本文選題：區(qū)間矩陣 + 周期　； 參考：《河北師范大學(xué)》2017年碩士論文

【摘要】：在生產(chǎn)制造、通訊、運輸?shù)群芏喾矫?我們都可以利用極大-加代數(shù)模型來解決相關(guān)問題,其中極大-加線性系統(tǒng)和區(qū)間極大-加系統(tǒng)是常用的兩個模型.可達性分析是系統(tǒng)理論和可靠性分析等領(lǐng)域中的基本問題,向前可達性包括從某個狀態(tài)開始繼續(xù)向前發(fā)展的可達集和可達管.學(xué)者們已經(jīng)利用極大-加多面體和極大-加錐體,或利用差分有界矩陣研究了極大-加代數(shù)和極大-加線性系統(tǒng)的可達性.而研究區(qū)間極大-加系統(tǒng)的向前可達性,用到了區(qū)間的加法和取極大兩種運算.這兩種運算的本質(zhì)是變量上下界的運算,會帶來誤差.因此,以往研究可達性的方法不能直接用于解決區(qū)間極大-加系統(tǒng)中向前可達性的問題,需要改善運算方法以減小誤差.而實際問題中,各變量的參數(shù)或無限制或經(jīng)常在某一個有限區(qū)間內(nèi)隨機變動.本文主要研究這樣一類矩陣,其元素或者為無限、或者為實數(shù)集上的閉區(qū)間.研究該類區(qū)間矩陣的周期,以簡化區(qū)間極大-加系統(tǒng)的向前可達性的計算,并研究由這類區(qū)間矩陣確定的、自治的區(qū)間極大-加系統(tǒng)的向前可達性,著重研究其可達集.首先,利用已有結(jié)論計算這類區(qū)間矩陣的周期,進而研究一類準對角矩陣和準對角區(qū)間矩陣的所有元素的周期,得到了關(guān)于冪矩陣的一些性質(zhì).其次,在自治的區(qū)間極大-加系統(tǒng)中,針對區(qū)間運算和向前可達性的特點,本文找到了一個準確計算可達集的方法  全部取點法,以及計算可達集的步驟.由此可以把比較復(fù)雜的初始狀態(tài)集,轉(zhuǎn)化為更為方便計算的初始狀態(tài)集.在二維自治的區(qū)間極大-加系統(tǒng)中,本文得到了三類初始狀態(tài)的系統(tǒng)可達集的計算規(guī)律,并給出了一個二維情況下更為簡單的方法——局部取點法.進而還研究了9)維情況時可達集的一些計算方法.最后,通過數(shù)值例子展示了計算可達集的步驟和兩種計算方法的運算過程.
[Abstract]:In many aspects, such as manufacturing, communication, transportation and so on, we can use the max-plus algebraic model to solve the related problems, in which the max-plus linear system and the interval max-additive system are two commonly used models. Reachability analysis is a fundamental problem in the field of system theory and reliability analysis. Forward reachability includes reachability sets and reachability tubes that continue to evolve from a certain state. Scholars have studied the reachability of Max-plus Algebra and Max-plus Linear Systems by using the maximal-plus polyhedron and the maximum-plus cone or by using the difference bounded matrix. In order to study the forward reachability of interval-maximum-additive systems, two operations, the addition of interval and the maximization of interval, are used. The essence of these two operations is the operation of upper and lower bounds of variables, which will bring errors. Therefore, the previous research methods of reachability can not be directly used to solve the problem of forward reachability in interval-maximum-additive systems, so it is necessary to improve the operation method to reduce the error. However, in practical problems, the parameters of each variable change randomly in a finite interval. In this paper, we study a class of matrices whose elements are either infinite or closed intervals on the set of real numbers. The period of the interval matrix is studied to simplify the calculation of the forward reachability of the interval maximal additive system, and the forward reachability of the autonomous interval maximum additive system determined by this kind of interval matrix is studied, with emphasis on its reachability set. First, the period of this kind of interval matrix is calculated by using the existing results, and then the period of all elements of a class of quasi-diagonal matrices and quasi-diagonal interval matrices is studied, and some properties of the power matrix are obtained. Secondly, according to the characteristics of interval operation and forward reachability in autonomous interval Max-Additive system, an accurate method of calculating reachability set is found in this paper, and the steps of calculating reachability set are given. Thus, the more complex initial state set can be transformed into a more computable initial state set. In this paper, we obtain the calculation law of reachability set of three kinds of initial state systems in the interval maximum additive system of two dimensional autonomy, and give a simpler method in two dimensional case, the local point taking method. Furthermore, some calculation methods for the reachable set in the case of 9) dimension are studied. Finally, numerical examples are given to show the steps of computing reachability set and the operation process of two methods.
【學(xué)位授予單位】：河北師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O151.2

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1 胡雪莎;一類自治的區(qū)間極大—加系統(tǒng)的向前可達性[D];河北師范大學(xué);2017年

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本文編號：1965730