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  本文關(guān)鍵詞：分數(shù)階耦合網(wǎng)絡(luò)的穩(wěn)定性和同步控制　出處：《新疆大學(xué)》2016年博士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 分數(shù)階 耦合網(wǎng)絡(luò) 穩(wěn)定性 同步 控制

【摘要】：分數(shù)階微積分作為整數(shù)階微積分在階數(shù)上的延伸和推廣,其在物理、化學(xué)、生物、電子工程和經(jīng)濟等諸多領(lǐng)域表現(xiàn)出強大的優(yōu)勢和廣泛的應(yīng)用前景,引起了國內(nèi)外學(xué)者的廣泛關(guān)注,已成為當(dāng)前的研究熱點,尤其是分數(shù)階耦合網(wǎng)絡(luò)的穩(wěn)定性和同步控制的研究.本文主要包含三部分內(nèi)容:分數(shù)階耦合網(wǎng)絡(luò)穩(wěn)定性問題;分數(shù)階復(fù)雜網(wǎng)絡(luò)的同步控制問題;分數(shù)階神經(jīng)網(wǎng)絡(luò)的同步控制與參數(shù)識別.具體的研究工作如下:第一部分,考慮了三類分數(shù)階耦合網(wǎng)絡(luò)的穩(wěn)定性問題.(1)研究了一類沒有控制的分數(shù)階耦合網(wǎng)絡(luò)的穩(wěn)定性問題.應(yīng)用Kirchhoff矩陣樹定理,我們對這類耦合網(wǎng)絡(luò)給出了一種構(gòu)造Lyapunov函數(shù)的方法.通過結(jié)合圖理論和Lyapunov方法,得到了耦合網(wǎng)絡(luò)穩(wěn)定、一致穩(wěn)定和一致漸近穩(wěn)定的充分條件.最后,通過數(shù)值仿真驗證了所得理論結(jié)果的正確性.(2)研究了一類具有反饋控制的分數(shù)階耦合網(wǎng)絡(luò)的全局Mittag-Leffler穩(wěn)定性.基于壓縮映射原理,得到一些充分條件確保了耦合網(wǎng)絡(luò)平衡點的存在性和唯一性.通過使用Lyapunov方法、圖理論和一些有用的不等式,給出了網(wǎng)絡(luò)全局Mittag-Leffler穩(wěn)定的判別準(zhǔn)則.最后,數(shù)值模擬驗證了理論結(jié)果的正確性并且展示了分數(shù)階和反饋控制對所考慮系統(tǒng)解的影響.(3)研究了一類具有反饋控制的脈沖分數(shù)階耦合網(wǎng)絡(luò).通過結(jié)合圖理論和Lyapunov方法,得到了系統(tǒng)全局漸近穩(wěn)定和全局Mittag-Leffler穩(wěn)定的充分條件,這些條件與網(wǎng)絡(luò)的拓撲性質(zhì)有密切的關(guān)系.最后,通過數(shù)值模擬證明了所得理論結(jié)果的正確性和有效性.第二部分,研究了一般的分數(shù)階復(fù)雜網(wǎng)絡(luò)在周期間歇性牽制控制下的全局同步.通過引入周期間歇牽制控制策略,運用Lyapunov穩(wěn)定性理論和一些分析技巧,得到了網(wǎng)絡(luò)同步的判別準(zhǔn)則.數(shù)值模擬驗證了理論結(jié)果的正確性和有效性.第三部分,研究了具有未知參數(shù)的分數(shù)階神經(jīng)網(wǎng)絡(luò)的同步和參數(shù)識別.首先,把眾所周知的Barbalat引理推廣到分數(shù)階情況.基于推廣的Barbalat引理和一些分析技巧,在自適應(yīng)控制器和參數(shù)識別規(guī)則下,可以實現(xiàn)神經(jīng)網(wǎng)絡(luò)的同步和參數(shù)識別.理論證明和數(shù)值模擬驗證了所提方法的有效性.
[Abstract]:As an extension and extension of integral order calculus in order, fractional calculus has shown great advantages and wide application prospects in many fields such as physics, chemistry, biology, electronic engineering and economy. It has attracted the attention of scholars both at home and abroad and has become a hot research topic. Especially the research on the stability and synchronization control of fractional coupled networks. This paper mainly includes three parts: the stability of fractional coupled networks; Synchronization control of fractional complex networks; The synchronization control and parameter identification of fractional neural networks. The specific research work is as follows: the first part. In this paper, we consider the stability problem of three kinds of fractional coupled networks. We study the stability of a class of fractional coupled networks without control. The Kirchhoff matrix tree theorem is applied. We give a method of constructing Lyapunov function for this kind of coupling network. By combining graph theory with Lyapunov method, we obtain the stability of the coupled network. Sufficient conditions for uniformly stable and uniformly asymptotically stable. The correctness of the theoretical results is verified by numerical simulation. The global Mittag-Leffler stability of a class of fractional coupled networks with feedback control is studied based on the contraction mapping principle. Some sufficient conditions are obtained to ensure the existence and uniqueness of the equilibrium point of the coupled network. By using the Lyapunov method, the graph theory and some useful inequalities are obtained. The criterion of global Mittag-Leffler stability is given. Finally. Numerical simulation verifies the correctness of the theoretical results and shows the effects of fractional order and feedback control on the solution of the system under consideration. A class of impulsive fractional order coupled networks with feedback control is studied by combining graph theory and Lyapunov method. Sufficient conditions for global asymptotic stability and global Mittag-Leffler stability of the system are obtained. These conditions are closely related to the topological properties of the network. The correctness and validity of the theoretical results are proved by numerical simulation. Part two. The global synchronization of general fractional order complex networks under periodic intermittent control is studied. By introducing periodic intermittent control strategy, Lyapunov stability theory and some analytical techniques are used. The discriminant criterion of network synchronization is obtained, and the correctness and validity of the theoretical results are verified by numerical simulation. In the third part, the synchronization and parameter identification of fractional neural networks with unknown parameters are studied. The well-known Barbalat Lemma is extended to fractional order cases. Based on the generalized Barbalat Lemma and some analytical techniques, the adaptive controller and parameter identification rules are used. The synchronization and parameter identification of neural network can be realized, and the validity of the proposed method is verified by theoretical proof and numerical simulation.
【學(xué)位授予單位】：新疆大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：O231

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相關(guān)博士學(xué)位論文 前2條

1 陳立平;分數(shù)階非線性系統(tǒng)的穩(wěn)定性與同步控制[D];重慶大學(xué);2013年

2 劉金桂;分數(shù)階復(fù)雜網(wǎng)絡(luò)同步及其控制研究[D];湖南大學(xué);2013年

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本文編號：1361524