【摘要】：近年來,分?jǐn)?shù)階神經(jīng)網(wǎng)絡(luò)系統(tǒng)由于其良好的動(dòng)力學(xué)性質(zhì),已經(jīng)成為非線性學(xué)科領(lǐng)域研究的一個(gè)重要課題。相對于整數(shù)階神經(jīng)網(wǎng)絡(luò)系統(tǒng),分?jǐn)?shù)階神經(jīng)網(wǎng)絡(luò)系統(tǒng)能夠有效描述系統(tǒng)的整體功能,并提高其計(jì)算能力。此外,對神經(jīng)元進(jìn)行建模時(shí)加入憶阻器電路元件,可以更加準(zhǔn)確地模擬人類大腦神經(jīng)系統(tǒng)。另一方面,神經(jīng)網(wǎng)絡(luò)系統(tǒng)在信號傳輸過程中會(huì)產(chǎn)生時(shí)滯現(xiàn)象,能夠造成系統(tǒng)的不穩(wěn)定甚至導(dǎo)致混沌。因此,本文提出了基于憶阻器的時(shí)滯分?jǐn)?shù)階神經(jīng)網(wǎng)絡(luò)系統(tǒng),并討論了該系統(tǒng)的穩(wěn)定性問題,具體工作如下:1.對給定的基于憶阻器的時(shí)滯分?jǐn)?shù)階神經(jīng)網(wǎng)絡(luò)系統(tǒng),分析其動(dòng)力學(xué)行為。通過應(yīng)用分?jǐn)?shù)階系統(tǒng)的比較定理和時(shí)滯系統(tǒng)的穩(wěn)定性理論,給出了該系統(tǒng)實(shí)現(xiàn)局部漸近穩(wěn)定性的條件。此外,對于實(shí)際運(yùn)行的系統(tǒng),由于測量誤差和傳輸噪聲的存在,有界擾動(dòng)是不可避免的。因此,本文考慮了有界擾動(dòng)對該系統(tǒng)的影響,討論了在有界擾動(dòng)條件下,該系統(tǒng)滿足一致穩(wěn)定的條件。并通過構(gòu)造一個(gè)全局漸近穩(wěn)定的系統(tǒng)具體估計(jì)了該系統(tǒng)一致穩(wěn)定的范圍。2.在控制系統(tǒng)中,外界干擾的不確定性使得理論與實(shí)際結(jié)果存在一定的差距,特別是參數(shù)的不確定性,可能會(huì)導(dǎo)致穩(wěn)定的系統(tǒng)出現(xiàn)震蕩現(xiàn)象。此外,由于系統(tǒng)中包含復(fù)值信號,此種信號能夠使時(shí)域信號對應(yīng)的頻譜具有共軛對稱性。因此研究復(fù)平面上的具有不確定參數(shù)的分?jǐn)?shù)階神經(jīng)網(wǎng)絡(luò)系統(tǒng)是很有必要的。在Filippov意義下,通過利用分?jǐn)?shù)階比較原理、時(shí)滯系統(tǒng)的穩(wěn)定性理論,M-矩陣及同態(tài)原理,在復(fù)值傳遞函數(shù)可轉(zhuǎn)化為實(shí)部與虛部條件下,證明了在參數(shù)未知條件下系統(tǒng)平衡點(diǎn)的存在唯一性。并在此基礎(chǔ)上,給出了相應(yīng)的參數(shù)及函數(shù)條件,討論了系統(tǒng)的全局漸近穩(wěn)定性。而當(dāng)復(fù)值傳遞函數(shù)不可轉(zhuǎn)化時(shí),通過加入復(fù)值傳遞函數(shù)有界條件保證了系統(tǒng)平衡點(diǎn)的存在性,并得出了系統(tǒng)實(shí)現(xiàn)局部漸近穩(wěn)定的條件。
[Abstract]:In recent years, fractional neural network (FNN) system has become an important subject in the field of nonlinear science because of its good dynamic properties. Compared with integer-order neural network system, fractional-order neural network system can effectively describe the whole function of the system and improve its computing ability. In addition, it is more accurate to simulate the neural system of human brain by adding the circuit element of memotor to the neuron modeling. On the other hand, the neural network system will produce time-delay phenomenon in the process of signal transmission, which can cause instability and even chaos of the system. Therefore, in this paper, a delay fractional neural network system based on memory is proposed, and the stability of the system is discussed. The specific work is as follows: 1. The dynamic behavior of a given time-delay fractional-order neural network system based on memory is analyzed. By applying the comparison theorem of fractional-order systems and the stability theory of time-delay systems, the conditions for achieving local asymptotic stability of the system are given. In addition, due to the existence of measurement error and transmission noise, bounded disturbance is inevitable for the practical system. Therefore, in this paper, the influence of bounded perturbation on the system is considered, and the condition of uniform stability of the system is discussed under the condition of bounded perturbation. By constructing a globally asymptotically stable system, the range of uniform stability of the system is estimated. In the control system, the uncertainty of the external interference leads to a certain gap between the theoretical and practical results, especially the uncertainty of the parameters, which may lead to the oscillation of the stable system. In addition, because the system contains complex-valued signals, such signals can make the corresponding spectrum of time-domain signals have conjugate symmetry. Therefore, it is necessary to study the fractional neural network system with uncertain parameters on the complex plane. In the sense of Filippov, by using the fractional comparison principle, the stability theory of time-delay system, the M-matrix and homomorphism principle, under the condition that the complex-valued transfer function can be transformed into real part and imaginary part, The existence and uniqueness of the equilibrium point of the system under the condition of unknown parameters are proved. On this basis, the corresponding parameters and function conditions are given, and the global asymptotic stability of the system is discussed. When the complex-valued transfer function is non-convertible, the existence of the equilibrium point is guaranteed by adding the bounded condition of the complex-valued transfer function, and the conditions for the system to achieve local asymptotic stability are obtained.
【學(xué)位授予單位】：北京交通大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175

【相似文獻(xiàn)】

相關(guān)期刊論文 前10條

1 王峰;;廣義對角占優(yōu)矩陣的新判據(jù)及其在神經(jīng)網(wǎng)絡(luò)系統(tǒng)中的應(yīng)用[J];貴州大學(xué)學(xué)報(bào)(自然科學(xué)版);2012年05期

2 戴泊生;;高木英行先生來我局講授神經(jīng)網(wǎng)絡(luò)系統(tǒng)[J];華北地震科學(xué);1989年02期

3 廖六生,陳安平;Hopfield神經(jīng)網(wǎng)絡(luò)系統(tǒng)的全局漸近穩(wěn)定性的一個(gè)充分條件[J];模糊系統(tǒng)與數(shù)學(xué);2000年04期

4 張繼業(yè),戴煥云,鄔平波;Hopfield神經(jīng)網(wǎng)絡(luò)系統(tǒng)的全局穩(wěn)定性分析(英文)[J];控制理論與應(yīng)用;2003年02期

5 沈世鎰;時(shí)間離散Hopfield神經(jīng)網(wǎng)絡(luò)系統(tǒng)的若干問題[J];高校應(yīng)用數(shù)學(xué)學(xué)報(bào)A輯(中文版);1999年01期

6 陳戍;張延p，

本文編號：2452340