本文選題：復(fù)雜系統(tǒng) + 復(fù)雜網(wǎng)絡(luò)��； 參考：《太原理工大學(xué)》2017年博士論文

【摘要】：進(jìn)入21世紀(jì)后,復(fù)雜系統(tǒng)為人類的生產(chǎn)與生活帶來了極大的提升與便利。與此同時(shí),復(fù)雜系統(tǒng)的失效也會(huì)造成災(zāi)難性的后果,如大范圍的停電事故、交通運(yùn)輸?shù)陌c瘓以及謠言或疾病的快速傳播等。因此,我們需要對(duì)復(fù)雜系統(tǒng)進(jìn)行有效地控制,從而盡可能地利用它的價(jià)值避免災(zāi)難發(fā)生。盡管現(xiàn)實(shí)中的復(fù)雜系統(tǒng)千差萬別,但是大部分復(fù)雜系統(tǒng)均可抽象為復(fù)雜網(wǎng)絡(luò)模型,從而把復(fù)雜系統(tǒng)的控制問題轉(zhuǎn)化為復(fù)雜網(wǎng)絡(luò)的控制問題。在進(jìn)行復(fù)雜網(wǎng)絡(luò)控制前,首先要明確被控對(duì)象是否可以被有效控制,即是否具備可控性。若確認(rèn)被控對(duì)象具備可控性,再進(jìn)行后續(xù)控制動(dòng)作,否則需要重新調(diào)整被控對(duì)象,直至使之具備可控性。因此,判定復(fù)雜網(wǎng)絡(luò)的可控性是開展控制的第一步。在前人工作的基礎(chǔ)上,本文討論了復(fù)雜網(wǎng)絡(luò)可控性的若干關(guān)鍵問題,主要貢獻(xiàn)如下:1.當(dāng)復(fù)雜網(wǎng)絡(luò)的整個(gè)拓?fù)浣Y(jié)構(gòu)未知時(shí),我們往往采用局部控制的手段,重點(diǎn)控制那些相對(duì)其他節(jié)點(diǎn)在某些方面起著重要作用的關(guān)鍵節(jié)點(diǎn)。那么,控制關(guān)鍵節(jié)點(diǎn)的前提是要確定是哪些節(jié)點(diǎn)。因此,本文從不同的角度選取具有代表性幾個(gè)指標(biāo),借鑒運(yùn)籌學(xué)的多屬性決策方法進(jìn)行融合,提出了一個(gè)度量復(fù)雜網(wǎng)絡(luò)中關(guān)鍵節(jié)點(diǎn)的綜合指標(biāo)。實(shí)驗(yàn)比較驗(yàn)證了本文所提方法的準(zhǔn)確性與有效性,說明了該綜合指標(biāo)能更好地挖掘出一個(gè)網(wǎng)絡(luò)的關(guān)鍵節(jié)點(diǎn),為控制網(wǎng)絡(luò)提供策略上的指導(dǎo)和幫助。2.當(dāng)我們需要對(duì)一個(gè)復(fù)雜網(wǎng)絡(luò)進(jìn)行精準(zhǔn)、完全控制時(shí),首先要找到網(wǎng)絡(luò)的最大匹配,并對(duì)非匹配節(jié)點(diǎn)進(jìn)行控制實(shí)現(xiàn)對(duì)網(wǎng)絡(luò)的精準(zhǔn)控制。因此,如何挖掘復(fù)雜網(wǎng)絡(luò)的最大匹配是一個(gè)必須解決的問題。本文研究了復(fù)雜網(wǎng)絡(luò)最大匹配的挖掘方法,提出了利用矩陣初等變換識(shí)別網(wǎng)絡(luò)中最大匹配的匹配節(jié)點(diǎn),發(fā)現(xiàn)最大匹配中匹配節(jié)點(diǎn)的個(gè)數(shù)由網(wǎng)絡(luò)矩陣特征值的最大幾何重?cái)?shù)決定。通過在真實(shí)網(wǎng)絡(luò)數(shù)據(jù)以及隨機(jī)網(wǎng)絡(luò)數(shù)據(jù)上的統(tǒng)計(jì)分析,發(fā)現(xiàn)網(wǎng)絡(luò)中最大匹配的匹配節(jié)點(diǎn)與節(jié)點(diǎn)的度分布密切相關(guān)。此外,本文也提出了挖掘最大匹配的一種啟發(fā)式算法,保證所找到的最大匹配是最優(yōu)的。大量真實(shí)網(wǎng)絡(luò)和模型網(wǎng)絡(luò)的計(jì)算結(jié)果表明了該方法的有效性與可行性。3.當(dāng)復(fù)雜網(wǎng)絡(luò)尺度較大時(shí),用求解最大匹配算法來控制網(wǎng)絡(luò)是很困難的。因此,本文從粒計(jì)算的角度入手模擬人類求解復(fù)雜問題的思維,提出了一種網(wǎng)絡(luò)粗�；姆椒�,將大規(guī)模網(wǎng)絡(luò)降維為規(guī)模較小的網(wǎng)絡(luò),再求解其最大匹配。最后,通過實(shí)驗(yàn)數(shù)據(jù)分析了應(yīng)用粗粒化算法的適應(yīng)場(chǎng)景與優(yōu)勢(shì),發(fā)現(xiàn):當(dāng)網(wǎng)絡(luò)中含有大量的有向圈或有向路徑時(shí),網(wǎng)絡(luò)粗�；笏尿�(qū)動(dòng)節(jié)點(diǎn)數(shù)會(huì)有所下降,而對(duì)于所含這兩種結(jié)構(gòu)相對(duì)較少的網(wǎng)絡(luò)來說,粗�；瘜�(duì)其影響較小。本文提出的關(guān)于復(fù)雜網(wǎng)絡(luò)可控性理論和研究方法具有一般性,研究結(jié)果有望為各種復(fù)雜系統(tǒng)的控制提供一定的借鑒價(jià)值,同時(shí)有助于我們更好地理解網(wǎng)絡(luò)結(jié)構(gòu)與其可控性之間的關(guān)系,為復(fù)雜系統(tǒng)的設(shè)計(jì)提供新的思路和理論依據(jù)。
[Abstract]:After twenty-first Century, complex systems have brought great improvements and conveniences to human production and life. At the same time, the failure of complex systems can also cause catastrophic consequences, such as a large scale of blackouts, traffic paralysis, and the rapid spread of rumors or diseases. Therefore, we need to effectively control complex systems. It can make use of its value as far as possible to avoid disaster. Although the complex systems in reality are different, most complex systems can be abstracted as complex network models, and the control problem of complex systems is transformed into a complex network control problem. Before the complex network control is carried out, the object is to be clearly defined. It can be effectively controlled, that is, whether it has controllability. If the controlled object is controllable, then follow the control action, otherwise the controlled object needs to be adjusted to make it controllable. Therefore, it is the first step to determine the controllability of the complex network. The main contributions of the network controllability are as follows: 1. when the whole topology of the complex network is unknown, we often use the local control method to control the key nodes which play an important role in some aspects. Then, the premise of controlling the key nodes is to determine which nodes are. In this paper, several representative indexes are selected from different angles, and the multi attribute decision-making method of operational research is used for reference. A comprehensive index of key nodes in a complex network is proposed. The experimental comparison shows the accuracy and effectiveness of the proposed method, which shows that the comprehensive index can better mine a network. Key nodes provide guidance and help to control network strategy and help.2. when we need accurate and complete control of a complex network, we must first find the maximum matching of the network and control the non matching nodes to realize the precise control of the network. In this paper, we study the mining method of the maximum matching of complex network, and propose a matching node identifying the maximum matching in the network by using matrix elementary transformation. It is found that the number of the matching nodes in the maximum match is determined by the maximum number of geometric weights of the eigenvalues of the network matrix. It is found that the maximum matching node in the network is closely related to the degree distribution of the nodes. In addition, a heuristic algorithm for mining maximum matching is proposed in this paper to ensure that the maximum matching is optimal. The results of a large number of real networks and model networks show that the effectiveness and feasibility of the method.3. is a complex network. When the scale is large, it is difficult to use the maximum matching algorithm to control the network. Therefore, this paper, starting with the point of grain computing, simulates the thinking of solving complex problems by human, and proposes a method of network coarse-graining, which reduces the dimension of large-scale network to a smaller network and then solves its maximum matching. Finally, the experimental data is analyzed. Using the adaptation scenarios and advantages of coarse graining algorithm, it is found that when the network contains a large number of directed loops or directed paths, the number of its driving nodes will decrease after the network coarse-grained, and coarse graining has little influence on the two networks with relatively few structures. The theory and research methods are general. The results of the study are expected to provide a certain reference value for the control of various complex systems, and help us to better understand the relationship between the network structure and its controllability, and provide new ideas and theoretical basis for the design of complex systems.
【學(xué)位授予單位】：太原理工大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2017
【分類號(hào)】：O157.5

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本文編號(hào)：1976897