Two new optimal models for controlling discrete event systems
Two new optimal models for controlling discrete event systems
复制标题
用于控制离散事件系统的两个新的最优模型
DOI：
10.3934/jimo.2005.1.65
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发表时间：
2005
影响因子：
1.3
通讯作者：
Wuyi Yue
中科院分区：
文献类型：
--
作者：
Q. Hu;Wuyi Yue
监督控制本质上属于逻辑
离散事件系统控制问题的层次及其
相应的控制任务艰巨。这与许多实际的最佳方案不同，
控制问题，属于性能水平，其控制
任务是软的。本文提出了两个新的最优控制问题
的DES：一个成本函数选择控制输入，和其他
发生的事件。它们的性能指标是最大限度地减少
在系统生成的所有可能的字符串中的贴现总成本。
由于这是一个非线性优化问题，我们对这样的系统进行建模，
使用马尔可夫决策过程。然后，我们提出了最优性方程
并求其最优解。费用时
函数是固定的，我们表明，最优性方程和
它们的解也是稳定的。然后，我们使用这些方程，
统一描述和解决基本综合问题的解决方案，
监督控制区的两个分支：
反馈控制和状态反馈控制。此外，我们表明，
控制不变语言和控制不变谓词及其
宽容的监督者和国家反馈不仅在
监督控制的DES，但也是一些最佳的解决方案，
最优控制问题这表明逻辑级别之间存在联系
和离散事件系统控制的性能水平。
最后，给出了一个数值例子来说明一些结果，
DES的监督控制。
Supervisory control belongs essentially to the logic
level for control problems in discrete event systems (DESs) and its
corresponding control task is hard. This is unlike many practical optimal
control problems which belong to the performance level and whose control
tasks are soft. In this paper, we present two new optimal control problems
of DESs: one with cost functions for choosing control inputs, and the other
for occurring events. Their performance measures are to minimize the maximal
discounted total cost among all possible strings that the system generates.
Since this is a nonlinear optimization problem, we model such systems by
using Markov decision processes. We then present the optimality equations
for both control problems and obtain their optimal solutions. When the cost
functions are stationary, we show that both the optimality equations and
their solutions are also stationary. We then use these equations and
solutions to describe and solve uniformly the basic synthesizing problems in
the two branches of the supervisory control area: those being the event
feedback control and the state feedback control. Moreover, we show that the
control invariant languages and the control invariant predicates with their
permissive supervisors and state feedbacks not only have meanings in
supervisory control of DESs, but are also the optimal solutions for some
optimal control problems. This shows a link existing between the logic level
and the performance level for the control of discrete event systems.
Finally, a numerical example is given to illustrate some results for
supervisory control of a DES.