【摘要】：分?jǐn)?shù)階微積分理論可以追溯到十七世紀(jì),由于其在科學(xué)與技術(shù)領(lǐng)域的廣泛應(yīng)用,使得分?jǐn)?shù)階微積分在二十世紀(jì)得到了全面的發(fā)展。另一方面,混沌作為非線性動力學(xué)系統(tǒng)的一種特有運(yùn)動形式,在物理、金融以及生命科學(xué)等眾多領(lǐng)域受到了廣泛的關(guān)注和研究。由于分?jǐn)?shù)階混沌的動力學(xué)行為和系統(tǒng)階次緊密關(guān)聯(lián)且具有一定的歷史記憶特性,所以動力學(xué)特性往往比整數(shù)階混沌系統(tǒng)更為復(fù)雜,在圖像處理和保密通信等領(lǐng)域的應(yīng)用前景非常廣闊。近年來,隨著計算機(jī)技術(shù)的迅猛發(fā)展,越來越多的研究者針對分?jǐn)?shù)階混沌系統(tǒng)的控制與同步問題展開了研究,但由于相關(guān)研究起步較晚,所以相關(guān)理論體系和技術(shù)還亟需進(jìn)一步的完善。因此,本論文將在前人工作的基礎(chǔ)上,進(jìn)一步研究分?jǐn)?shù)階混沌系統(tǒng)的控制、同步及其應(yīng)用問題。具體內(nèi)容和已取得的研究結(jié)果簡要敘述如下:首先,針對分?jǐn)?shù)階混沌系統(tǒng)的控制問題,提出了兩種不同的控制策略。一種是針對分?jǐn)?shù)階統(tǒng)一混沌系統(tǒng),研究了非脆弱模糊控制;另一種是針對一類分?jǐn)?shù)階非線性系統(tǒng),研究了有限時間鎮(zhèn)定問題。數(shù)值仿真驗證了所提方法對于解決分?jǐn)?shù)階混沌系統(tǒng)鎮(zhèn)定問題的有效性。其次,針對分?jǐn)?shù)階混沌系統(tǒng)的同步問題,提出了兩種不同的同步策略。一種是針對三個結(jié)構(gòu)相同階次相同的分?jǐn)?shù)階混沌和超混沌系統(tǒng),研究了模糊自適應(yīng)函數(shù)組合投影同步問題;另一種是針對兩個異結(jié)構(gòu)異階次分?jǐn)?shù)階混沌系統(tǒng),研究了基于主動控制的自適應(yīng)投影同步問題。數(shù)值仿真驗證了所提方法的有效性。最后,基于所提出的同步策略,設(shè)計了一種基于異結(jié)構(gòu)異階次分?jǐn)?shù)階混沌系統(tǒng)同步的混沌保密通信方案。該方案不僅能夠有效的實(shí)現(xiàn)信息傳輸而且進(jìn)一步提高了通信的安全性。利用正弦函數(shù)和方波信號作為有用信號對基于分?jǐn)?shù)階混沌同步的保密通信方案進(jìn)行了仿真驗證,結(jié)果表明了所提保密通信方案的有效性。
[Abstract]:Fractional calculus can be traced back to the seventeenth Century. Because of its extensive application in the field of science and technology, fractional calculus has been developed in a comprehensive way in twentieth Century. On the other hand, chaos is a unique form of motion of nonlinear dynamic systems, in many fields, such as physics, finance and life science. The dynamic behavior of fractional order chaos is more complex than integer order chaotic system because of the dynamic behavior of fractional chaos and the order of system order. So the application prospect in image processing and secure communication is very broad. In recent years, with the rapid development of computer technology More and more researchers have studied the control and synchronization of fractional chaotic systems, but because of the late start of the related research, the relevant theoretical system and technology need to be further improved. Therefore, this paper will further study the control, synchronization and synchronization of fractional chaotic systems on the basis of previous work. The specific content and the results obtained are briefly described as follows: firstly, two different control strategies are proposed for the control problem of fractional order chaotic systems. One is to study the non fragile fuzzy control for a fractional order unified chaotic system, and the other is for a class of fractional nonlinear systems. Time stabilization problem. Numerical simulation shows the effectiveness of the proposed method for solving the stabilization problem of fractional order chaotic systems. Secondly, two different synchronization strategies are proposed for the synchronization of fractional order chaotic systems. One is a fractional order chaos and hyperchaotic system with the same order of the same order of three structures, and the fuzzy self is studied. The adaptive projection synchronization problem is adapted to the combination of functions. The other is an adaptive projection synchronization problem based on active control for two different order fractional order chaotic systems. Numerical simulation shows the effectiveness of the proposed method. Finally, based on the proposed synchronization strategy, a kind of different order fractional order chaos is set up. The system synchronization chaotic secure communication scheme. This scheme not only can effectively carry out information transmission but further improve the security of communication. Using sinusoidal and square wave signals as useful signals, the simulation verification of secure communication scheme based on fractional chaotic synchronization is carried out. The results show that the proposed secure communication scheme is proposed. Validity.
【學(xué)位授予單位】：河南科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O415.5;O231

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