Discrete event systems (DES) have been established and deeply developed in the framework of probabilistic and fuzzy computing models due to the necessity of practical applications in fuzzy and probabilistic systems. With the development of quantum computing and quantum control, a natural problem is to simulate DES by means of quantum computing models and to establish {\it quantum DES} (QDES). The motivation is twofold: on the one hand, QDES have potential applications when DES are simulated and processed by quantum computers, where quantum systems are employed to simulate the evolution of states driven by discrete events, and on the other hand, QDES may have essential advantages over DES concerning state complexity for imitating some practical problems. The goal of this paper is to establish a basic framework of QDES by using {\it quantum finite automata} (QFA) as the modelling formalisms, and the supervisory control theorems of QDES are established and proved. Then we present a polynomial-time algorithm to decide whether or not the controllability condition holds. In particular, we construct a number of new examples of QFA to illustrate the supervisory control of QDES and to verify the essential advantages of QDES over DES in state complexity.

本文旨在利用量子有限自动机(QFA)作为建模形式建立量子离散事件系统(QDES)的基本框架，并对QDES的监督控制定理进行建立和证明。同时，我们介绍了一种用于判断可控性条件是否成立的多项式时间算法。特别地，我们构造了许多新的QFA示例，以说明QDES在状态复杂性方面的优势。

量子离散事件系统的监督控制