本文關(guān)鍵詞：基于M-矩陣理論的脈沖時滯神經(jīng)網(wǎng)絡(luò)穩(wěn)定性分析與同步控制　出處：《電子科技大學》2015年博士論文　論文類型：學位論文

  更多相關(guān)文章： M-矩陣 時滯神經(jīng)網(wǎng)絡(luò) 指數(shù)穩(wěn)定 脈沖擾動和鎮(zhèn)定 同步控制

【摘要】：神經(jīng)網(wǎng)絡(luò)的研究經(jīng)過不斷發(fā)展和完善,現(xiàn)已被成功地應(yīng)用到計算機科學、人工智能、自動控制、模式識別、圖像處理、組合最優(yōu)化、聯(lián)想記憶等學科研究領(lǐng)域。而這些應(yīng)用的關(guān)鍵依賴于神經(jīng)網(wǎng)絡(luò)的動力學行為。在實際中,由于時滯的客觀存在性和脈沖現(xiàn)象的普遍性,且時滯和脈沖對神經(jīng)網(wǎng)絡(luò)動力學行為有著不可忽視的影響。因此,兼具時滯和脈沖神經(jīng)網(wǎng)絡(luò)的動力學研究引起了眾多學者的關(guān)注,并成為非線性系統(tǒng)動力學研究方面的重要課題之一。本文系統(tǒng)地研究了脈沖影響下具有不同時滯類型的幾類神經(jīng)網(wǎng)絡(luò)的動力學行為。概括地講,研究內(nèi)容包括脈沖擾動下平衡點、周期軌的穩(wěn)定性;脈沖控制下平衡點的指數(shù)鎮(zhèn)定,脈沖擾動和脈沖鎮(zhèn)定下混沌同步控制。具體地講,本文的研究工作可歸納為如下的六個方面:(一)研究了一類以Hopfield神經(jīng)網(wǎng)絡(luò)、細胞神經(jīng)網(wǎng)絡(luò)為背景的更一般的神經(jīng)網(wǎng)絡(luò)模型在具有連續(xù)分布時滯和非線性脈沖干擾下平衡點的穩(wěn)定性問題。運用拓撲度理論、M-矩陣理論和不等式技巧,獲得了保證網(wǎng)絡(luò)模型平衡點存在性和唯一性的M-矩陣新判據(jù);在該M-矩陣條件下,利用分析的方法證明了網(wǎng)絡(luò)平衡點在一定的非線性脈沖干擾下仍然能保持全局指數(shù)穩(wěn)定性;通過一個具體例子驗證了理論結(jié)果的有效性和優(yōu)越性。(二)作為上述研究內(nèi)容的繼續(xù)和深入,進一步討論了(一)中的神經(jīng)網(wǎng)絡(luò)模型在具有變時滯和更具一般性的非線性脈沖擾動下平衡點的穩(wěn)定性問題。與(一)中所運用到的拓撲度方法不同,基于同胚映射原理,M-矩陣理論和不等式技巧,給出了網(wǎng)絡(luò)模型平衡點存在且唯一的更一般形式的M-矩陣判定標準;在該M-矩陣條件下,利用分析的方法證明了網(wǎng)絡(luò)平衡點在更一般非線性脈沖擾動下仍然是全局指數(shù)穩(wěn)定的;通過兩個具體例子驗證了理論結(jié)果的有效性和優(yōu)越性。(三)研究了一類以神經(jīng)元的狀態(tài)直接作為基本變量所得到的靜態(tài)神經(jīng)網(wǎng)絡(luò)模型在具有比例時滯和線性脈沖干擾下平衡點的穩(wěn)定性問題。這里所考慮的時滯類型既不同于(一)中所討論的連續(xù)分布時滯,也不同于(二)中所考慮的有界變時滯,它是一種無界的時變時滯�；趶V義的矩陣測度和推廣的Halanay不等式,得到了所考慮網(wǎng)絡(luò)模型平衡點全局指數(shù)穩(wěn)定矩陣測度形式的判定標準。通過兩個具體例子驗證了理論結(jié)果的有效性和優(yōu)越性。(四)在原始雙向聯(lián)想記憶(BAM)神經(jīng)網(wǎng)絡(luò)的基礎(chǔ)上,研究了一類更為復(fù)雜(具有周期性變系數(shù)和外界輸入,連續(xù)分布時滯,非線性脈沖干擾和高階項)BAM神經(jīng)網(wǎng)絡(luò)模型的周期振蕩動力學行為�；贛-矩陣理論、構(gòu)造Lyapunov-Krasovskii泛函、不等式技巧和分析的方法,給出了所研究網(wǎng)絡(luò)模型周期解存在唯一且全局指數(shù)穩(wěn)定的充分條件。通過一個具體例子驗證了理論結(jié)果的有效性和優(yōu)越性。(五)研究了一類憶阻神經(jīng)網(wǎng)絡(luò)模型(即用新的非線性電子元件憶阻器代替?zhèn)鹘y(tǒng)神經(jīng)網(wǎng)絡(luò)模型中的電阻所得到的一種新的神經(jīng)網(wǎng)絡(luò)模型)在脈沖控制下平衡點的鎮(zhèn)定性問題�；诿}沖控制的觀點,聯(lián)合運用集值映射和脈沖微分包含理論、非光滑分析及新建立的脈沖微分不等式,給出了所考慮網(wǎng)絡(luò)模型可全局指數(shù)鎮(zhèn)定到平衡點零解的代數(shù)不等式判定準則。通過兩個數(shù)值例子驗證了理論結(jié)果的有效性和可行性。(六)基于兩種不同形式的脈沖影響(脈沖擾動和脈沖控制),首先研究了以混沌憶阻神經(jīng)網(wǎng)絡(luò)為驅(qū)動系統(tǒng)并受到外界脈沖干擾時與其響應(yīng)系統(tǒng)的同步問題,然后討論了只在響應(yīng)系統(tǒng)中加入適當脈沖控制時驅(qū)動-響應(yīng)系統(tǒng)的同步問題。針對這兩類問題,綜合運用脈沖擾動型和脈沖鎮(zhèn)定型的Halanay不等式及前面(二)和(五)中的思想方法,分別獲得了狀態(tài)反饋和脈沖控制下的同步標準。最后,通過一個數(shù)值例子驗證了這兩種同步標準的有效性和可行性。
[Abstract]:The research of neural network through the continuous development and improvement, has been successfully applied to computer science, artificial intelligence, automatic control, pattern recognition, image processing, combinatorial optimization, associative memory and other research fields. The dynamic behavior and the key of these applications depends on the neural network. In practice, due to the universal existence time delay and pulse delay and pulse phenomenon, and has an important influence on the dynamic behavior of the neural network. Therefore, both the kinetics of delay and impulsive neural network has attracted the attention of many scholars, and has become one of the important issue of nonlinear dynamic system. Dynamics with several kinds of neural networks of different types of delay this paper systematically studied the effect of pulse condition. Generally speaking, the research content including pulse disturbance equilibrium, stability of periodic orbits; pulse Under the control of the equilibrium point of exponential stabilization, impulsive perturbations and Impulsive Stabilization of chaotic synchronization control. Specifically, the research work of this paper can be summarized into six aspects as follows: (a) to study a class of Hopfield neural network, the neural network model of general cellular neural network as the background of the continuous distribution delay and nonlinear in the impulsive stability problem under the equilibrium point. By using the theory of topological degree, M- matrix theory and inequality technique, the new criterion of M- matrix to guarantee the existence and uniqueness of the network equilibrium; in the condition of the M- matrix, it is proved that network equilibrium can still maintain global exponential stability in certain nonlinear pulse the interference by using the method of analysis; through a concrete example to verify the validity and superiority of the theoretical results. (two) as to the above research contents and in-depth, further discussed ( A) neural network model with time-varying delays and general nonlinear impulsive stability problem of equilibrium point in it. (a) with different topological method used in the homeomorphism mapping based on the principle of M- matrix theory and inequality technique, gives the network model equilibrium exists and criteria only the more general form of M- matrix; in condition of the M- matrix, it is proved that network equilibrium in pulse more general nonlinear perturbation is globally exponentially stable by using the method of analysis; through two specific examples to verify the theoretical validity and superiority of the results. (three) studied the static neural network a class of models directly to the states of the neurons as the basic variables obtained with proportional delays and linear pulse interference under the stability problem of the equilibrium point. The delay type considered here is different from (a) in the sea Continuous distributed delay theory, but also different from (two) in consideration of the bounded delay, it is a kind of unbounded time-varying delay. Halanay inequalities of matrix measure and generalized based on the network model considering the globally exponential stability of the equilibrium point matrix measure form criteria by two. An example shows the effectiveness and superiority of the theoretical results. (four) in the original bidirectional associative memory (BAM) based on neural network is studied for a class of more complex (with periodic coefficients and external input, continuous distribution delay, nonlinear pulse interference and high order) periodic oscillation dynamics of BAM the neural network model. The M- matrix based on the theory of constructing Lyapunov-Krasovskii functional method and inequality analysis, gives the research cycle network model with sufficient conditions for the existence and uniqueness and global exponential stability. Through a Body examples to verify the validity and superiority of the theoretical results. (five) studied a class of memristive neural network model (the resistance of new nonlinear electronic components memristor instead of the traditional neural network model obtained by a new neural network model) in the impulsive control stabilization problem under equilibrium the pulse control. Based on the view of the joint use of set-valued mapping and impulsive differential inclusions theory, nonsmooth analysis and new impulsive differential inequality, given the network model decidable algebraic inequalities global exponential stabilization to the equilibrium point of the zero solution criterion. Through two numerical examples verify the effectiveness of the theoretical results and feasibility. (six) effects of two kinds of pulse (pulse and pulse control based on disturbance), first studies on chaotic memristive neural network driven system and external interference and pulse response Synchronization of system, and then discusses the synchronization in the response system with appropriate pulse control when the drive response system. According to the two kinds of problems, the integrated use of pulse Halanay inequality and disturbance type and pulse shaping in front of the town (two) and (five) thought method, were given the standard synchronization state feedback and impulsive control. Finally, through a numerical example to verify the effectiveness of the two kinds of synchronization standard and feasibility.

【學位授予單位】：電子科技大學
【學位級別】：博士
【學位授予年份】：2015
【分類號】：O175

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