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Title: | 利用L∞測量機率性離散事件系統之可控制性 Using L∞ Norm to Measure Controllability of Probabilistic Discrete Event Systems |
Authors: | Wen-Hung Tseng 曾文鴻 |
Advisor: | 顏嗣鈞 |
Keyword: | 離散事件系統,控制理論, Discrete Event Systems,DES,Control Theory, |
Publication Year : | 2007 |
Degree: | 碩士 |
Abstract: | 離散事件系統是一個動態的系統,在這個系統中的每一個狀態下,可能會有許多事件會發生,離散事件系統常被派屈網路或是不同的自動機來描述,而在這篇論文中會使用布基自動機來描述離散事件系統。通常在離散事件系統上我們都會加上一個控制器,它的作用是控制在每一狀態下的每一個事件,使其可以被執行或是不可被執行。一些典型在控制上會討論的議題包含了:這個被控制器控制的系統,是否會造成這個系統無法運作,或是會讓整個系統變成不具控制性。以及如果這個控制之下的系統是不具控制性的,要如何找到一個比這個被控制的系統小,但是被控制器控制之後,卻又成為了可控制性的系統,而且這個找到的新系統要是最大的。以及要如何找到一個比這個被控制的系統還要大,但是被控制器控制之後,卻又成為了可控制性的系統,而且這個找到的新系統要是最小的。
在現實生活中的許多系統經常都是含有機率的,因此在此論文中,我們會運用布基自動機來探討機率性的離散事件系統。首先會把機率性的離散事件系統的行為限制在有限長度的事件底下。接著討論一些上述的問題,並找到其解決方法,之後會證明在一些充分及必要的條件之下,這些解決方法的正確性。在此篇論文的第二部分,同樣地,會運用布基自動機來探討機率性的離散事件系統,不過卻會把此系統的行為推廣到無限多個事件發生的情形。接著同樣討論一些無限行為上產生的問題,並找到其解決方法,之後會證明在一些充分及必要的條件之下,這些在無限行為的解決方法的正確性。 本篇論文的貢獻有:我們使用 L∞-準則來測量二個機率性語言的之間距離,而機率性語言包含了有限長度字串的語言和無限長度字串的語言。我們提出如何去計算無限長度字串的機率。我們也提出如果給定一個具有有限長度或是無限長度的語言,該如何去找到一個比這個語言大的最小語言,同時又是可被控制的;以及該如何去找到一個比這個語言小的最大語言。我們同時也使用機率性的控制器來縮短用L∞量測二個機率性語言下所產生的距離。 A discrete-event system is a dynamic system in which a state change takes place according to the events.Discrete-event systems are usually modeled by various automata as well as Petri nets. In this thesis, discrete-event systems will be modeled by Büchi automata. A supervisor for a discrete-event system is a controller that can enable or disable each event in each state of the system. Some typical controllability issues of discrete–event systems include: Is a discrete-event system controllable by a supervisor? If the controlled discrete-event system is not controllable, does there exist a smaller discrete-event system which is controllable when supervised by the controller? Moreover, how to find the new discrete-event system? On the other hand, does there exist a larger discrete-event system which is controllable when supervised by the controller? How to find the new larger discrete-event system? In the real life many systems are of probabilistic nature. In this thesis, we discuss some supervisory control problems of probabilistic discrete-event systems which are modeled by Büchi automata. In the first part, we restrict the behavior of a discrete-event system to be of finite length. Further, we prove the necessary and sufficient conditions for the supervisory control problem on probabilistic discrete-event systems. In the second part of the thesis, we discuss the infinite behaviors of probabilistic discrete-event systems. Then, we extend the controller to probabilistic controller and also prove the problems on infinite behavior. The contributions of this thesis include: we have used the L∞-norm to measure the distance between two probabilistic languages of finite length and infinite length. Moreover, we have given the computation of probabilistic languages of infinite length. We have presented how to find the supremal controllable sublanguage and the infimal closed controllable superlanguage if given a language of finite length or infinite length. We have also used the probabilistic supervisor to reduce the L∞ distance between two probabilistic languages. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/30568 |
Fulltext Rights: | 有償授權 |
Appears in Collections: | 電機工程學系 |
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