Journal of Applied Mathematics
Volume 2013 (2013), Article ID 315894, 11 pages
Research Article

Supervisor Reconfiguration for Deadlock Prevention by Resources Reallocation

1School of Electro-Mechanical Engineering, Xidian University, Xi’an 710071, China
2School of Information & Electronic Engineering, Zhejiang Gongshang University, Hangzhou 310018, China

Received 12 December 2012; Accepted 9 March 2013

Academic Editor: Constantinos Siettos

Copyright © 2013 Miao Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Analysis and control of deadlocks play an important role in the design and operation of automated flexible manufacturing systems (FMSs). In FMS, deadlocks are highly undesirable situations, which always cause unnecessary cost. The design problem of an optimal supervisor is in general NP-hard. A computationally efficient method often ends up with a suboptimal one. This paper develops a deadlock prevention policy based on resources reallocation and supervisor reconfiguration. First, given a plant model, we reallocate the marking of each resource place to be one, obtaining a net model whose reachable states are much less than that of the original one. In this case, we find a controlled system for it by using the theory of regions. Next, the markings of the resource places in the controlled system are restored to their original ones. Without changing the structure of the obtained controlled system, we compute the markings of the monitors gradually, which can be realized by two algorithms proposed in this paper. Finally, we decide a marking for each monitor such that it makes the controlled system live with nearly optimal permissive behavior. Two FMS examples are used to illustrate the application of the proposed method and show its superior efficiency.