This paper proposes an iterative approach to separate a set of admissible markings of a nonlinear constraint into a number of subsets. At each iteration, we find a maximal subset of admissible markings that are separated from inadmissible markings by linear constraints. Then, the union of all the obtained subsets constitutes the set of all admissible markings. For each subset of admissible markings, we obtain a set of conjunctive linear constraints. Accordingly, we can equivalently transform a given nonlinear constraint to be a set of disjunctive/conjunctive linear constraints, which can deal with the case that both admissible and inadmissible marking spaces of a nonlinear constraint cannot be separated by linear constraints from each other. Furthermore, we propose a method to design a Petri net supervisor for a derived set of disjunctive/conjunctive constraints. Some examples are used to demonstrate the proposed approach. Note to Practitioners—Linear constraints on Petri nets have been widely studied in the literature. However, not all control specifications can be represented as linear constraints. This paper proposes to enforce nonlinear constraints on Petri nets. A maximally permissive supervisor is designed to make the controlled net live with all admissible markings with respect to a given nonlinear constraint. Meanwhile, the structural complexity is also considered by compressing the number of control places in the supervisor. Experimental results show that the proposed approach can implement the control specifications represented by nonlinear constraints.

中文翻译：

---

Petri 网上非线性约束实施的最优监督器设计


本文提出了一种迭代方法，将非线性约束的一组可接受标记分成多个子集。在每次迭代中，我们都会找到可接受标记的最大子集，这些标记通过线性约束与不可接受标记分开。然后，所有获得的子集的并集构成所有可接受标记的集合。对于每个可接受标记的子集，我们获得一组联合线性约束。因此，我们可以等价地将给定的非线性约束变换为一组析取/合取线性约束，这可以处理非线性约束的允许和不允许的标记空间不能被线性约束彼此分开的情况。此外，我们提出了一种为派生的析取/合取约束集设计 Petri 网监督器的方法。使用一些示例来演示所提出的方法。从业者注意事项——Petri 网的线性约束已在文献中得到广泛研究。然而，并非所有控制规范都可以表示为线性约束。本文提出对 Petri 网实施非线性约束。最大许可监控器旨在使受控网络在给定非线性约束条件下具有所有允许的标记。同时，还通过压缩supervisor中控制位的数量来考虑结构的复杂性。实验结果表明，该方法能够实现非线性约束表示的控制规范。