量子离散事件系统的监督控制
Supervisory Control of Quantum Discrete Event Systems
AI总结：
针对经典离散事件系统状态复杂度难题，本文以量子有限自动机为建模工具建立量子离散事件系统框架，证明其监督控制定理，提出可控性判定多项式算法，并验证其状态复杂度优势。
摘要：
离散事件系统（DES）已得到深入发展并在实践中得到应用，但离散事件系统的状态复杂度仍是一个需要用创新方法更好解决的重要问题。随着量子计算与量子控制的发展，一个自然的问题是借助量子计算模型模拟离散事件系统，并建立量子离散事件系统（QDES）。其动机有两方面：一方面，当用量子计算机模拟和处理离散事件系统时，量子离散事件系统具有潜在应用价值，此时量子系统被用于模拟由离散事件驱动的状态演化；另一方面，在模拟某些实际问题时，量子离散事件系统在状态复杂度方面可能比经典离散事件系统具备本质优势。因此，本文的目标是以量子有限自动机（QFA）为建模形式体系，建立量子离散事件系统的基本框架，并推导证明量子离散事件系统的监督控制定理。随后我们提出一种多项式时间算法，用于判定可控性条件是否成立。特别地，我们构建了若干新的量子有限自动机示例，用以阐释量子离散事件系统的监督控制，并验证量子离散事件系统在状态复杂度上相较于经典离散事件系统的本质优势。
英文摘要：
Discrete event systems (DES) have been deeply developed and applied in practice, but state complexity in DES still is an important problem to be better solved with innovative methods. 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. So, 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 classical DES in state complexity.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
