【摘要】：近年來,遞歸神經(jīng)網(wǎng)絡(luò)(RNNs)系統(tǒng)被廣泛的應(yīng)用到模式識別、圖像處理、聯(lián)想記憶過程、最優(yōu)化問題等各個方面。本文研究時滯神經(jīng)網(wǎng)絡(luò)的穩(wěn)定性分析和狀態(tài)估計問題,但在實際系統(tǒng)中,卻不可避免地出現(xiàn)時滯、非線性、不確定性等現(xiàn)象。在這樣一個擁有大量神經(jīng)元并且神經(jīng)元之間高度互聯(lián)的神經(jīng)網(wǎng)絡(luò)模型中,要完全獲知所有神經(jīng)元的狀態(tài)信息往往是非常困難的,這就要求人們近似地估計出這些神經(jīng)元的狀態(tài)�；谶@些考慮,對時滯遞歸神經(jīng)網(wǎng)絡(luò)的狀態(tài)估計理論的研究就具有非常重要的理論價值和實際意義。本文針對神經(jīng)網(wǎng)絡(luò)系統(tǒng)研究系統(tǒng)的穩(wěn)定性和非脆弱狀態(tài)估計問題,并給出更加寬松的穩(wěn)定性條件,得到保守性更弱的結(jié)果。其主要結(jié)果包括四個方面:第一部分:針對具有常時滯的離散神經(jīng)網(wǎng)絡(luò)系統(tǒng),設(shè)計非脆弱狀態(tài)估計器�；贚yapunov-Krsasovskii穩(wěn)定性理論和一些矩陣不等式的變換技巧,以線性矩陣不等式(LMI)的形式給出神經(jīng)網(wǎng)絡(luò)系統(tǒng)時滯漸近穩(wěn)定的充分條件,并求得狀態(tài)估計器的增益。第二部分:研究系統(tǒng)模型和估計器模型同時存在不確定性因素的神經(jīng)網(wǎng)絡(luò)狀態(tài)估計問題。通過構(gòu)造合適的李雅普諾夫函數(shù),得到系統(tǒng)漸近穩(wěn)定及狀態(tài)估計器增益存在的充分條件。在這個條件下,非脆弱狀態(tài)估計器的設(shè)計實現(xiàn)就轉(zhuǎn)化為求解一個相應(yīng)的線性矩陣不等式的可行解。第三部分:考慮到時間驅(qū)動機制的網(wǎng)絡(luò)冗余現(xiàn)象,在時滯離散神經(jīng)網(wǎng)絡(luò)系統(tǒng)中引入事件驅(qū)動機制,實現(xiàn)有效地解決這一問題。通過構(gòu)造新的Lyapunov泛函,獲得保證系統(tǒng)在均方意義下漸近穩(wěn)定的時滯相關(guān)充分條件,以LMI的形式給出時滯相關(guān)的神經(jīng)網(wǎng)絡(luò)狀態(tài)估計器的設(shè)計方法,并得到標準線性矩陣不等式問題的可行解。第四部分:研究依概率分布的時變時滯神經(jīng)網(wǎng)絡(luò)系統(tǒng)非脆弱狀態(tài)估計問題。使用相互獨立的伯努利隨機過程和布朗運動分別刻畫依概率分布的時變時滯與隨機發(fā)生非線性擾動現(xiàn)象。通過設(shè)計一個非脆弱狀態(tài)估計器,獲得保證系統(tǒng)穩(wěn)定的時滯相關(guān)充分條件,通過求解一個相應(yīng)的線性矩陣不等式得到估計器的增益矩陣。
[Abstract]:In recent years, recursive neural network (RNNs) systems have been widely used in pattern recognition, image processing, associative memory processes, optimization problems and so on. In this paper, the stability analysis and state estimation of neural networks with time-delay are studied. However, in practical systems, delay, nonlinearity, uncertainty and so on are inevitable. In such a neural network model with a large number of neurons and highly interconnected neurons, it is often very difficult to obtain the state information of all neurons completely, which requires people to estimate the state of these neurons approximately. Based on these considerations, it is of great theoretical and practical significance to study the state estimation theory of recurrent neural networks with time delay. In this paper, the stability and non-fragile state estimation of neural network systems are studied, and the more relaxed stability conditions are given, and the less conservative results are obtained. The main results include four aspects: in the first part, a non-fragile state estimator is designed for discrete-time neural networks with constant delays. Based on Lyapunov-Krsasovskii stability theory and some transformation techniques of matrix inequalities, a sufficient condition for the asymptotic stability of neural network systems with time delay is given in the form of linear matrix inequalities (LMI), and the gain of the state estimator is obtained. In the second part, the problem of neural network state estimation with uncertainties in both the system model and the estimator model is studied. By constructing a suitable Lyapunov function, sufficient conditions for the asymptotic stability of the system and the existence of the gain of the state estimator are obtained. Under this condition, the design and implementation of a non-fragile state estimator is transformed into a feasible solution for solving a corresponding linear matrix inequality (LMI). In the third part, considering the network redundancy of time-driven mechanism, the event-driven mechanism is introduced into the time-delay discrete neural network system to solve this problem effectively. By constructing a new Lyapunov functional, the delay-dependent sufficient conditions for the asymptotic stability of the system in the mean square sense are obtained, and the design method of the delay-dependent neural network state estimator is given in the form of LMI. The feasible solution of the standard linear matrix inequality problem is obtained. In the fourth part, the non-fragile state estimation problem of time-varying time-delay neural network systems with probability distribution is studied. Independent Bernoulli stochastic processes and Brownian motions are used to characterize the time-varying delays and random nonlinear perturbations respectively. By designing a non-fragile state estimator, the delay-dependent sufficient conditions for the stability of the system are obtained, and the gain matrix of the estimator is obtained by solving a corresponding linear matrix inequality.
【學(xué)位授予單位】：東北石油大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TP183

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