2016, 6(3): 305-317. doi: 10.3934/naco.2016013

Development of concurrent structural decentralised discrete event system using bisimulation concept

1. 

The School of Engineering, The University of South Australia, Mawson Lakes, SA 5095, Australia

Received  April 2015 Revised  September 2016 Published  September 2016

This paper presents a concurrent structural decentralised control in the framework of supervisory control theory using bisimulation concept. It is a way to weaken the shared-event-marking condition of structural decentralised control developed by Lee and Wong [7]. The sufficient conditions to guarantee the global optimality achieved by the concurrent actions of simpler decentralised control have been presented. The developed condition becomes specification dependent, however, the other structural condition, the mutual controllability condition, is still applied on the structure of the system. Hence the computational savings are still achievable. An example is provided to illustrate the result.
Citation: Sang-Heon Lee. Development of concurrent structural decentralised discrete event system using bisimulation concept. Numerical Algebra, Control and Optimization, 2016, 6 (3) : 305-317. doi: 10.3934/naco.2016013
References:
[1]

G. Barrett and S. Lafortune, Bisimulation, the supervisory control problems and strong model matching for finite state machines, Discrete-Event Dynamic Systems: theory and Applications, 8 (1998), 377-429. doi: 10.1023/A:1008301317459.

[2]

K. Cai and W. M. Wonham, Supervisor localization: A top-down approach to distributed control of discrete-event systems, IEEE Transaction on Automatic Control, 55 (2010), 605-618. doi: 10.1109/TAC.2009.2039237.

[3]

P. Gohari and W. M. Wonham, On the complexity of supervisory control design in the RW framework IEEE transaction on systems, man and cybernetics, part B: cybernetics, 30 (2000), 643-652.

[4]

R. C. Hill, J. R. Cury, M. H. de Queiroz, D. M. Tilbury and S. Lafortune, Multi-level hierarchical interface-based supervisory control, Automatica, 46 (2010), 1152-1164. doi: 10.1016/j.automatica.2010.04.002.

[5]

J. Komenda and J. van Schuppen, Modular control of discrete-event systems with coalgebra IEEE transaction Automatic Control, 53 (2008), 447-460. doi: 10.1109/TAC.2007.915164.

[6]

P. Kozak and W. M. Wonham, Fully decentralised solutions of supervisory control problems, IEEE Transactions on Automatic Control, 40 (1995), 2094-2097. doi: 10.1109/9.478331.

[7]

S. H. Lee and K. C. Wong, Structural decentralised control of concurrent discrete-event systems, European Journal of Control, 8 (2002), 477-491.

[8]

F. Lin and W. M. Wonham, Decentralised supervisory control of discrete-event systems, Information Sciences, 44 (1988), 199-224. doi: 10.1016/0020-0255(88)90002-3.

[9]

R. Milner, Communication and Concurrency, Prentice Hall, NJ, USA, 1989.

[10]

P. J. Ramadge and W. M. Wonham, Supervisory control of a class of discrete-event processes, SIAM J. Control and Optimization, 25 (1987), 206-230. doi: 10.1137/0325013.

[11]

P. J. Ramadge and W. M. Wonham, Modular supervisory control of discrete event systems, Mathematics of Control, Signal and Systems, 1 (1988), 13-30. doi: 10.1007/BF02551233.

[12]

O. Stursberg, Hierarchical and distributed discrete event control of manufacturing Processes, in the 17th IEEE conference on emerging technologies and factory automation IEEE, (2012), 1-8.

[13]

Y. Sun, H. Lin and B. M. Chen, Decentralised bisimilarity control of discrete event systems, in Proceedings of 31st Chinese control conference, IEEE, (2012), 2134-2139.

[14]

Y. Willner and M. Heymann, Supervisory control of concurrent discrete-event systems, International Journal of Control, 54 (1991), 1143-1169. doi: 10.1080/00207179108934202.

[15]

W. M. Wonham, Notes on Control of Discrete-Event Systems, ECE 1636F/1637S 2012-13, Department of Electrical Engineering, University of Toronto, Toronto, Canada, 2013.

[16]

K. C. Wong and W. M. Wonham, Hierarchical control of discrete-event systems, Discrete Event Dynamic System, 6 (1996), 241-273.

[17]

T. S. Yoo and S. Lafortune, A general architecture for decentralized supervisory control of discrete-event systems, Discrete Event Dynamic System, 12 (2002), 335-377. doi: 10.1023/A:1015625600613.

[18]

C. Zhou, R. Kumar and S. Jiang, Control of nondeterministic discrete-event systems for bisimulation equivalence, IEEE transactions on automatic control, 51 (2006), 754-765. doi: 10.1109/TAC.2006.875036.

[19]

C. Zhou and R. Kumar, Bisimilarity enforcement for discrete event systems using deterministic control IEEE transactions on automatic control, 56 (2011), 2986-2991. doi: 10.1109/TAC.2011.2161790.

show all references

References:
[1]

G. Barrett and S. Lafortune, Bisimulation, the supervisory control problems and strong model matching for finite state machines, Discrete-Event Dynamic Systems: theory and Applications, 8 (1998), 377-429. doi: 10.1023/A:1008301317459.

[2]

K. Cai and W. M. Wonham, Supervisor localization: A top-down approach to distributed control of discrete-event systems, IEEE Transaction on Automatic Control, 55 (2010), 605-618. doi: 10.1109/TAC.2009.2039237.

[3]

P. Gohari and W. M. Wonham, On the complexity of supervisory control design in the RW framework IEEE transaction on systems, man and cybernetics, part B: cybernetics, 30 (2000), 643-652.

[4]

R. C. Hill, J. R. Cury, M. H. de Queiroz, D. M. Tilbury and S. Lafortune, Multi-level hierarchical interface-based supervisory control, Automatica, 46 (2010), 1152-1164. doi: 10.1016/j.automatica.2010.04.002.

[5]

J. Komenda and J. van Schuppen, Modular control of discrete-event systems with coalgebra IEEE transaction Automatic Control, 53 (2008), 447-460. doi: 10.1109/TAC.2007.915164.

[6]

P. Kozak and W. M. Wonham, Fully decentralised solutions of supervisory control problems, IEEE Transactions on Automatic Control, 40 (1995), 2094-2097. doi: 10.1109/9.478331.

[7]

S. H. Lee and K. C. Wong, Structural decentralised control of concurrent discrete-event systems, European Journal of Control, 8 (2002), 477-491.

[8]

F. Lin and W. M. Wonham, Decentralised supervisory control of discrete-event systems, Information Sciences, 44 (1988), 199-224. doi: 10.1016/0020-0255(88)90002-3.

[9]

R. Milner, Communication and Concurrency, Prentice Hall, NJ, USA, 1989.

[10]

P. J. Ramadge and W. M. Wonham, Supervisory control of a class of discrete-event processes, SIAM J. Control and Optimization, 25 (1987), 206-230. doi: 10.1137/0325013.

[11]

P. J. Ramadge and W. M. Wonham, Modular supervisory control of discrete event systems, Mathematics of Control, Signal and Systems, 1 (1988), 13-30. doi: 10.1007/BF02551233.

[12]

O. Stursberg, Hierarchical and distributed discrete event control of manufacturing Processes, in the 17th IEEE conference on emerging technologies and factory automation IEEE, (2012), 1-8.

[13]

Y. Sun, H. Lin and B. M. Chen, Decentralised bisimilarity control of discrete event systems, in Proceedings of 31st Chinese control conference, IEEE, (2012), 2134-2139.

[14]

Y. Willner and M. Heymann, Supervisory control of concurrent discrete-event systems, International Journal of Control, 54 (1991), 1143-1169. doi: 10.1080/00207179108934202.

[15]

W. M. Wonham, Notes on Control of Discrete-Event Systems, ECE 1636F/1637S 2012-13, Department of Electrical Engineering, University of Toronto, Toronto, Canada, 2013.

[16]

K. C. Wong and W. M. Wonham, Hierarchical control of discrete-event systems, Discrete Event Dynamic System, 6 (1996), 241-273.

[17]

T. S. Yoo and S. Lafortune, A general architecture for decentralized supervisory control of discrete-event systems, Discrete Event Dynamic System, 12 (2002), 335-377. doi: 10.1023/A:1015625600613.

[18]

C. Zhou, R. Kumar and S. Jiang, Control of nondeterministic discrete-event systems for bisimulation equivalence, IEEE transactions on automatic control, 51 (2006), 754-765. doi: 10.1109/TAC.2006.875036.

[19]

C. Zhou and R. Kumar, Bisimilarity enforcement for discrete event systems using deterministic control IEEE transactions on automatic control, 56 (2011), 2986-2991. doi: 10.1109/TAC.2011.2161790.

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