Synthesis of Petri net supervisors for FMS via redundant constraint elimination
Synthesis of Petri net supervisors for FMS via redundant constraint elimination
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DOI：
10.1016/j.automatica.2015.08.011
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发表时间：
2015-11
期刊：
影响因子：
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通讯作者：
B. Huang;Mengchu Zhou;Gongxuan Zhang
中科院分区：
文献类型：
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作者：
B. Huang;Mengchu Zhou;Gongxuan Zhang
最小控制场所问题（MCPP）是为了获得最优和结构最小的监督而提出的，它需要大量的计算。目前减少计算负担的方法主要集中在对MCPP原公式的修改上。相反，本文提出了通过消除冗余的可达性约束来加速其求解的方法。因此，监控器合成所需的优化问题规模大大减少。首先，基于新提出的监管者可行域概念，以整数线性规划（ILP）的形式建立了可达性约束冗余的充要条件。然后，提出了两种冗余消除方法：ILP和非ILP。我们的方法可以在短时间内消除大部分冗余的可达性约束。消去后，求解MCPP的计算时间大大减少，特别是对于大型系统。得到的监督器仍然是最优的和结构最小的。最后，通过数值试验验证了所提方法的有效性。
The Minimal number of Control Places Problem (MCPP), which is formulated to obtain optimal and structurally minimal supervisors, needs extensive computation. The current methods to reduce the computational burden have mainly focused on revision of the original formulation of MCPP. Instead, this paper presents methods to accelerate its solution by eliminating its redundant reachability constraints. The optimization problem scale required for supervisor synthesis is thus drastically reduced. First, a sufficient and necessary condition for a reachability constraint to be redundant is established in the form of an integer linear program (ILP), based on a newly proposed concept called feasible region of supervisors. Then, two kinds of redundancy elimination methods are proposed: an ILP one and a non-ILP one. Most of the redundant reachability constraints can be eliminated by our methods in a short time. The computational time to solve MCPP is greatly reduced after the elimination, especially for large-scale systems. The obtained supervisors are still optimal and structurally minimal. Finally, numerical tests are conducted to show the efficiency and effectiveness of the proposed methods.