畢業(yè)論文 混沌系統(tǒng)控制與同步若干問題的研究.doc
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畢業(yè)論文 混沌系統(tǒng)控制與同步若干問題的研究,摘要混沌運動是自然界中客觀存在的、最終有界的、有一定隨機規(guī)則的、非常復(fù)雜的運動形式。近十幾年來，混沌科學(xué)與其它科學(xué)互相滲透，在工程領(lǐng)域、智能信息處理、計算科學(xué)、通訊領(lǐng)域、生命科學(xué)和社會經(jīng)濟等領(lǐng)域有著廣泛的應(yīng)用前景，混沌控制與混沌同步控制成為了非線性科學(xué)中的研究熱點。但混沌控制及混沌同步理論尚不完善，許多混沌控制及同步方...
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摘 要
混沌運動是自然界中客觀存在的、最終有界的、有一定隨機規(guī)則的、非常復(fù)雜的運動形式。近十幾年來，混沌科學(xué)與其它科學(xué)互相滲透，在工程領(lǐng)域、智能信息處理、計算科學(xué)、通訊領(lǐng)域、生命科學(xué)和社會經(jīng)濟等領(lǐng)域有著廣泛的應(yīng)用前景，混沌控制與混沌同步控制成為了非線性科學(xué)中的研究熱點。但混沌控制及混沌同步理論尚不完善，許多混沌控制及同步方法有待進一步發(fā)掘，如何設(shè)計簡單實用的控制器需要進一步研究。本文針對混沌系統(tǒng)控制（包括同步控制）的一些問題進行研究，主要包括以下幾個方面：
1. 由于受系統(tǒng)物理器件的限制，混沌系統(tǒng)的線性輸入不可避免的存在干擾，從而引起線性輸入變成非線性輸入。運用滑?？刂品椒?，嚴(yán)格證明了混沌系統(tǒng)在非線性輸入和兩種情況的外部干擾（即匹配擾動和非匹配擾動）下實現(xiàn)穩(wěn)定控制，改進和推廣了一些現(xiàn)有文獻中僅限于無擾動或匹配擾動，得到了更系統(tǒng)的結(jié)論。
2. 根據(jù)二階滑模的概念和Lyapunov函數(shù)穩(wěn)定性理論，針對一類帶有非匹配外部擾動的混沌系統(tǒng)，提出了非奇異二階滑模控制方法，不僅使得混沌的狀態(tài)向量趨近到平衡點附近的鄰域，而且抖動現(xiàn)象得到消除。數(shù)值仿真驗證其優(yōu)于現(xiàn)有一些文獻的方法。
3. 通過引入一個非線性狀態(tài)反饋控制器到一類三維混沌系統(tǒng)，產(chǎn)生一新的四維系統(tǒng)，運用Lyapunov指數(shù)對該系統(tǒng)進行分岔分析，驗證其結(jié)構(gòu)具有超混沌行為，再運用反饋控制方法和脈沖控制方法對其進行穩(wěn)定性控制。
4. 討論混沌系統(tǒng)的修正投影同步問題，分兩種情況，一是混沌系統(tǒng)出現(xiàn)參數(shù)不確定項，外部擾動和帶有死區(qū)非線性輸入的修正投影同步；二是混沌系統(tǒng)的外部擾動產(chǎn)生于未知外源系統(tǒng)的修正投影同步，并給出了相應(yīng)的數(shù)值仿真，證實了所提出控制策略的有效性。
5. 討論一類含有傳遞信號混沌系統(tǒng)的估計問題，基于觀測器方法和自適應(yīng) 同步相關(guān)概念，視混沌系統(tǒng)的傳遞信號為系統(tǒng)外在的狀態(tài)變量，以可測的輸出向量構(gòu)建狀態(tài)觀測器，通過設(shè)置合適的條件，減小外在擾動和未知參數(shù)的影響，使得觀測器的估計誤差狀態(tài)實現(xiàn)自適應(yīng) 同步，從而估計傳遞信號的相關(guān)信息。
6. 對全文工作進行了總結(jié)，并對以后進一步的工作進行了展望。
關(guān)鍵詞：混沌系統(tǒng)， Lyapunov函數(shù)，滑模面，穩(wěn)定性，同步，觀測器 ，滑?？刂?br>
ABSTRACT
Chaos is a very complex motion with definite stochastic rules and a final bound in nature. In recent years, chaos is widely applied to engineering, intelligent information processing, computational science, communications, life sciences, socio-economic areas and so on. The control and synchr- onization of chaos become a hot issue of study in nonlinear science. However, the theories of control and synchronization for chaos systems are not perfect enough. The methods for the control and synchronization of chaos systems need to be further investigation, for example, to design simple and effective controllers. In this thesis, some problems in control and parameter identification of chaos systems are studied. The main work and research results are as follows:
1. Due to the limitations of physical devices, there exists the inevitable interference in linear input so that causes the linear input into the nonlinear input. Using sliding mode control, The proof of the chaotic systems to be realized stable under the effection of two different dirturbance (ie, matched the external dirtuebance and unmatched external dirturbance) is strictly proved. It improves and extends the results in existing literature that only to discuss the case that no disturbance or matching external disturbance and get more general conclusions.
2. According to the concept of second-order sliding mode and the stability theory of Lyapunov function, the stabilization for a class of chaotic systems with unmatiched external disturbances is investigated. Using non-sigular second-order sliding mode control approach, makes the state of chaotic system converge to the neighborhood of the equilibrium point and the chattering phenomenon has been eliminated. Numerical simulations show its better than the existing method of some literatures.
3. By introducing a nonlinear state feedback controller into a three-dimensional chaotic system to produce a new 4D system. Basic bifurcation analysis of the new system is investigated by means of Lyapunov exponent spectrum and bifurcation diagrams. This can verify the system has hyperchaotic behavior. Feedback control and implusive control approaches are employed here to stabilize the new hyperchaotic system.
4. Discuss the modified projective synchronization of chaotic systems under two conditions, one is that the chaotic systems suffers parameter uncertainty, external disturbance and dead-zone nonlinear input; the orther is that the disturbances of chaotic systems generate the unknown exogenous systems. The corresponding numerical simulation show the effectiveness of proposed methods.
5. Discuss a class of chaotic systems with transimitted signal. Based on the concepts of observer and adaptive synchronization, taking the transimitted signal as an external system state and designing an observer by using the measured output to estimate the state and transimitted signal. By setting the suitable conditions to reduce the influence of the external disturbance and unknown parameters so that estimation error of the observer can achieve adaptive synchronization. Then, the transmitted signal can be..
混沌運動是自然界中客觀存在的、最終有界的、有一定隨機規(guī)則的、非常復(fù)雜的運動形式。近十幾年來，混沌科學(xué)與其它科學(xué)互相滲透，在工程領(lǐng)域、智能信息處理、計算科學(xué)、通訊領(lǐng)域、生命科學(xué)和社會經(jīng)濟等領(lǐng)域有著廣泛的應(yīng)用前景，混沌控制與混沌同步控制成為了非線性科學(xué)中的研究熱點。但混沌控制及混沌同步理論尚不完善，許多混沌控制及同步方法有待進一步發(fā)掘，如何設(shè)計簡單實用的控制器需要進一步研究。本文針對混沌系統(tǒng)控制（包括同步控制）的一些問題進行研究，主要包括以下幾個方面：
1. 由于受系統(tǒng)物理器件的限制，混沌系統(tǒng)的線性輸入不可避免的存在干擾，從而引起線性輸入變成非線性輸入。運用滑?？刂品椒?，嚴(yán)格證明了混沌系統(tǒng)在非線性輸入和兩種情況的外部干擾（即匹配擾動和非匹配擾動）下實現(xiàn)穩(wěn)定控制，改進和推廣了一些現(xiàn)有文獻中僅限于無擾動或匹配擾動，得到了更系統(tǒng)的結(jié)論。
2. 根據(jù)二階滑模的概念和Lyapunov函數(shù)穩(wěn)定性理論，針對一類帶有非匹配外部擾動的混沌系統(tǒng)，提出了非奇異二階滑模控制方法，不僅使得混沌的狀態(tài)向量趨近到平衡點附近的鄰域，而且抖動現(xiàn)象得到消除。數(shù)值仿真驗證其優(yōu)于現(xiàn)有一些文獻的方法。
3. 通過引入一個非線性狀態(tài)反饋控制器到一類三維混沌系統(tǒng)，產(chǎn)生一新的四維系統(tǒng)，運用Lyapunov指數(shù)對該系統(tǒng)進行分岔分析，驗證其結(jié)構(gòu)具有超混沌行為，再運用反饋控制方法和脈沖控制方法對其進行穩(wěn)定性控制。
4. 討論混沌系統(tǒng)的修正投影同步問題，分兩種情況，一是混沌系統(tǒng)出現(xiàn)參數(shù)不確定項，外部擾動和帶有死區(qū)非線性輸入的修正投影同步；二是混沌系統(tǒng)的外部擾動產(chǎn)生于未知外源系統(tǒng)的修正投影同步，并給出了相應(yīng)的數(shù)值仿真，證實了所提出控制策略的有效性。
5. 討論一類含有傳遞信號混沌系統(tǒng)的估計問題，基于觀測器方法和自適應(yīng) 同步相關(guān)概念，視混沌系統(tǒng)的傳遞信號為系統(tǒng)外在的狀態(tài)變量，以可測的輸出向量構(gòu)建狀態(tài)觀測器，通過設(shè)置合適的條件，減小外在擾動和未知參數(shù)的影響，使得觀測器的估計誤差狀態(tài)實現(xiàn)自適應(yīng) 同步，從而估計傳遞信號的相關(guān)信息。
6. 對全文工作進行了總結(jié)，并對以后進一步的工作進行了展望。
關(guān)鍵詞：混沌系統(tǒng)， Lyapunov函數(shù)，滑模面，穩(wěn)定性，同步，觀測器 ，滑?？刂?br>
ABSTRACT
Chaos is a very complex motion with definite stochastic rules and a final bound in nature. In recent years, chaos is widely applied to engineering, intelligent information processing, computational science, communications, life sciences, socio-economic areas and so on. The control and synchr- onization of chaos become a hot issue of study in nonlinear science. However, the theories of control and synchronization for chaos systems are not perfect enough. The methods for the control and synchronization of chaos systems need to be further investigation, for example, to design simple and effective controllers. In this thesis, some problems in control and parameter identification of chaos systems are studied. The main work and research results are as follows:
1. Due to the limitations of physical devices, there exists the inevitable interference in linear input so that causes the linear input into the nonlinear input. Using sliding mode control, The proof of the chaotic systems to be realized stable under the effection of two different dirturbance (ie, matched the external dirtuebance and unmatched external dirturbance) is strictly proved. It improves and extends the results in existing literature that only to discuss the case that no disturbance or matching external disturbance and get more general conclusions.
2. According to the concept of second-order sliding mode and the stability theory of Lyapunov function, the stabilization for a class of chaotic systems with unmatiched external disturbances is investigated. Using non-sigular second-order sliding mode control approach, makes the state of chaotic system converge to the neighborhood of the equilibrium point and the chattering phenomenon has been eliminated. Numerical simulations show its better than the existing method of some literatures.
3. By introducing a nonlinear state feedback controller into a three-dimensional chaotic system to produce a new 4D system. Basic bifurcation analysis of the new system is investigated by means of Lyapunov exponent spectrum and bifurcation diagrams. This can verify the system has hyperchaotic behavior. Feedback control and implusive control approaches are employed here to stabilize the new hyperchaotic system.
4. Discuss the modified projective synchronization of chaotic systems under two conditions, one is that the chaotic systems suffers parameter uncertainty, external disturbance and dead-zone nonlinear input; the orther is that the disturbances of chaotic systems generate the unknown exogenous systems. The corresponding numerical simulation show the effectiveness of proposed methods.
5. Discuss a class of chaotic systems with transimitted signal. Based on the concepts of observer and adaptive synchronization, taking the transimitted signal as an external system state and designing an observer by using the measured output to estimate the state and transimitted signal. By setting the suitable conditions to reduce the influence of the external disturbance and unknown parameters so that estimation error of the observer can achieve adaptive synchronization. Then, the transmitted signal can be..
