本文選題：耦合反應(yīng)擴(kuò)散系統(tǒng) + 時滯　； 參考：《哈爾濱工業(yè)大學(xué)》2017年碩士論文

【摘要】：復(fù)雜網(wǎng)絡(luò)存在于生活的方方面面,如經(jīng)濟(jì)網(wǎng)絡(luò)、交通網(wǎng)以及電力網(wǎng)。許多物理及化學(xué)反應(yīng),如核反應(yīng)、地下水滲流和熱傳導(dǎo)等,它們系統(tǒng)的狀態(tài)同時依賴于時間和空間,當(dāng)這類系統(tǒng)所處的空間是非均勻的時候,擴(kuò)散現(xiàn)象不可避免地發(fā)生。因為同步問題具有廣泛的應(yīng)用價值,近幾十年來已經(jīng)成為了許多學(xué)者研究的熱點。對于同步的分類,根據(jù)系統(tǒng)實現(xiàn)同步狀態(tài)的時間可以分為漸近同步和有限時間同步。相較于漸近同步,有限時間同步因為實現(xiàn)同步狀態(tài)需要的時間有限且可計算而在工程等領(lǐng)域中受到高度重視。由于系統(tǒng)中存在大量需要被傳輸?shù)臄?shù)據(jù),而系統(tǒng)各個節(jié)點之間有限的傳輸速度以及系統(tǒng)各個節(jié)點本身的處理器速度限制使得時滯不可避免的發(fā)生。本文將分別通過施加全域控制、邊界控制以及牽制控制的方法來使系統(tǒng)在有限時間內(nèi)達(dá)到同步狀態(tài)。本文針對具有變時滯的耦合反應(yīng)擴(kuò)散系統(tǒng),研究了有限時間同步問題,通過對具有變時滯的反應(yīng)擴(kuò)散系統(tǒng)施加全域控制器,利用Lyapunov-Krasovskii泛函方法并結(jié)合線性矩陣不等式技巧,得到了系統(tǒng)實現(xiàn)有限時間同步的充分性判據(jù)。同時針對具有常時滯耦合反應(yīng)擴(kuò)散系統(tǒng)的有限時間同步問題給出了簡要說明。最后,給出了相應(yīng)的算例仿真,演示了所得理論結(jié)果的有效性。接著研究了耦合反應(yīng)擴(kuò)散系統(tǒng)的有限時間邊界控制問題,分別研究了不具有時滯的耦合反應(yīng)擴(kuò)散系統(tǒng)有限時間邊界控制以及具有時滯的耦合反應(yīng)擴(kuò)散系統(tǒng)有限時間邊界控制。對兩種耦合反應(yīng)擴(kuò)散系統(tǒng)的有限時間同步問題,分別針對混合邊界和Neumann邊界設(shè)計了不同的控制器,得到了系統(tǒng)實現(xiàn)有限時間同步的充分性判據(jù)。最后,給出了相應(yīng)的算例,演示了所得理論結(jié)果的有效性。然后討論了自適應(yīng)耦合反應(yīng)擴(kuò)散系統(tǒng)有限時間牽制控制問題。通過使用自適應(yīng)技巧以及設(shè)計牽制控制器,得到了使系統(tǒng)實現(xiàn)有限時間同步的充分性判據(jù)。最后,給出了相應(yīng)的算例,演示了所得理論結(jié)果的有效性。
[Abstract]:Complex networks exist in all aspects of life, such as economic networks, transportation networks and power networks. Many physical and chemical reactions, such as nuclear reactions, groundwater seepage and heat conduction, depend on both time and space for the state of their systems. Because of its wide application value, synchronization has become a hot topic for many scholars in recent decades. For the classification of synchronization, it can be divided into asymptotic synchronization and finite time synchronization according to the time of realizing synchronization. Compared with asymptotic synchronization, finite time synchronization has attracted great attention in engineering and other fields because of the limited time required to realize the synchronization state and its computability. Due to the large amount of data needed to be transmitted in the system, the limited transmission speed between each node of the system and the processor speed limit of each node in the system make the delay inevitable. In this paper, global control, boundary control and containment control are applied to make the system synchronize in finite time. In this paper, the finite time synchronization problem is studied for coupled reaction-diffusion systems with time-varying delays. By applying a global controller to the reaction-diffusion systems with time-varying delays, the Lyapunov-Krasovskii functional method and the techniques of linear matrix inequality (LMI) are used. A sufficient criterion for realizing finite time synchronization is obtained. At the same time, the finite time synchronization of coupled reaction diffusion systems with constant delay is briefly described. Finally, an example is given to demonstrate the effectiveness of the theoretical results. Then the finite time boundary control problem of coupled reaction diffusion systems is studied. The finite time boundary control of coupled reaction diffusion systems without time delay and the finite time boundary control of coupled reaction diffusion systems with time delay are studied respectively. For two kinds of coupled reaction-diffusion systems, different controllers are designed for the mixed boundary and Neumann boundary respectively, and the sufficient criteria for realizing the finite time synchronization are obtained. Finally, an example is given to demonstrate the validity of the theoretical results. Then the finite time control problem of adaptive coupled reaction diffusion system is discussed. By using adaptive techniques and designing a containment controller, a sufficient criterion for the system to achieve finite time synchronization is obtained. Finally, an example is given to demonstrate the validity of the theoretical results.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O157.5;O231

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 ;Uniformed model of networked control systems with long time delay[J];Journal of Systems Engineering and Electronics;2008年02期

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本文編號：2028398