An improved iterative synthesis method for liveness enforcing supervisors of flexible manufacturing systems

Uzam, Murat; Zhou, M.

doi:10.1080/00207540500431321

Cited by 208 publications

(146 citation statements)

References 32 publications

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“…Compared with most of traditional global-conquer methods of Uzam and Zhou [15,16], the computational efficiency of PN supervisors is improved. Nevertheless, as the number of shared resources in uncontrolled systems has increased, too many subsystems should be disposed.…”

Section: Introductionmentioning

confidence: 99%

“…Besides, in [18], a new method is developed for deadlocks prevention to decrease the number of reachability conditions of TR in order to facilitate the supervisor calculation. Their experimental results seems to be the most effective approach in deadlock prevention policy compared with existing works of [15,19,20]. Unfortunately, the computation of RG and its analysis to determine the basic cycles and the legal/forbidden markings for this method are still heavy.…”

Section: Introductionmentioning

confidence: 99%

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Theory of Regions for Control Synthesis without Computing Reachability Graph

2017

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This paper addresses the design of Petri net (PN) supervisor using the theory of regions for forbidden state problem with a set of general mutual exclusion constraints. In fact, as any method of supervisory control based on reachability graph, the theory of regions suffers from a technical obstacle in control synthesis, which is the necessity of computing the graph at each iteration step. Moreover, based on the reachability graph, which may contain a large number of states, with respect to the structural size of the system, the computation of PN controllers becomes harder and even impossible. The main contribution of this paper, compared to previous works, is the development of a control synthesis method in order to decrease significantly the computation cost of the PN supervisor. Thus, based on PN properties and mathematical concepts, the proposed methodology provides an optimal PN supervisor for bounded Petri nets following the interpretation of the theory of regions. Finally, case studies are solved by CPLEX software to compare our new control policy with previous works which use the theory of regions for control synthesis.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Theory of Regions for Control Synthesis without Computing Reachability Graph

2017

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“…Thus, DPP are classified into two categories: siphon-based method (SBM) 25,29,30,[33][34][35] and reachability graph-based method (RGBM). 6,10,32,[36][37][38] Generally, behavioral permissiveness (BP), structural complexity (SC), and computational complexity (CC) are three major criteria to evaluate SBM or RGBM. By means of explicit enumeration of all state nodes of an RG of the given Petri net model (PNM), RGBM can divide the corresponding RG into two parts: deadlock zone (DZ) including deadlocks and critical bad states that inevitably lead to deadlocks and a deadlock-free zone (DFZ) representing the good states that definitely keep the correct evolutions of PNM.…”

Section: Introductionmentioning

confidence: 99%

“…However, such RGBM usually suffers from a state explosion problem of the corresponding RG for a largesized PNM with the large initial markings. 38 In order to cope with the state explosion problem, a few novel methods are successively developed to design the liveness-enforcing supervisors with MPB. Among them, Chen and Li 15 propose a non-iterative approach to design a maximally permissive control place (CP) by a place invariant (PI) that forbids one of the first-met bad markings (FBMs) and none of legal markings is forbidden.…”

Section: Introductionmentioning

confidence: 99%

“…(denoted as HHJ + ), 3,44 (denoted as HJX + ), 22,23 (denoted as LZ), 38 (denoted as UZ), 25 (denoted as PCF), 7 (denoted as C1), 40 (denoted as C2) and Li et al 41 (denoted as LAW + ) is also carried out via some tables, where Ã, J, R, DS, and DFS denote maximally reachable state, MPB, the ratio of the number of reachable states of the live controlled system (N Ã , M Ã ) to MRN, deadlock states, and deadlock-free states of the corresponding Petri net system, respectively.…”

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confidence: 99%

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An elementary siphon-based deadlock control algorithm with maximally reachable number to cope with deadlock problems in ordinary Petri nets

Wei

Cai

et al. 2017

Advances in Mechanical Engineering

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Elementary siphons play an important role in designing deadlock prevention policies for flexible manufacturing systems modeling by Petri nets. This article proposes a deadlock control algorithm with maximally reachable number to cope with deadlock problems in ordinary Petri nets. First, we solve all elementary siphons and dependent siphons and then add both a control place and a control transition to each elementary siphon so that an extended net system (N 0 , M 0 ) is obtained. Second, by constructing an integer programming problem of P-invariants of (N 0 , M 0 ), the controllability test for dependent siphons in N 0 is performed via this integer programming problem. Accordingly, a few of control places and control transitions are added for those dependent siphons that do not meet controllability as well. Therefore, a live controlled system (N Ã , M Ã ) with maximally reachable number rather than number of maximally permissive behavior can be achieved. The correctness and efficiency of the proposed deadlock control algorithm is verified by a theoretical analysis and several examples that belong to ordinary Petri nets. Unlike these deadlock prevention policies with number of maximally permissive behavior in the existing literature, the proposed deadlock control algorithm can generally obtain a live controlled system (N Ã , M Ã ) whose reachable number is the same as that of an original uncontrolled net (N 0 , M 0 ), that is, maximally reachable number is greater than number of maximally permissive behavior.

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2020

Supervisory Control and Scheduling of Resource Allocation Systems

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An improved iterative synthesis method for liveness enforcing supervisors of flexible manufacturing systems

Cited by 208 publications

References 32 publications

Theory of Regions for Control Synthesis without Computing Reachability Graph

Theory of Regions for Control Synthesis without Computing Reachability Graph

An elementary siphon-based deadlock control algorithm with maximally reachable number to cope with deadlock problems in ordinary Petri nets

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