【摘要】：隨著信息時代的發(fā)展,現(xiàn)實生活中的許多實際模型可以用復雜網(wǎng)絡上的系統(tǒng)來刻畫。此外,為了更精確地描述自然界的一些現(xiàn)象,隨機因素和時間延遲應該被考慮。因此,研究復雜網(wǎng)絡上帶有延遲的隨機系統(tǒng)動力學行為十分有意義。最近,許多學者研究了復雜網(wǎng)絡上隨機延遲系統(tǒng)的動力學行為,其中控制方法是一種十分有效的策略。然而,從控制學角度來看,控制成本以及效率等因素也應該被考慮。本文設計了一種不同于連續(xù)時間的控制器,即離散時間狀態(tài)可觀測的反饋控制器。主要使用隨機分析技巧、圖理論知識和Lyapunov方法相結合的方法,研究了復雜網(wǎng)絡上帶有離散時間狀態(tài)可觀測反饋控制的隨機系統(tǒng)穩(wěn)定性和同步性。本文的第二章,通過設計一種基于離散時間狀態(tài)可觀測的反饋控制器,研究復雜網(wǎng)絡上帶有時間延遲的隨機系統(tǒng)穩(wěn)定性。本文使用的方法是Lyapunov方法和圖理論中的Kirchhoff矩陣數(shù)定理,并且給出三個充分性準則,主要包括漸近穩(wěn)定性和均方漸近穩(wěn)定性。為了說明該理論具有實際應用價值,本文將新穎的結果應用到復雜網(wǎng)絡上的耦合振子系統(tǒng)中。隨后,給出一個數(shù)值算例及其數(shù)值仿真。本文的第三章,通過設計基于離散時間狀態(tài)可觀測的反饋控制器,討論了復雜網(wǎng)絡上隨機系統(tǒng)不同類型的同步性,使用Lyapunov方法和圖理論中的Kirchhoff矩陣數(shù)定理,得到三個充分性準則,主要包括均方同步和均方漸近同步,而且得到兩個連續(xù)時間狀態(tài)之間觀測時間的一個上界。隨后,本文研究了微電網(wǎng)模型的漸近同步性并給出了判定微電網(wǎng)模型均方漸近同步的一個充分性準則。最后,給出了一個數(shù)值算例及其數(shù)值仿真。
[Abstract]:With the development of information age, many practical models in real life can be described by systems on complex networks. In addition, in order to describe some phenomena in nature more accurately, random factors and time delays should be taken into account. Therefore, it is very meaningful to study the dynamic behavior of stochastic systems with delays on complex networks. Recently, many scholars have studied the dynamic behavior of stochastic delay systems on complex networks, in which the control method is a very effective strategy. However, from the point of view of control science, the factors such as cost control and efficiency should also be considered. In this paper, a feedback controller is designed, which is different from continuous time, that is, discrete time observable feedback controller. In this paper, the stability and synchronization of stochastic systems with discrete time state observable feedback control on complex networks are studied by using stochastic analysis technique, graph theory and Lyapunov method. In the second chapter, the stability of stochastic systems with time delay on complex networks is studied by designing a feedback controller based on discrete time state observability. The method used in this paper is Lyapunov method and Kirchhoff matrix number theorem in graph theory, and three sufficient criteria are given, including asymptotic stability and mean square asymptotic stability. In order to show that the theory has practical application value, the novel results are applied to the coupled oscillator system on complex networks. Then, a numerical example and its numerical simulation are given. In the third chapter, by designing a feedback controller based on discrete time state observability, the synchronization of different types of stochastic systems on complex networks is discussed. Using Lyapunov method and Kirchhoff matrix number theorem in graph theory, three sufficient criteria are obtained, including mean square synchronization and mean square asymptotic synchronization, and an upper bound of observation time between two continuous time states is obtained. Then, the asymptotic synchronization of the microgrid model is studied and a sufficient criterion for determining the mean square asymptotic synchronization of the microgrid model is given. Finally, a numerical example and its numerical simulation are given.
【學位授予單位】：哈爾濱工業(yè)大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O231

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