【摘要】：隨著信息時(shí)代的發(fā)展,現(xiàn)實(shí)生活中的許多實(shí)際模型可以用復(fù)雜網(wǎng)絡(luò)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(jī)因素和時(shí)間延遲應(yīng)該被考慮。因此,研究復(fù)雜網(wǎng)絡(luò)上帶有延遲的隨機(jī)系統(tǒng)動(dòng)力學(xué)行為十分有意義。最近,許多學(xué)者研究了復(fù)雜網(wǎng)絡(luò)上隨機(jī)延遲系統(tǒng)的動(dòng)力學(xué)行為,其中控制方法是一種十分有效的策略。然而,從控制學(xué)角度來看,控制成本以及效率等因素也應(yīng)該被考慮。本文設(shè)計(jì)了一種不同于連續(xù)時(shí)間的控制器,即離散時(shí)間狀態(tài)可觀測(cè)的反饋控制器。主要使用隨機(jī)分析技巧、圖理論知識(shí)和Lyapunov方法相結(jié)合的方法,研究了復(fù)雜網(wǎng)絡(luò)上帶有離散時(shí)間狀態(tài)可觀測(cè)反饋控制的隨機(jī)系統(tǒng)穩(wěn)定性和同步性。本文的第二章,通過設(shè)計(jì)一種基于離散時(shí)間狀態(tài)可觀測(cè)的反饋控制器,研究復(fù)雜網(wǎng)絡(luò)上帶有時(shí)間延遲的隨機(jī)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(gè)充分性準(zhǔn)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(shí)際應(yīng)用價(jià)值,本文將新穎的結(jié)果應(yīng)用到復(fù)雜網(wǎng)絡(luò)上的耦合振子系統(tǒng)中。隨后,給出一個(gè)數(shù)值算例及其數(shù)值仿真。本文的第三章,通過設(shè)計(jì)基于離散時(shí)間狀態(tài)可觀測(cè)的反饋控制器,討論了復(fù)雜網(wǎng)絡(luò)上隨機(jī)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(gè)充分性準(zhǔn)則,主要包括均方同步和均方漸近同步,而且得到兩個(gè)連續(xù)時(shí)間狀態(tài)之間觀測(cè)時(shí)間的一個(gè)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(gè)充分性準(zhǔn)則。最后,給出了一個(gè)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(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O231

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