Lexicographic Multiobjective Integer Programming for Optimal and Structurally Minimal Petri Net Supervisors of Automated Manufacturing Systems
Lexicographic Multiobjective Integer Programming for Optimal and Structurally Minimal Petri Net Supervisors of Automated Manufacturing Systems
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DOI：
10.1109/tsmc.2015.2415765
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发表时间：
2015-04
期刊：
影响因子：
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通讯作者：
B. Huang;Mengchu Zhou;Gongxuan Zhang;A. Ammari;Ahmed Alabdulwahab;A. Fayoumi
中科院分区：
文献类型：
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作者：
B. Huang;Mengchu Zhou;Gongxuan Zhang;A. Ammari;Ahmed Alabdulwahab;A. Fayoumi
基于自动化制造系统的Petri网（PN）模型，提出了一种死锁预防方法，以获得最大许可（最优）的监督者，同时使其结构最小化。在PN模型中，通过禁止所有的首遇坏标记（FBM）和允许所有的法律的标记，可以实现最优的监督者。通过在法律的标记上发射单个转换而获得的FBM是死锁或不可避免地演变成死锁的标记。一个字典式多目标整数规划问题，多个目标要实现顺序制定设计这样一个最佳的和结构最小的监督。作为一个非线性函数，其有向弧的数量最小。提出了一种将非线性模型转换为线性模型的转换方法。在监督器中的每一个库所都与一个非负库所不变量相关联的前提下，受控网包含网模型的所有法律的标记，并且监督器具有最小结构.最后通过实例说明了该方法的应用。
Based on Petri net (PN) models of automated manufacturing systems, this paper proposes a deadlock prevention method to obtain a maximally permissive (optimal) supervisor while minimizing its structure. The optimal supervisor can be achieved by forbidding all first-met bad markings (FBMs) and permitting all legal markings in a PN model. An FBM obtained via a single transition's firing at a legal marking is a deadlock or marking that inevitably evolves into a deadlock. A lexicographic multiobjective integer programming problem with multiple objectives to be achieved sequentially is formulated to design such an optimal and structurally minimal supervisor. As a nonlinear function, the quantity of its directed arcs is minimized. A conversion method is proposed to convert the nonlinear model into a linear one. With the premise that each place in the supervisor is associated with a nonnegative place invariant, the controlled net holds all legal markings of the net model, and the supervisor has the minimal structure. Finally, some examples are used to illustrate the application of the proposed approach.