEEE, 2007, pp. 901-906.

[23] A. Afzalian, A. Saadatpoor, W. Wonham, Systematic supervisory control solutions for under-load tap-changing transformers, Control Engineering Practice, 16(9) (2008) 1035-1054.

[24] R. Zhang, K. Cai, Y. Gan, W.M. Wonham, Distributed supervisory control of discrete-event systems with communication delay, Discrete Event Dynamic Systems, 26(2) (2016) 263-293.

[25] W. Wonham, Control design software: TCT, Developed by Systems Control Group, Univ. Toronto. Toronto, Canada, (2014).

Keywords

References