基于非纯网结构的Petri网控制器优化设计

Petri nets are an important tool to model and control discrete event systems. There are three criteria to evaluate the design of a Petri net supervisor: behavioral permissiveness, structural complexity, and computational complexity. Based on Petri nets, most approaches design pure net supervisors by enforcing linear constraints on the systems to be controlled. In fact, there exist some Petri net models that have no maximally permissive Petri net supervisors in the framework of pure net structures. This project tries to overcome the limitations of pure net supervisors by considering nonpure net structures. The goal is to resolve the existence problem of maximally permissive Petri net supervisors. Meanwhile, structural complexity and computational complexity are also considered. The following topics are considered in this project. (1) Self-loops and inhibitor arcs are used to design maximally permissive Petri nets and the supervisory structures are minimized; (2) Based on a novel Petri net structure, data inhibitor arc, a maximally permissive Petri net supervisor is designed with a simple supervisory structure and efficient computation for any bounded Petri nets and control specification; (3) Nonpure Petri net structures are applied to complex discrete event system; (4) Design maximally permissive Petri net supervisors for nonlinear constraints.

Petri网是离散事件系统建模和控制的重要工具。行为许可性，结构复杂性和计算复杂性是活性Petri网控制器设计的主要指标。基于Petri网的传统控制方法是通过对网系统施加线性约束来构成不变式的方式设计纯网结构的控制器。而实际上存在一些Petri网模型在纯网范围内不存在最大许可行为的Petri网控制器。本项目拟克服纯网控制能力的局限性，研究非纯网结构的Petri网控制器设计问题。在考虑最大许可行为Petri网控制器存在性问题的同时兼顾考虑结构复杂性和计算复杂性问题。研究内容主要有：(1) 研究自环和抑止弧的最优控制器设计并使其结构极小化；(2) 基于新的Petri网结构，数据抑止弧，致力于设计最大许可行为Petri网控制器的同时考虑结构复杂性及计算代价问题；(3) 研究非纯网结构在复杂系统中的应用；(4) Petri网中非线性约束的最大许可行为Petri网控制器设计。

Petri网是离散事件系统建模和控制的重要工具。行为许可性，结构复杂性和计算复杂性是活性Petri网控制器设计的主要指标。基于Petri网的传统控制方法是通过对网系统施加线性约束来构成不变式的方式设计纯网结构的控制器。而实际上存在一些Petri网模型在纯网范围内不存在最大许可行为的Petri网控制器。本项目致力于克服纯网控制能力的局限性，研究非纯网结构的Petri网控制器设计问题。在考虑最大许可行为Petri网控制器存在性问题的同时兼顾考虑结构复杂性和计算复杂性问题。研究成果主要有：(1)提出非纯网结构的最优控制器设计并优化其计算代价；(2)提出最大许可行为Petri网控制器设计的计算代价化简；(3)系统中存在不可控不可观事件时的最优监督控制；(4)存在不可观变迁的Petri网系统不透明性验证；(5)带有时间参数的离散事件系统调度与控制策略。