【摘要】：近年來(lái),隨著神經(jīng)網(wǎng)絡(luò)的快速發(fā)展,其在工程方面的應(yīng)用也變得越來(lái)越多,但在實(shí)際的工程應(yīng)用中,總會(huì)不可避免的出現(xiàn)諸如脆弱性、非線性、時(shí)滯等問(wèn)題,此類問(wèn)題的存在將直接導(dǎo)致只有部分神經(jīng)元的狀態(tài)信息可以通過(guò)網(wǎng)絡(luò)輸出。由此可見,盡可能準(zhǔn)確的估計(jì)神經(jīng)元的狀態(tài)具有重要的科研價(jià)值以及實(shí)際意義。本文研究的內(nèi)容是針對(duì)連續(xù)神經(jīng)網(wǎng)絡(luò)系統(tǒng)進(jìn)行建模,并且基于Lyapunov穩(wěn)定性定理,結(jié)合線性矩陣不等式(Linear Matrix Inequality,LMI)技術(shù)、矩陣分析技術(shù)等,討論系統(tǒng)的穩(wěn)定性并且對(duì)非脆弱性狀態(tài)估計(jì)器設(shè)計(jì)方法進(jìn)行驗(yàn)證。首先,針對(duì)具有時(shí)變時(shí)滯的連續(xù)神經(jīng)網(wǎng)絡(luò)系統(tǒng),進(jìn)行系統(tǒng)穩(wěn)定性分析,并且討論考慮加性增益變化的非脆弱性狀態(tài)估計(jì)器研究方法。采用LMI方法,獲得保證系統(tǒng)漸近穩(wěn)定和滿足其他約束條件的非脆弱性狀態(tài)估計(jì)器存在的充分條件,以及狀態(tài)估計(jì)器的增益,并對(duì)研究結(jié)果進(jìn)行分析。其次,建立一類具有加性增益變化和時(shí)變時(shí)滯的連續(xù)神經(jīng)網(wǎng)絡(luò)模型,分析系統(tǒng)穩(wěn)定性并設(shè)計(jì)非脆弱性狀態(tài)估計(jì)器。定義連續(xù)神經(jīng)網(wǎng)絡(luò)增廣系統(tǒng)和約束條件,選取李雅普諾夫函數(shù)并按照其穩(wěn)定性定理,分析得到系統(tǒng)漸近穩(wěn)定及狀態(tài)估計(jì)器增益存在的充分條件。此時(shí),非脆弱性狀態(tài)估計(jì)器的設(shè)計(jì)實(shí)現(xiàn)就轉(zhuǎn)化為求解相應(yīng)LMI的可行解。再次,考慮到時(shí)變時(shí)滯的神經(jīng)網(wǎng)絡(luò)的穩(wěn)定性和非脆弱性狀態(tài)估計(jì)算法。采用乘性范數(shù)有界形式的估計(jì)器增益變化,利用Lipschitz條件刻畫神經(jīng)元狀態(tài)依賴非線性擾動(dòng),研究帶有非脆弱性的狀態(tài)估計(jì)器。利用Lyapunov穩(wěn)定性定理、矩陣分析技術(shù)、LMI技術(shù)、Leibniz-Newton公式,得到非脆弱性狀態(tài)估計(jì)器存在的充分條件,以及標(biāo)準(zhǔn)LMI問(wèn)題的可行解。最后,研究伴隨噪聲的連續(xù)神經(jīng)網(wǎng)絡(luò)系統(tǒng)穩(wěn)定性和非脆弱性狀態(tài)估計(jì)算法。利用兩個(gè)不同的函數(shù)表示噪聲,即系統(tǒng)產(chǎn)生的噪聲序列和系統(tǒng)的觀測(cè)噪聲序列。結(jié)合上述神經(jīng)網(wǎng)絡(luò)模型,設(shè)計(jì)具有增益變量的非脆弱性狀態(tài)估計(jì)器。通過(guò)分析誤差動(dòng)態(tài)增廣系統(tǒng)的穩(wěn)定性以及H?性能,得到非脆弱性狀態(tài)估計(jì)器存在并且需要滿足的LMI,即將非脆弱性狀態(tài)估計(jì)器設(shè)計(jì)變換成用標(biāo)準(zhǔn)線性矩陣不等式方法解決凸優(yōu)化問(wèn)題,并通過(guò)實(shí)際算例說(shuō)明研究的準(zhǔn)確性。
[Abstract]:In recent years, with the rapid development of neural network, its application in engineering has become more and more, but in practical engineering applications, there are always inevitable problems such as vulnerability, nonlinearity, time-delay and so on. The existence of this kind of problem will directly result in the state information of some neurons can be outputted through the network. It can be seen that estimating the state of neurons as accurately as possible has important scientific research value and practical significance. The content of this paper is to model the continuous neural network system, and based on the Lyapunov stability theorem, combining with the linear matrix inequality (Linear Matrix Inequality,LMI) technology, matrix analysis technology, etc. The stability of the system is discussed and the design method of the non-fragile state estimator is verified. Firstly, the stability of continuous neural network systems with time-varying delays is analyzed, and the research method of non-vulnerability state estimators considering additive gain variation is discussed. By using the LMI method, the sufficient conditions for the existence of a non-fragile state estimator, which guarantees the asymptotic stability of the system and satisfies other constraints, are obtained, as well as the gain of the state estimator. The results of the study are analyzed. Secondly, a class of continuous neural network models with additive gain variation and time-varying delay are established to analyze the stability of the system and to design a non-fragile state estimator. The continuous neural network augmented system and its constraint conditions are defined. The Lyapunov function is selected and the sufficient conditions for the asymptotic stability of the system and the existence of the gain of the state estimator are obtained according to its stability theorem. In this case, the design and implementation of the non-vulnerability state estimator is transformed into a feasible solution to solve the corresponding LMI. Thirdly, the stability and non-vulnerability state estimation algorithms of neural networks with time-varying delays are considered. The gain variation of the estimator in the bounded form of multiplicative norm is used to characterize the neuron state dependent nonlinear disturbance by using the Lipschitz condition. The state estimator with non-vulnerability is studied. By using the Lyapunov stability theorem, matrix analysis technique, LMI technique and Leibniz-Newton formula, the sufficient conditions for the existence of non-fragile state estimators and the feasible solutions of the standard LMI problem are obtained. Finally, the stability and non-vulnerability state estimation algorithms for continuous neural networks with noise are studied. Two different functions are used to represent the noise, that is, the noise sequence generated by the system and the observed noise sequence of the system. Based on the above neural network model, a non-vulnerability state estimator with gain variables is designed. By analyzing the stability of dynamic augmentation system with error and H? The performance of the non-fragile state estimator is obtained and the LMI, that needs to be satisfied is transformed into a standard linear matrix inequality (LMI) method to solve the convex optimization problem. An example is given to illustrate the accuracy of the study.
【學(xué)位授予單位】：東北石油大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TP183

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