Control and Analysis of Real-Time Discrete Event Systems Using Max-Algebra

9414780加尔格随着自动化工厂、通信网络和计算机等人造系统的规模不断扩大，“试试看”的设计和监督方法变得不太现实。取而代之的是控制器综合技术，它允许从数学上推导出最优控制律，并且具有可以自动验证的性能特性。对于没有显式实时约束的系统的控制，存在一个良好的框架。然而，如果定时在系统动力学及其性能规范中受到关注，那么情况就会变得复杂得多。在称为极大代数的非传统代数系统中，某些实时离散事件系统可以用线性方程来描述。对于这些系统，监督控制的问题是对选定事件的执行施加延迟，以实现特定的性能目标。所提出的研究的目的是检查包含此类时间约束的离散事件系统控制器的存在性和综合。我们的方法依赖于时间DES的极大代数模型，该模型允许非时间DES的控制理论结果与时间系统相关。***

9414780 Garg As man-made systems such as automated factories, communication networks, and computers continue to grow in size, "cut and try" approaches to design and supervision become less realistic. What is needed instead are controller synthesis techniques that allow optimal control laws to be derived mathematically and with performance properties that can be verified automatically. A well-established framework exists for control of systems without explicit real-time constraints. However, if timing is of concern in the system dynamics and its performance specification then the situation becomes much more complex. Certain real-time discrete event systems can be described by linear equations in a non-traditional algebraic system called max-algebra. For these systems, the problem of supervisory control is to impose delays on the execution of selected events to achieve some specified performance goal. The objective of the proposed research is to examine the existence and synthesis of controllers for DES which include such time constraints. Our method relies on the max-algebra model for timed DES which permits control theory results for untimed DES to be related to timed systems. ***