本文選題：復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò) + 同步�。� 參考：《哈爾濱工業(yè)大學(xué)》2015年博士論文

【摘要】：近年來(lái),由于在理論領(lǐng)域的重要意義以及在工程領(lǐng)域的廣泛應(yīng)用,復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò)成為了一個(gè)熱門(mén)的研究領(lǐng)域。總體而言,復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò)由許多個(gè)動(dòng)態(tài)節(jié)點(diǎn)組成,這些節(jié)點(diǎn)按照一定拓?fù)浣Y(jié)構(gòu)進(jìn)行信息交換從而展示出群體特性。復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò)在現(xiàn)實(shí)世界中的典型應(yīng)用包括因特網(wǎng)、生物神經(jīng)網(wǎng)絡(luò)、電力網(wǎng)絡(luò)、社交網(wǎng)絡(luò)等。同步問(wèn)題作為復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò)中的一個(gè)基礎(chǔ)性問(wèn)題受到了研究學(xué)者越來(lái)越多的重視。需要指出的是,時(shí)滯現(xiàn)象廣泛存在于復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò)中,包括單個(gè)節(jié)點(diǎn)內(nèi)部的時(shí)滯特性以及節(jié)點(diǎn)之間通信存在的信息交換延遲。眾所周知,時(shí)滯的存在將可能降低復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò)的同步性能甚至破壞復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò)的同步。因此,時(shí)滯現(xiàn)象應(yīng)該在復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò)的同步問(wèn)題中被考慮。此外,復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò)還常常展示出一定的隨機(jī)特性,這些特性包括隨機(jī)非線性、隨機(jī)時(shí)滯、隨機(jī)參數(shù)不確定性等。這些隨機(jī)特性的引入將進(jìn)一步完善復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò)模型的描述�？紤]到上述問(wèn)題,本文重點(diǎn)研究了具有時(shí)滯及隨機(jī)特性的復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò)的同步問(wèn)題,主要研究工作可以總結(jié)為以下幾個(gè)方面:針對(duì)存在外部擾動(dòng)與時(shí)變時(shí)滯的復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò),在驅(qū)動(dòng)-響應(yīng)框架下研究了混合H_∞與無(wú)源性指標(biāo)下的復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò)同步問(wèn)題。在混合H_∞與無(wú)源性指標(biāo)的基礎(chǔ)上,通過(guò)構(gòu)造Lyapunov-Krasovskii泛函建立了時(shí)滯依賴(lài)的充分性條件從而確保驅(qū)動(dòng)網(wǎng)絡(luò)可以同步響應(yīng)網(wǎng)絡(luò)。仿真結(jié)果表明了所設(shè)計(jì)控制方案的有效性與適用性。在驅(qū)動(dòng)-響應(yīng)框架下,由于同步控制器在實(shí)際應(yīng)用中往往難以精確的按照設(shè)計(jì)參數(shù)實(shí)施,研究了帶有隨機(jī)非線性以及隨機(jī)控制器增益波動(dòng)的復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò)同步問(wèn)題。此外,模型還考慮了節(jié)點(diǎn)中存在的時(shí)變時(shí)滯現(xiàn)象。通過(guò)引入隨機(jī)變量描述隨機(jī)現(xiàn)象,構(gòu)造了一組非脆弱同步控制器用于解決同步問(wèn)題。利用隨機(jī)分析得到了實(shí)現(xiàn)同步的時(shí)滯依賴(lài)充分性條件。通過(guò)一個(gè)數(shù)值仿真例子證明了所得到的理論結(jié)果的正確性。進(jìn)一步研究了擾動(dòng)環(huán)境下的復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò)的驅(qū)動(dòng)-響應(yīng)H_∞非脆弱同步問(wèn)題。特別地,在復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò)的模型中考慮了隨機(jī)參數(shù)不確定性以及隨機(jī)控制器增益波動(dòng)對(duì)于同步性能的影響,從而更好的反應(yīng)現(xiàn)實(shí)世界中復(fù)雜網(wǎng)絡(luò)的動(dòng)態(tài)特性。建立了實(shí)現(xiàn)滿(mǎn)足所設(shè)定的H_∞同步性能指標(biāo)的充分性條件。在所得到結(jié)果的基礎(chǔ)上,進(jìn)一步設(shè)計(jì)了一組同步控制器從而實(shí)現(xiàn)擾動(dòng)環(huán)境下的同步。給出了一個(gè)解釋性的例子,仿真結(jié)果表明所設(shè)計(jì)的控制器可以實(shí)現(xiàn)給定H_∞指標(biāo)下的同步。此外,針對(duì)復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò)節(jié)點(diǎn)間信息傳輸過(guò)程中存在的時(shí)滯問(wèn)題,研究了帶有隨機(jī)時(shí)變信息傳輸時(shí)滯的非脆弱受控自同步問(wèn)題。其中,節(jié)點(diǎn)的模型為非線性有利于更好的描述網(wǎng)絡(luò)的動(dòng)態(tài)特性。此外,控制器中的增益波動(dòng)也被描述為隨機(jī)發(fā)生的。通過(guò)利用Lyapunov-Krasovskii泛函方法得到了時(shí)滯依賴(lài)的同步準(zhǔn)則。進(jìn)一步地,根據(jù)得到的同步條件設(shè)計(jì)了一組非脆弱控制器從而確保受控自同步可以實(shí)現(xiàn)。通過(guò)數(shù)值仿真的例子證明了所設(shè)計(jì)的控制方案的有效性與可行性。最后,進(jìn)一步考慮了控制器存在信息丟失以及外部擾動(dòng)情況下的復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò)的非脆弱受控耗散自同步問(wèn)題。需要指出的是,由于實(shí)際應(yīng)用中信息丟失的發(fā)生往往是隨機(jī)的,因此采用隨機(jī)模型來(lái)描述同步控制器存在的隨機(jī)信息丟失。此外,討論了復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò)中的時(shí)變隨機(jī)耦合時(shí)滯對(duì)于同步性能的影響。通過(guò)引入耗散性同步指標(biāo),建立了相應(yīng)的時(shí)滯依賴(lài)充分性條件。在此基礎(chǔ)上設(shè)計(jì)了一組控制器來(lái)確保受控同步的實(shí)現(xiàn)。相應(yīng)的給出了一個(gè)解釋性的例子,仿真結(jié)果表明了所得到理論結(jié)果的正確性與有效性。
[Abstract]:In recent years, complex dynamic networks have become a hot research field because of their importance in the field of theory and in the field of engineering. In general, complex dynamic networks are composed of many dynamic nodes. These nodes display group characteristics according to a certain topology. Complex dynamic networks. The typical applications of the collaterals in the real world include the Internet, the biological neural network, the power network, the social network and so on. As a fundamental problem in the complex dynamic network, the synchronization problem has been paid more and more attention by the researchers. It is necessary to point out that the time-delay phenomenon is widely stored in the complex dynamic network, including the internal of a single node. It is well known that the existence of time delay may reduce the synchronization performance of complex dynamic networks and even destroy the synchronization of complex dynamic networks. Therefore, time delay should be considered in the synchronization of complex dynamic networks. In addition, complex dynamic networks are often shown. These characteristics include random nonlinear, random time delay, random parameter uncertainty, etc. the introduction of these random properties will further improve the description of the complex dynamic network model. Considering the above problems, this paper focuses on the synchronization problems of complex dynamic networks with time delay and randomness. The work can be summed up in the following aspects: for complex dynamic networks with external disturbances and time-varying delays, the complex dynamic network synchronization problem under the hybrid H_ infinity and passivity index is studied under the drive response framework. On the basis of the mixed H_ infinity and passivity index, the time delay is established through the construction of the Lyapunov-Krasovskii functional. The simulation results show the effectiveness and applicability of the designed control scheme. In the drive response framework, the synchronization controller is often difficult to implement accurately according to the design parameters in the practical application, and studies the random nonlinear and random control. In addition, the model also takes into account the time-varying time-delay phenomena in the nodes. By introducing random variables to describe random phenomena, a group of non fragile synchronization controllers are constructed to solve synchronization problems. The time delay dependence sufficiency conditions for synchronization are obtained by random analysis. An example of numerical simulation proves the correctness of the theoretical results. The driving response H_ infinity synchronization problem of complex dynamic networks under disturbance environment is further studied. In particular, the uncertainty of random parameters and the effect of random controller gain fluctuation on synchronization performance are considered in the model of complex dynamic networks. In order to respond better to the dynamic characteristics of the complex network in the real world, a sufficient condition to meet the set of H_ infinity synchronization performance indicators is established. On the basis of the results obtained, a set of synchronization controllers are designed to achieve synchronization in the disturbance environment. An explanatory example is given and the simulation result table is given. The controller designed by Ming can realize the synchronization under given H_ infinity. In addition, the non fragile controlled self synchronization problem with random time-varying information transmission delay is studied for the time delay problem in the process of information transmission between nodes in complex dynamic networks. The model of the node is nonlinear, which is beneficial to describe the network movement better. Furthermore, the gain fluctuation in the controller is also described as a random occurrence. By using the Lyapunov-Krasovskii functional method, a synchronization criterion for time delay dependence is obtained. Further, a set of non fragile controllers is designed to ensure that the controlled self synchronization can be realized according to the obtained synchronization conditions. An example of numerical simulation is proved. The effectiveness and feasibility of the proposed control scheme is clear. Finally, the non fragile controlled dissipative self synchronization problem of the complex dynamic network under the condition of information loss and external disturbance is further considered. It is necessary to point out that the occurrence of information loss in practical applications is often random, so the random model is used. In addition, the effect of time-varying random coupling time delay on synchronization performance in complex dynamic networks is discussed. By introducing dissipative synchronization index, the corresponding delay dependence sufficiency conditions are established. On this basis, a set of controllers is designed to ensure the realization of controlled synchronization. An explanatory example is given, and the simulation results show the correctness and effectiveness of the theoretical results obtained.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2015
【分類(lèi)號(hào)】：O157.5

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