本文選題：泛化函數(shù)投影同步 + 自適應同步　； 參考：《大連理工大學》2015年博士論文

【摘要】：混沌系統(tǒng)具有復雜而獨特的動力學特征,其在許多科學領域都有著很大的應用潛力.目前對混沌同步控制的研究已成為國際上的熱點.其中混沌投影同步是一種重要的同步方式,實現(xiàn)同步時,驅動系統(tǒng)狀態(tài)與響應系統(tǒng)狀態(tài)依某比例因子演化.國內外許多學者將比例因子擴展成對角矩陣、函數(shù)以及函數(shù)矩陣等,得到了各種類型的投影同步方式.這些擴展增大了投影同步的適用范圍,增強了其應用的靈活性.本文考慮驅動系統(tǒng)和響應系統(tǒng)之間存在某種“位移”的情形,提出了混沌泛化函數(shù)投影同步的概念,并應用自適應控制方法實現(xiàn)了參數(shù)未知混沌系統(tǒng)的泛化函數(shù)投影同步.針對混沌系統(tǒng)存在不確定性時的泛化函數(shù)投影同步問題,分別設計了主動變論域自適應模糊控制器和快速終端滑�？刂破�.基于模糊推理建模方法,定義了一類新的混沌系統(tǒng)—HX型混沌系統(tǒng),并應用并行分布補償技術實現(xiàn)了其泛化函數(shù)投影同步.考慮到時間延遲的存在,提出了泛化函數(shù)投影延遲同步的概念,并給出了積分滑�？刂撇呗�.具體工作及結果總結如下：1.考慮到驅動系統(tǒng)和響應系統(tǒng)之間存在某種“位移”的情形,我們定義了混沌系統(tǒng)的泛化函數(shù)投影同步的概念,進一步推廣了混沌投影同步的概念.這種“位移”是由一個參考系統(tǒng)的狀態(tài)來表示的.這個參考系統(tǒng)可以是常向量、周期系統(tǒng)、擬周期系統(tǒng)、混沌系統(tǒng)或超混沌系統(tǒng)以及它們的組合.通過調節(jié)參考系統(tǒng)和函數(shù)尺度因子矩陣,泛化函數(shù)投影同步可以退化為完全同步、反同步、投影同步、修正同步、函數(shù)投影同步和修正函數(shù)投影同步等同步方式.針對含未知參數(shù)的混沌系統(tǒng)的泛化函數(shù)投影同步,我們提出了自適應控制方法,并采用Lyapunov穩(wěn)定性理論論證了其合理性,分別對常向量、函數(shù)向量、超混沌系統(tǒng)、含未知參數(shù)的超混沌系統(tǒng)這四種參考系統(tǒng)意義下的混沌泛化函數(shù)投影同步進行研究.仿真結果證實了控制策略的有效性.2.基于產(chǎn)生超混沌系統(tǒng)的三個必要條件,在Lorenz系統(tǒng)基礎上構造了一個具有收斂直線的超混沌系統(tǒng).我們對該系統(tǒng)的耗散性、平衡點、分岔圖、Lyapunov指數(shù)、Lyapunov維數(shù)及Poincare截面等進行了研究,指出該系統(tǒng)僅有一個平衡點,并且指出在一定的參數(shù)條件下系統(tǒng)呈現(xiàn)周期、擬周期、混沌及超混沌等動力學性態(tài).在較大的參數(shù)區(qū)間內,這個系統(tǒng)是超混沌的.針對構造的超混沌系統(tǒng)帶有不確定性時的泛化函數(shù)投影同步問題,我們提出了主動變論域自適應模糊控制方法.以超混沌Liu系統(tǒng)作為參考系統(tǒng)進行仿真,結果證實了控制策略的有效性.3.通過在Loreng系統(tǒng)的第二個方程之上增加一個反饋項,我們構造了一個有三個平衡點的四維自治系統(tǒng).分析了其耗散性、吸引子的存在性、平衡點、分岔圖、Lyapunov指數(shù)等非線性特征.通過Lyapun ov指數(shù)譜可以發(fā)現(xiàn)該系統(tǒng)具有豐富的動態(tài)特性.在參數(shù)變化的一個大的范圍內,系統(tǒng)是超混沌的.對于帶有不確定性的混沌系統(tǒng)的泛化函數(shù)投影同步,我們提出了快速終端滑模控制方法.以該新超混沌系統(tǒng)與超混沌Chen系統(tǒng)分別作為驅動系統(tǒng)和響應系統(tǒng),對其泛化函數(shù)投影同步進行仿真研究,結果證實了所述控制方法的有效性.4.對于右端為多項式的混沌系統(tǒng),我們采用逐項模糊推理建模再進行線性疊加的方法,得到其HX方程組.通過分析,發(fā)現(xiàn)這樣的HX方程組并非每一項都是變系數(shù)的,甚至一些系統(tǒng)的HX方程組與原混沌系統(tǒng)相同.對于混沌(超混沌)系統(tǒng)的HX方程組,若其為變系數(shù)的,由模糊系統(tǒng)的萬能逼近性,在適當?shù)哪：齽澐窒?其為混沌(超混沌)系統(tǒng),稱之為HX型混沌(超混沌)系統(tǒng).這樣我們就通過現(xiàn)有混沌(超混沌)系統(tǒng)得到新的混沌(超混沌)系統(tǒng).可以通過簡單的改變模糊劃分來改變HX型混沌(超混沌)系統(tǒng)的系數(shù),實現(xiàn)混沌切換.我們通過逐片精確T-S模糊建模再組合的方法,得到了四維HX型超混沌系統(tǒng)的精確T-S模糊模型,逐片應用并行分布補償(PDC)技術實現(xiàn)了HX型超混沌系統(tǒng)的泛化函數(shù)投影同步.5.考慮到現(xiàn)實控制工程中時間延遲的客觀存在,我們提出了泛化函數(shù)投影延遲同步的概念.這拓展了修正函數(shù)延遲投影同步和泛化函數(shù)投影同步,其應用范圍更廣泛.分別應用主動滑�？刂品椒ê椭鲃幽：？刂品椒▽в胁谎芯啃猿煦缦到y(tǒng)的泛化函數(shù)投影延遲同步進行了研究.
[Abstract]:Chaotic systems have complex and unique dynamic characteristics, and they have great potential in many fields of science. At present, the research of chaotic synchronization control has become a hot spot in the world. Chaotic projection synchronization is an important synchronization mode. When the synchronization is realized, the state of the drive system and the state of the response system are proportional to a certain factor. Many scholars at home and abroad extend the proportion factor into diagonal matrix, function and function matrix, and get various types of projection synchronization. These extensions increase the scope of application of the projection synchronization and enhance the flexibility of its application. The concept of projection synchronization of chaotic generalization function is presented, and an adaptive control method is applied to realize the projection synchronization of the generalization function of the unknown chaotic system. The adaptive fuzzy controller and the fast terminal sliding mode controller are designed for the problem of the projection synchronization of the generalization function in the uncertainty of the chaotic system. In the fuzzy reasoning modeling method, a new chaotic system - HX type chaotic system is defined, and the generalization function projection synchronization is realized by the parallel distribution compensation technology. Considering the existence of time delay, the concept of the generalized function projection delay synchronization is proposed, and the product partition sliding mode control strategy is given. The specific work and the results are summarized as follows. 1.: considering the existence of some "displacement" between the driving system and the response system, we define the concept of the projection synchronization of the generalization function of the chaotic system, and further generalized the concept of chaotic projection synchronization. This "displacement" is shown by the state of a reference system. This reference system can be a constant vector, a week. Phase system, quasi periodic system, chaotic system or hyperchaotic system and their combination. By adjusting the reference system and function scale factor matrix, the generalization function projection synchronization can degenerate into complete synchronization, anti synchronization, projection synchronization, modified synchronization, function projection synchronization and modified function projection synchronization. The generalization function of a number of chaotic systems is projected synchronously. We propose an adaptive control method, and demonstrate its rationality by using the Lyapunov stability theory, and study the projection synchronization of the chaotic generalization function under the meaning of four reference systems, such as constant vector, function vector, hyperchaotic system and hyperchaotic system with unknown parameters. The true results confirm the effectiveness of the control strategy.2. based on three necessary conditions for the generation of hyperchaotic systems. On the basis of the Lorenz system, a hyperchaotic system with convergent straight lines is constructed. We have studied the system's dissipation, equilibrium point, bifurcation diagram, Lyapunov index, Lyapunov dimension and Poincare cross section. The system has only one equilibrium point, and points out that under certain parameter conditions, the system presents the dynamic state of periodic, quasi periodic, chaotic and hyperchaos. In the larger parameter range, this system is hyperchaotic. We propose an active variable theory for the projection synchronization of the generalization function when the hyperchaotic system with the structure is uncertain. The domain adaptive fuzzy control method is simulated with the hyperchaotic Liu system as a reference system. The results confirm the effectiveness of the control strategy.3. by adding a feedback item over the second equations of the Loreng system. We construct a four dimensional autonomous system with three equilibrium points. The dissipation and existence of the attractor are analyzed. The nonlinear characteristics of the equilibrium point, the bifurcation diagram, the Lyapunov exponent and so on. Through the Lyapun ov exponent spectrum, it is found that the system has rich dynamic characteristics. In a large range of parameter changes, the system is hyperchaotic. For the generalization function projection synchronization with uncertain chaotic systems, we propose a fast terminal sliding mode controller. Method. Using the new hyperchaotic system and hyperchaotic Chen system as the driving system and the response system respectively, the simulation of the projection synchronization of its generalization function is studied. The results prove that the effectiveness of the control method.4. is a chaotic system with polynomial on the right end. Through the analysis of the HX equations, it is found that such HX equations are not all variable coefficients, and even some system HX equations are the same as those of the original chaotic system. For the HX equations of the chaotic (hyperchaos) system, if it is a variable coefficient, the universal compel of the fuzzy system is chaotic (hyperchaos) under proper fuzzy division. The system is called HX chaotic (hyperchaos) system. In this way, we can get new chaotic (hyperchaos) system through the existing chaotic system. We can change the coefficients of the HX chaotic (hyperchaos) system by simply changing the fuzzy partition to realize the chaotic switching. We get the method of combining the exact T-S fuzzy modeling by piece by piece. To the exact T-S fuzzy model of the four dimensional HX hyperchaotic system, the piecewise application parallel distribution compensation (PDC) technology is used to realize the generalization function projection synchronization.5. of HX hyperchaos system, which takes into account the objective existence of time delay in the real control project. We propose the concept of the delay synchronization of the generalization function. This extends the modified function extension. The application scope of the delayed projection synchronization and the generalization function projection is more extensive. The active sliding mode control method and the active fuzzy sliding mode control method are applied to the generalization function projection delay synchronization with the non research hyperchaos system respectively.
【學位授予單位】：大連理工大學
【學位級別】：博士
【學位授予年份】：2015
【分類號】：O415.5;O231

【參考文獻】

相關期刊論文 前10條

1 張保杰;李洪興;;模糊控制系統(tǒng)建模的一種線性化方法[J];模糊系統(tǒng)與數(shù)學;2015年03期

2 金運國;鐘守銘;安娜;;Function projective synchronization between two different complex networks with correlated random disturbances[J];Chinese Physics B;2015年04期

3 王立明;唐永光;柴永泉;吳峰;;Generalized projective synchronization of the fractional-order chaotic system using adaptive fuzzy sliding mode control[J];Chinese Physics B;2014年10期

4 楊文光;韓元良;;自治Lienard系統(tǒng)邊緣線性化簡化HX表示[J];華北科技學院學報;2014年05期

5 王莎;于永光;王虎;Ahmed Rahmani;;Function projective lag synchronization of fractional-order chaotic systems[J];Chinese Physics B;2014年04期

6 袁學海;李洪興;楊雪;;基于模糊變換的模糊系統(tǒng)和模糊推理建模法[J];電子學報;2013年04期

7 方潔;胡智宏;江泳;;耦合混沌系統(tǒng)自適應修正函數(shù)投影同步[J];信息與控制;2013年01期

8 趙緯經(jīng);李洪興;;自治Lienard系統(tǒng)的簡化HX方法[J];模糊系統(tǒng)與數(shù)學;2013年01期

9 李春來;禹思敏;羅曉曙;;一個新的混沌系統(tǒng)的構建與實現(xiàn)[J];物理學報;2012年11期

10 李建芬;李農(nóng);;一類混沌系統(tǒng)的修正函數(shù)投影同步[J];物理學報;2011年08期

相關博士學位論文 前2條

1 陳玉明;基于Lorenz型系統(tǒng)的四維超混沌系統(tǒng)的復雜動力學研究[D];華南理工大學;2014年

2 方潔;混沌修正函數(shù)投影同步控制與應用研究[D];南京航空航天大學;2012年

相關碩士學位論文 前1條

1 唐潔;超混沌系統(tǒng)設計及其性能分析[D];南京航空航天大學;2007年

，

本文編號：2099794