發(fā)布時(shí)間：2018-07-05 09:45

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

【摘要】：混沌系統(tǒng)具有復(fù)雜而獨(dú)特的動(dòng)力學(xué)特征,其在許多科學(xué)領(lǐng)域都有著很大的應(yīng)用潛力.目前對(duì)混沌同步控制的研究已成為國(guó)際上的熱點(diǎn).其中混沌投影同步是一種重要的同步方式,實(shí)現(xiàn)同步時(shí),驅(qū)動(dòng)系統(tǒng)狀態(tài)與響應(yīng)系統(tǒng)狀態(tài)依某比例因子演化.國(guó)內(nèi)外許多學(xué)者將比例因子擴(kuò)展成對(duì)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(kuò)展增大了投影同步的適用范圍,增強(qiáng)了其應(yīng)用的靈活性.本文考慮驅(qū)動(dòng)系統(tǒng)和響應(yīng)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(yīng)用自適應(yīng)控制方法實(shí)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(duì)混沌系統(tǒng)存在不確定性時(shí)的泛化函數(shù)投影同步問(wèn)題,分別設(shè)計(jì)了主動(dòng)變論域自適應(yīng)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(yīng)用并行分布補(bǔ)償技術(shù)實(shí)現(xiàn)了其泛化函數(shù)投影同步.考慮到時(shí)間延遲的存在,提出了泛化函數(shù)投影延遲同步的概念,并給出了積分滑模控制策略.具體工作及結(jié)果總結(jié)如下：1.考慮到驅(qū)動(dòng)系統(tǒng)和響應(yīng)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(jìn)一步推廣了混沌投影同步的概念.這種“位移”是由一個(gè)參考系統(tǒng)的狀態(tài)來(lái)表示的.這個(gè)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(guò)調(diào)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(duì)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(yīng)控制方法,并采用Lyapunov穩(wěn)定性理論論證了其合理性,分別對(duì)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(jìn)行研究.仿真結(jié)果證實(shí)了控制策略的有效性.2.基于產(chǎn)生超混沌系統(tǒng)的三個(gè)必要條件,在Lorenz系統(tǒng)基礎(chǔ)上構(gòu)造了一個(gè)具有收斂直線的超混沌系統(tǒng).我們對(duì)該系統(tǒng)的耗散性、平衡點(diǎn)、分岔圖、Lyapunov指數(shù)、Lyapunov維數(shù)及Poincare截面等進(jìn)行了研究,指出該系統(tǒng)僅有一個(gè)平衡點(diǎn),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(dòng)力學(xué)性態(tài).在較大的參數(shù)區(qū)間內(nèi),這個(gè)系統(tǒng)是超混沌的.針對(duì)構(gòu)造的超混沌系統(tǒng)帶有不確定性時(shí)的泛化函數(shù)投影同步問(wèn)題,我們提出了主動(dòng)變論域自適應(yīng)模糊控制方法.以超混沌Liu系統(tǒng)作為參考系統(tǒng)進(jìn)行仿真,結(jié)果證實(shí)了控制策略的有效性.3.通過(guò)在Loreng系統(tǒng)的第二個(gè)方程之上增加一個(gè)反饋?lái)?xiàng),我們構(gòu)造了一個(gè)有三個(gè)平衡點(diǎn)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(diǎn)、分岔圖、Lyapunov指數(shù)等非線性特征.通過(guò)Lyapun ov指數(shù)譜可以發(fā)現(xiàn)該系統(tǒng)具有豐富的動(dòng)態(tài)特性.在參數(shù)變化的一個(gè)大的范圍內(nèi),系統(tǒng)是超混沌的.對(duì)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(qū)動(dòng)系統(tǒng)和響應(yīng)系統(tǒng),對(duì)其泛化函數(shù)投影同步進(jìn)行仿真研究,結(jié)果證實(shí)了所述控制方法的有效性.4.對(duì)于右端為多項(xiàng)式的混沌系統(tǒng),我們采用逐項(xiàng)模糊推理建模再進(jìn)行線性疊加的方法,得到其HX方程組.通過(guò)分析,發(fā)現(xiàn)這樣的HX方程組并非每一項(xiàng)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(duì)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(wàn)能逼近性,在適當(dāng)?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(guò)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(guò)簡(jiǎn)單的改變模糊劃分來(lái)改變HX型混沌(超混沌)系統(tǒng)的系數(shù),實(shí)現(xiàn)混沌切換.我們通過(guò)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(yīng)用并行分布補(bǔ)償(PDC)技術(shù)實(shí)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(shí)控制工程中時(shí)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(yīng)用范圍更廣泛.分別應(yīng)用主動(dòng)滑�？刂品椒ê椭鲃�(dòng)模糊滑模控制方法對(duì)帶有不研究性超混沌系統(tǒng)的泛化函數(shù)投影延遲同步進(jìn)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(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2015
【分類號(hào)】：O415.5;O231

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