本文選題：復(fù)雜網(wǎng)絡(luò) + 同步��； 參考：《太原科技大學(xué)》2017年碩士論文

【摘要】：復(fù)雜網(wǎng)絡(luò)是由具有一定特征和功能的節(jié)點(diǎn),通過節(jié)點(diǎn)之間的相互影響和關(guān)聯(lián)所形成的集合體。近年來,復(fù)雜網(wǎng)絡(luò)得到來自不同領(lǐng)域?qū)W者的廣泛關(guān)注。復(fù)雜網(wǎng)絡(luò)的同步,指的是隨著時(shí)間的推移,其所有節(jié)點(diǎn)的狀態(tài)與目標(biāo)節(jié)點(diǎn)的狀態(tài)達(dá)到一致。由于網(wǎng)絡(luò)同步不僅可以解釋許多自然現(xiàn)象,而且具有潛在的應(yīng)用價(jià)值,因此同步已成為研究的熱點(diǎn)。由于網(wǎng)絡(luò)結(jié)構(gòu)的日益復(fù)雜化,時(shí)滯對(duì)復(fù)雜網(wǎng)絡(luò)的影響是不可避免的,從而影響著網(wǎng)絡(luò)同步的實(shí)現(xiàn)。學(xué)者們對(duì)時(shí)滯耦合復(fù)雜網(wǎng)絡(luò)的同步問題進(jìn)行了較為深入的研究。本文在分析了大量國內(nèi)外文獻(xiàn)的基礎(chǔ)上,利用時(shí)滯分解法,通過選取適當(dāng)?shù)腖yapunovKrasovskii泛函,結(jié)合線性矩陣不等式技術(shù),對(duì)兩類時(shí)滯耦合復(fù)雜網(wǎng)絡(luò)的同步問題進(jìn)行研究。具體而言,本論文的主要內(nèi)容如下:(1)研究了一般時(shí)滯耦合復(fù)雜網(wǎng)絡(luò)的同步穩(wěn)定問題。為分析方便,將同步穩(wěn)定問題轉(zhuǎn)化為同步誤差的關(guān)于零解的穩(wěn)定問題。采用時(shí)滯分割方法將時(shí)滯區(qū)間分成兩個(gè)相等的子區(qū)間和可調(diào)的子區(qū)間,分別為每個(gè)子區(qū)間構(gòu)造不同的Lyapunov-Krasovskii泛函,利用互凸組合技術(shù)得到具有弱保守性的穩(wěn)定性判據(jù)。最后給出數(shù)值算例表明本文所得結(jié)論的有效性。(2)研究了中立型時(shí)滯耦合復(fù)雜系統(tǒng)的同步穩(wěn)定性問題。首先將同步穩(wěn)定問題轉(zhuǎn)化為同步誤差的關(guān)于零解的穩(wěn)定性分析問題。然后將時(shí)滯區(qū)間分成兩個(gè)子區(qū)間,充分考慮時(shí)變時(shí)滯的有用信息,為每一個(gè)子區(qū)間選取不同的Lyapunov-Krasovskii泛函,最后結(jié)合互凸組合不等式技術(shù)和自由權(quán)矩陣的方法,得到了具有較低保守性的時(shí)滯相關(guān)同步穩(wěn)定性判據(jù)。通過數(shù)值算例驗(yàn)證了結(jié)果的弱保守性。(3)當(dāng)網(wǎng)絡(luò)依靠自身的耦合作用不能實(shí)現(xiàn)同步時(shí),研究了中立型時(shí)滯耦合復(fù)雜網(wǎng)絡(luò)的同步控制問題。對(duì)網(wǎng)絡(luò)節(jié)點(diǎn)施加一個(gè)簡單的線性反饋控制器,將同步控制問題轉(zhuǎn)化為誤差系統(tǒng)的穩(wěn)定性分析問題,利用時(shí)滯分解方法獲得了同步穩(wěn)定準(zhǔn)則。通過求解線性矩陣不等式,可以獲得最小的控制器增益。數(shù)值仿真例子表明結(jié)論的正確性。
[Abstract]:Complex network is a collection of nodes with certain characteristics and functions, which is formed by the interaction and association between nodes. In recent years, complex networks have received extensive attention from scholars in different fields. The synchronization of complex networks means that the state of all nodes is consistent with that of the target nodes over time. Because network synchronization can not only explain many natural phenomena, but also has potential application value, synchronization has become a hot research topic. Due to the increasing complexity of network structure, the influence of time delay on complex network is inevitable, thus affecting the realization of network synchronization. The synchronization problem of time-delay coupled complex networks has been studied deeply by scholars. Based on the analysis of a large number of literatures at home and abroad, the synchronization problem of two classes of time-delay coupled complex networks is studied by selecting appropriate LyapunovKrasovskii functional and combining with the technique of linear matrix inequality (LMI) by using the time-delay decomposition method. Specifically, the main contents of this thesis are as follows: 1) the synchronization stability problem of a general time-delay coupled complex network is studied. For the convenience of analysis, the problem of synchronization stability is transformed into the stability problem of zero solution of synchronization error. The delay-division method is used to divide the delay-interval into two equal subintervals and adjustable subintervals, respectively, to construct different Lyapunov-Krasovskii Functionals for each subinterval, and to obtain a weak conservative stability criterion by using the cross-convex combination technique. Finally, a numerical example is given to show the validity of the conclusions obtained in this paper. (2) the synchronization stability of neutral time-delay coupled complex systems is studied. First, the problem of synchronization stability is transformed into the stability analysis of zero solution of synchronization error. Then the time-delay interval is divided into two sub-regions, and the useful information of time-varying delays is fully considered, and different Lyapunov-Krasovskii functional is selected for each subinterval. Finally, the method of combining the technique of cross-convex combinatorial inequalities and the freedom matrix is combined. A delay-dependent synchronization stability criterion with lower conservatism is obtained. A numerical example is given to verify the weak conservatism of the results. When the network can not achieve synchronization by its own coupling, the synchronization control problem of neutral time-delay coupled complex networks is studied. Applying a simple linear feedback controller to the network nodes, the synchronization control problem is transformed into the stability analysis problem of the error system, and the synchronization stability criterion is obtained by using the time-delay decomposition method. The minimum controller gain can be obtained by solving linear matrix inequalities. Numerical simulation examples show that the conclusion is correct.
【學(xué)位授予單位】：太原科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O157.5;O231

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本文編號(hào)：1928971