本文選題：混沌反控制 + 超混沌系統(tǒng)��； 參考：《廣東工業(yè)大學(xué)》2017年博士論文

【摘要】：混沌作為20世紀(jì)物理學(xué)里輝煌的科學(xué)奇跡之一,引起了國內(nèi)外科學(xué)家們的廣泛關(guān)注�；煦绶纯刂�(混沌化)是混沌理論研究的重要課題,連續(xù)時(shí)間系統(tǒng)反控制取得了一些相關(guān)結(jié)果,但尚未形成具有普適性的系統(tǒng)理論,如何設(shè)計(jì)具有多個(gè)正李氏指數(shù)的超混沌系統(tǒng)依然是一個(gè)研究熱點(diǎn)課題。同時(shí),混沌系統(tǒng)具有初始值高度敏感性、有界性、偽隨機(jī)性等特點(diǎn),使得混沌系統(tǒng)在保密通信和信息加密設(shè)計(jì)上有顯著優(yōu)勢,適合于流密碼設(shè)計(jì)和應(yīng)用,因而如何設(shè)計(jì)基于混沌系統(tǒng)的密碼算法也是信息安全的重要研究方向。為此,本論文進(jìn)一步研究了動力系統(tǒng)混沌反控制方法和基于混沌系統(tǒng)的信息加密應(yīng)用,主要工作如下:1.研究了基于QR正交分解和SVD正交分解方法的兩種李氏指數(shù)(李雅普諾夫指數(shù))計(jì)算的改進(jìn)算法。離散時(shí)間系統(tǒng)李氏指數(shù)的特征值算法,理論上使用該算法計(jì)算李氏指數(shù)時(shí),迭代次數(shù)k越大,計(jì)算結(jié)果越準(zhǔn)確,并且極限也是存在的。然而,在實(shí)際的數(shù)值計(jì)算中,因計(jì)算機(jī)有限精度等原因,計(jì)算結(jié)果會出現(xiàn)數(shù)值溢出、無法識別、計(jì)算結(jié)果不準(zhǔn)確等問題,可以表述為如下三個(gè)方面:(1)迭代次數(shù)k不能過大,否則仿真結(jié)果將出現(xiàn)NaN或Inf的錯誤提示;(2)隨著迭代次數(shù)k增加,所有的計(jì)算結(jié)果將趨近于最大李氏指數(shù);(3)如果迭代次數(shù)k太小,將使得計(jì)算結(jié)果不準(zhǔn)確。最后,通過幾個(gè)實(shí)例來說明改進(jìn)算法的可行性和有效性。2.探討了一些高維超混沌系統(tǒng)的反控制理論和設(shè)計(jì)方法。首先,給出李氏指數(shù)算法定義的理論分析,進(jìn)而討論了正李氏指數(shù)與雅可比矩陣正實(shí)部特征根之間的定性關(guān)系,即受控系統(tǒng)配置越多具有正實(shí)部的特征根,則受控系統(tǒng)具有正李氏指數(shù)的個(gè)數(shù)也越多。因而,可通過設(shè)計(jì)受控系統(tǒng)雅可比矩陣具有正實(shí)部的特征根個(gè)數(shù)來解決正李氏指數(shù)的配置問題。最后,給出了兩個(gè)高維超混沌反控制例子。3.提出了構(gòu)造具有n-2個(gè)正李氏指數(shù)n維超混沌系統(tǒng)(無簡并超混沌系統(tǒng))的平均特征值準(zhǔn)則法。該方法由以下四個(gè)步驟組成:(1)設(shè)計(jì)一個(gè)漸近穩(wěn)定的標(biāo)稱系統(tǒng)并對其作相似變換,用一致有界的控制器和控制矩陣對相似變換后的標(biāo)稱系統(tǒng)進(jìn)行混沌反控制,得到一個(gè)軌道全局有界的受控系統(tǒng)。(2)通過控制器和控制矩陣的閉環(huán)極點(diǎn)配置,使得受控系統(tǒng)在兩類鞍焦平衡點(diǎn)處對應(yīng)的具有正實(shí)部的特征值個(gè)數(shù)分別滿足n-1和n-2。(3)在控制器的一個(gè)周期內(nèi),所有雅可比矩陣所對應(yīng)的平均特征值的正實(shí)部個(gè)數(shù)滿足n-2。(4)平均特征值正實(shí)部的最小值大于某個(gè)給定的閾值Th。最后,給出了若干典型實(shí)例,驗(yàn)證該方法的可行性和有效性。4.提出了具有多個(gè)控制器的高維無簡并超混沌系統(tǒng)構(gòu)造方法。首先,設(shè)計(jì)n維耗散的線性系統(tǒng),經(jīng)過變換矩陣的相似變換。其次,施加主控制器,并尋找主控制器的最佳控制位置和控制參數(shù),使得在主控制器的一個(gè)周期內(nèi),受控系統(tǒng)雅克比矩陣對應(yīng)的平均特征值的正實(shí)部個(gè)數(shù)為n-2,且平均特征值的最小正實(shí)部滿足某個(gè)給定的閾值條件。然后施加多個(gè)非主控制器,并預(yù)先給定控制參數(shù)和固定控制位置,從而生成軌道全局有界的受控系統(tǒng)。最后,給出了構(gòu)造具有多個(gè)控制器的高維無簡并超混沌系統(tǒng)兩個(gè)例子。5.設(shè)計(jì)了一個(gè)新的三維混沌動力系統(tǒng),并根據(jù)拓?fù)漶R蹄理論,利用計(jì)算機(jī)輔助證明該受控系統(tǒng)龐加萊截面映射存在一個(gè)不變緊集,使其拓?fù)浒牍曹椨?移位動力系統(tǒng)。同時(shí),基于該混沌系統(tǒng)設(shè)計(jì)了圖像加密方案。首先,根據(jù)混沌系統(tǒng)生成的偽隨機(jī)序列對圖像像素位置進(jìn)行置亂。然后,利用混沌流密碼對圖像像素進(jìn)行多輪加密,從而達(dá)到雙重加密效果。最后,給出了統(tǒng)計(jì)分析來說明該加密方案的安全性和可行性。6.研究了一種基于分?jǐn)?shù)階超混沌系統(tǒng)的圖像加密算法。首先,一個(gè)已知明文圖像用來對原始明文進(jìn)行像素混淆。然后利用分?jǐn)?shù)階超混沌系統(tǒng)生成的偽隨機(jī)序列對混淆后的圖像進(jìn)行加密。根據(jù)加密算法,得到了經(jīng)過置亂和擴(kuò)散后的加密圖像,該加密方案具有較好的安全性和加密效果。仿真實(shí)驗(yàn)驗(yàn)證了該加密方案的可行性,并給出一些統(tǒng)計(jì)測試說明該方案的安全性。
[Abstract]:Chaos, as one of the brilliant scientific wonders of physics in the twentieth Century, has aroused wide attention of scientists at home and abroad. Chaos anti control (chaos) is an important subject in the study of chaos theory. The inverse control of continuous time system has obtained some related results, but it has not yet formed a universal system theory and how to design a number of positive. The hyperchaotic system of Li's exponent is still a hot topic of research. At the same time, the chaotic system has the characteristics of high sensitivity, boundedness and pseudo randomness of the initial value, which makes the chaotic system have remarkable advantages in the design of secure communication and information encryption. It is suitable for the design and application of stream ciphers, so how to design the cipher based on the chaotic system The algorithm is also an important research direction of information security. Therefore, this thesis further studies the chaotic anti control method of power system and the information encryption application based on chaotic systems. The main work is as follows: 1. the improved algorithm for calculating two kinds of Liapunov exponents (Lyapunov exponents) based on QR orthogonal decomposition and SVD orthogonal decomposition method is studied. The eigenvalue algorithm of the Li's exponent of the scattered time system, when the algorithm is used to calculate the Li's exponent, the greater the number of iterations is k, the more accurate the calculation results are, and the limit also exists. However, in the actual numerical calculation, the numerical overflow will appear because of the limited accuracy of the computer and so on, the results are inaccurate and the results are inaccurate. The following three aspects can be expressed as following three aspects: (1) the number of iterations can not be too large, otherwise the result of the simulation will appear the error of NaN or Inf; (2) as the number of iterations increases, all calculation results will be close to the maximum Li's index; (3) if the number of iterations is too small, the calculation results will be inaccurate. Finally, through several examples .2. discusses the anti control theory and design method of some high dimensional super chaotic systems. First, we give the theoretical analysis of the definition of the Li's exponent algorithm, and then discuss the qualitative relation between the positive real part of the positive lie index and the real part of the Jacobi matrix, that is, the more the controlled system has the positive real part. With the characteristic root, the number of the controlled system with the positive lie index is also more. Therefore, the number of eigenvalues of the positive real part of the Jacobi matrix of the controlled system can be solved by designing the number of eigenvalues of the positive real part of the system. Finally, two high dimensional super chaotic anti control examples.3. are given to construct n-2 positive lie index n-dimensional hyperchaos. This method consists of four steps: (1) design an asymptotically stable nominal system and make a similar transformation. A uniform bounded controller and a control matrix are used to control the nominal system after the similar transformation, and a global boundedness of the orbit is obtained. (2) through the closed loop pole configuration of the controller and the control matrix, the number of eigenvalues of the controlled system with the positive real part corresponding to the two kind of saddle coke equilibrium point satisfies n-1 and n-2. (3) in one period of the controller, and the positive real number of the average eigenvalues corresponding to all Jacobi matrices satisfies the average characteristic of the n-2. (4). The minimum value of the positive real part is greater than a given threshold Th.. A number of typical examples are given to verify the feasibility and effectiveness of the method..4. proposes a construction method for high dimensional hyperchaotic systems with multiple controllers. First, a linear system with n-dimensional dissipation is designed, and the transformation of the transformation matrix is transformed. Secondly, master control is applied. The optimal control position and control parameters of the master controller are found, so that the number of positive real parts of the average eigenvalue of the Jacobian matrix of the controlled system is n-2 within a period of the main controller, and the minimum positive real part of the average eigenvalue satisfies a given threshold bar. The control system with fixed control parameters and fixed control position is made to generate the controlled system of orbit global bounded. Finally, two examples of high dimensional non simple hyperchaos system with multiple controllers,.5., are given to design a new three-dimensional chaotic dynamic system, and the controlled system Poincare is proved by computer aided according to the topology horse's hoof theory. The cross section mapping has an invariant compact set, which makes its topology semi conjugate to the 2 shift power system. At the same time, the image encryption scheme is designed based on the chaotic system. First, the image pixel position is scrambled according to the pseudo random sequence generated by the chaotic system. Then, the image pixels are encrypted by the chaotic stream density code, thus achieving the double image pixels. Finally, a statistical analysis is given to illustrate the security and feasibility of the encryption scheme..6. research an image encryption algorithm based on fractional hyperchaos system. First, a known plaintext image is used to confuse the original plaintext in pixels. According to the encryption algorithm, the encrypted image after the scrambling and spreading is obtained. The encryption scheme has good security and encryption effect. The simulation experiment verifies the feasibility of the encryption scheme, and gives some statistical tests to illustrate the security of the scheme.
【學(xué)位授予單位】：廣東工業(yè)大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2017
【分類號】：TP309.7;TP391.41

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本文編號：1956962