本文選題：復動力系統(tǒng)　切入點：混沌控制　出處：《山東大學》2014年博士論文　論文類型：學位論文

【摘要】：目前,復動力系統(tǒng)己廣泛地應(yīng)用到通信、金融、生物等多個學科中.復混沌系統(tǒng)就是一個典型的復動力系統(tǒng).自從1982年復Lorenz方程被提出以來,復混沌系統(tǒng)在物理學的許多領(lǐng)域發(fā)揮了重要作用,尤其是通信系統(tǒng).復變量增加了所傳輸信息的內(nèi)容并提高了安全性.復混沌系統(tǒng)的控制和同步成為混沌保密通信的熱點問題.因此,本文對復混沌系統(tǒng)的控制和同步及其在安全通信中的應(yīng)用進行了一系列基礎(chǔ)研究,其主要工作和創(chuàng)新點如下： 1.實混沌系統(tǒng)的控制與同步 對于連續(xù)系統(tǒng),提出了累積誤差控制器.該控制器采用了累積誤差的線性函數(shù),在實際工程上可由RC電路實現(xiàn).對于離散系統(tǒng),提出了誤差反饋矩陣控制.它類似于線性系統(tǒng)的狀態(tài)反饋,但是該矩陣是時變的,包含狀態(tài)變量的耦合信息,根據(jù)梯度下降法在線更新,并趨于一個恒定矩陣.結(jié)合變量間的耦合關(guān)系,本文還提出了部分矩陣控制和全矩陣控制.部分矩陣控制僅采用對部分變量的控制就實現(xiàn)全部變量達到期望值,易于工程實現(xiàn).但是,上述控制器只能實現(xiàn)不動點控制和自同步.因此,結(jié)合速度梯度法和非線性函數(shù)控制,本文實現(xiàn)了帶有未知參數(shù)的連續(xù)混沌系統(tǒng)的跟蹤任意有界參考信號和參數(shù)辨識. 2.復混沌系統(tǒng)的復比例因子投影同步與參數(shù)辨識 提出了復比例因子投影同步(CMPS).完全同步(CS),反同步(AS),投影同步(PS)和修正投影同步(MPS)都是CMPS的特殊情況,因此它包含了以前的工作并進行推廣.考慮到復混沌系統(tǒng)的未知參數(shù)和有界干擾的各種可能情形,本文設(shè)計了帶有收斂因子和動態(tài)控制力量CMPS控制器；同時基于可持續(xù)激勵和線性獨立給出了參數(shù)收斂到真值的充分條件和必要條件,給出了改變比例因子的方法以辨識出參數(shù)真值.另外,CMPS在實混沌系統(tǒng)和復混沌系統(tǒng)之間建立同步聯(lián)接.因此,本文首次討論了實混沌系統(tǒng)和復混沌系統(tǒng)的復比例因子投影同步,基于速度梯度法設(shè)計了包含偽梯度條件的同步控制器. 3.復混沌系統(tǒng)的復函數(shù)同步及其通信方案 提出復函數(shù)投影同步(CFPS). CS, AS, PS, MPS,全狀態(tài)組合投影同步(FSHPS),函數(shù)投影同步(FPS),修正函數(shù)投影同步(MFPS),廣義函數(shù)投影同步(GFPS)和CMPS都是CFPS的特殊情形.CFPS幾乎沒有被研究過,而且將包括大部分存在的同步情形.針對帶有未知參數(shù)的復混沌系統(tǒng),設(shè)計了CFPS控制器,并針對耦合復混沌系統(tǒng),設(shè)計了基于CFPS的通信方案.該通信方案本質(zhì)上是混沌掩蓋,但是所傳輸?shù)男盘柺切畔⑿盘?作為復比例函數(shù))與混沌信號積的導數(shù).因為復比例函數(shù)比實函數(shù)更加不可預測和復雜,則入侵者從傳輸信號中提取信息的可能性更小. 4.復混沌系統(tǒng)的差函數(shù)投影同步及其通信方案 從兩復函數(shù)相減的角度提出了差函數(shù)投影同步(DFPS),自同步和相位同步均是其特殊情形.設(shè)計了DFPS控制器,并將其應(yīng)用到耦合復混沌系統(tǒng)中,提出了基于DFPS的通信方案.該通信方案本質(zhì)上仍是混沌掩蓋,但是所傳輸?shù)男盘柺切畔⑿盘柡突煦缧盘柕暮偷膶?shù).它避免了CFPS中由于驅(qū)動系統(tǒng)狀態(tài)(作為除數(shù))接近零時產(chǎn)生的算法誤差. 5.時滯復混沌系統(tǒng)的自時滯同步及其通信方案 提出了復混沌系統(tǒng)的自時滯同步(STDS),它是自同步的擴展,進一步拓寬了同步問題的視野,并避免了因時滯而產(chǎn)生的各種問題.時滯復混沌系統(tǒng)能產(chǎn)生高度隨機性和不可預測性的時間序列,應(yīng)用在混沌保密通信中能夠提高保密性能.因此,本文研究了時滯復Lorenz系統(tǒng)的混沌特性,并設(shè)計控制器實現(xiàn)了時滯復Lorenz系統(tǒng)的自時滯同步.針對耦合時滯復混沌系統(tǒng),給出了基于STDS的通信方案.該通信方案考慮了信息傳輸中產(chǎn)生的時滯,更接近實際情況,時滯復混沌系統(tǒng)也進一步增強了保密效果. 綜上所述,本文圍繞復動力系統(tǒng)的混沌控制與同步及其在通信中的應(yīng)用展開了研究,提出了復比例因子投影同步,復函數(shù)投影同步,差函數(shù)投影同步及自時滯同步等概念,并將復變量引入到混沌通信中,促進了復動力系統(tǒng)的發(fā)展,為進一步加強通信安全提供了理論依據(jù).
[Abstract]:At present, the complex dynamic system has been widely applied to communications, finance, biology and other disciplines. More complex chaotic system is a typical complex dynamic system. Since 1982 the complex Lorenz equation is proposed, the chaotic system has played an important role in many areas of physics, especially the complex variable increase communication system. The transmission of information content and improve security. The complex control and synchronization of the chaotic systems has become a hot issue of chaotic secure communication. Therefore, the control of complex chaotic system and synchronization and its application in secure communication of a series of basic research, the main work and innovation are as follows:
Control and synchronization of 1. real chaotic systems
For the continuous system, put forward the cumulative error controller. The controller uses a linear function of accumulated error in practical engineering can be realized by the RC circuit. For the discrete system, put forward the error feedback control matrix. It is similar to the linear system state feedback, but the matrix is time-varying, contains the coupling information of state variables according to the gradient descent method, online updates, and tends to be a constant matrix. Combined with the coupling relationship between the variables, this paper also put forward the part matrix control and full matrix control. Some matrix control using only part of the control variables on all variables reached expectations, easy to realize. However, the controller can only control and self synchronization of the fixed point. Therefore, combined with the velocity gradient method and nonlinear control function, this paper realizes continuous chaotic system with unknown parameters tracking arbitrary bounded reference letter Number and parameter identification.
Complex proportional factor projection synchronization and parameter identification of 2. complex chaotic systems
The complex scaling factor of projective synchronization (CMPS) (CS). The complete synchronization, anti synchronization, projective synchronization (AS) (PS) and modified projective synchronization (MPS) is a special case of CMPS, so it contains the previous work and promotion. Considering the unknown parameters of chaotic systems and complex all the possible interference, this paper designed a convergence factor and dynamic power control CMPS controller; at the same time, sustainable motivation and linear independence parameters converge to the true value of the sufficient conditions and necessary conditions are given based on the proposed change scale factor to identify the true value of the parameters. In addition, the establishment of synchronous connection between CMPS chaotic systems and complex chaotic system. Therefore, this paper first discusses the complex chaotic systems and complex real projective synchronization of chaotic systems, based on the velocity gradient method to design the synchronization controller contains pseudo gradient conditions.
Complex function synchronization of 3. complex chaotic systems and its communication scheme
The complex function projective synchronization (CFPS). CS, AS, PS, MPS, a combination of full state projective synchronization (FSHPS), function projective synchronization (FPS), modified function projective synchronization (MFPS), the generalized function projective synchronization (GFPS) and CMPS CFPS are the special cases of.CFPS have been little studied, and most will include synchronization scenarios exist. For complex chaotic systems with unknown parameters, a CFPS controller is designed, and the complex coupled chaotic systems, designs the communication scheme based on CFPS. The communication scheme is essentially chaotic signal, but the transmission of information signals (as complex function) derivative and chaos signal product. Because the more unpredictable than real function and complex complex function, is less likely to extract information from the signal transmission.
Differential projection synchronization and communication scheme for 4. complex chaotic systems
From the two points of complex function subtraction difference function projective synchronization (DFPS), self synchronization and phase synchronization are its special cases. DFPS controller is designed, and its application to complex coupled chaotic systems, proposes a communication scheme based on DFPS. The communication scheme is essentially chaotic, but signal transmission is a derivative information signal and chaotic signal. And it avoids CFPS due to driving system state (as close to zero divisor) algorithm error generated.
Self time delay synchronization and communication scheme for 5. time delay complex chaotic systems
The complex chaotic system of self synchronization of time delay (STDS), it is a self synchronous expansion, to further expand the synchronization problem of vision, and to avoid the problems caused by time delay. Delay complex chaotic system can produce highly random and unpredictable time series should be used, can improve the security performance in the chaotic secure communication. Therefore, the chaotic characteristics are studied in this paper with complex Lorenz system, self synchronization of time delay and time delay controller is designed to realize the complex Lorenz system. Aiming at the complex chaotic system coupling delay, gives the communication scheme based on STDS. The communication scheme considering the delay of information transmission, closer to the actual situation. Complex chaotic systems with time delay but also further enhance the security effect.
To sum up, this paper focuses on the complex dynamic system synchronization control and its application in communication research, the complex scaling factor of projective synchronization, synchronization of complex function projection difference function projective synchronization and self synchronization of time delay concepts and complex variables into chaotic communication, promote the development of complex dynamic system. To provide a theoretical basis for further strengthening the communication security.

【學位授予單位】：山東大學
【學位級別】：博士
【學位授予年份】：2014
【分類號】：TN918;O415.5

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本文編號：1626198