本文選題：分數(shù)階混沌系統(tǒng) + 變結構控制��； 參考：《東北石油大學》2017年碩士論文

【摘要】：在實際工程應用與現(xiàn)實生活中,廣泛的存在非線性現(xiàn)象,而在近年來,分數(shù)階混沌系統(tǒng)已經(jīng)成為非線性科學中的熱點問題。對于分數(shù)階混沌系統(tǒng)的同步控制是一種特殊的控制問題,在生物工程和信號安全等領域內具有潛在應用價值�；煦缋碚撛谠S多高精尖的領域中都有運用。分數(shù)階混沌系統(tǒng)同時兼具混沌系統(tǒng)和分數(shù)階動力學系統(tǒng)的特性,這個巨大的優(yōu)勢使得分數(shù)階混沌系統(tǒng)在混沌保密通信領域中占有一席之地。因此十分有必要對分數(shù)階混沌動態(tài)系統(tǒng)的同步與控制展開理論和應用方面的研究。本文結合分數(shù)階微積分理論,利用分數(shù)階穩(wěn)定性和Lyapunov穩(wěn)定性理論與性質,對于分數(shù)階混沌系統(tǒng)進行穩(wěn)定性分析,控制與同步研究,主要研究內容如下:1.研究混沌系統(tǒng),分數(shù)階微積分的概念以及分數(shù)階混沌系統(tǒng)的基本概念,研究滑模變結構控制的基本概念,并應用傳統(tǒng)滑模變結構控制方法及分數(shù)階微分方程的穩(wěn)定性理論,設計滑�？刂破鱽磉_成分數(shù)階Liu系統(tǒng)的同步。然后進行數(shù)值模擬,證明控制器的有效性。2.在分數(shù)階混沌系統(tǒng)和滑模變結構控制理論的基礎上,基于終端滑�？刂评碚�,設計了一種分數(shù)階非奇異終端滑模面,針對系統(tǒng)中存在未知邊界的擾動與不確定性設計了自適應控制器,使誤差系統(tǒng)在有限時間內到達平衡點,并應用Lyapunov穩(wěn)定性理論證明其穩(wěn)定性。運用Matlab-simulink對于三維分數(shù)階Chen混沌系統(tǒng)進行數(shù)值仿真;在不消除非線性項的情況下,設計了一種自適應滑�？刂破�,并證明了其穩(wěn)定性。最后對于四維分數(shù)階Lorenz系統(tǒng)進行數(shù)值仿真,證實了控制器的可行性。3.對分數(shù)階混沌系統(tǒng)所得到的誤差系統(tǒng)中的線性與非線性部分構建模型,對線性部分進行動態(tài)柔性變結構控制器的設計,而對于非線性部分則進行自適應滑�？刂破鞯脑O計,并運用分數(shù)階穩(wěn)定性和Lyapunov穩(wěn)定性理論證明控制器的穩(wěn)定性。最后分別對與三維分數(shù)階Chen系統(tǒng)進行仿真,證實了柔性變結構同步控制器的優(yōu)勢以及有效性。
[Abstract]:In practical engineering applications and in real life, there are widespread nonlinear phenomena, but in recent years, fractional chaotic systems have become a hot issue in nonlinear science. Synchronization control for fractional chaotic systems is a special control problem, which has potential application value in the fields of bioengineering and signal security. Chaos theory is applied in many sophisticated fields. Fractional chaotic systems have the characteristics of both chaotic systems and fractional order dynamical systems. This great advantage makes fractional chaotic systems have a place in the field of chaotic secure communication. Therefore, it is necessary to study the theory and application of synchronization and control of fractional chaotic dynamic systems. In this paper, the fractional order stability and Lyapunov stability theory are used to analyze, control and synchronize the fractional order chaotic system. The main contents of this paper are as follows: 1. The concepts of chaotic systems, fractional calculus and fractional chaotic systems are studied, and the basic concepts of sliding mode variable structure control are studied. The traditional sliding mode variable structure control method and the stability theory of fractional differential equations are applied. A sliding mode controller is designed to synchronize fractional-order Liu systems. Then numerical simulation is carried out to prove the effectiveness of the controller. 2. 2. Based on fractional chaotic system and sliding mode variable structure control theory, a fractional order nonsingular terminal sliding mode surface is designed based on terminal sliding mode control theory. An adaptive controller is designed for disturbances and uncertainties with unknown boundaries in order to make the error system reach the equilibrium point in a finite time. The Lyapunov stability theory is applied to prove its stability. Using Matlab-Simulink to simulate the three-dimensional fractional Chen chaotic system, an adaptive sliding mode controller is designed without eliminating the nonlinear term, and its stability is proved. Finally, the numerical simulation of the four-dimensional fractional Lorenz system proves the feasibility of the controller. The linear and nonlinear parts of the error system obtained from fractional chaotic systems are modeled, the dynamic flexible variable structure controller is designed for the linear part, and the adaptive sliding mode controller is designed for the nonlinear part. The stability of the controller is proved by the theory of fractional stability and Lyapunov stability. Finally, the simulation results with the three-dimensional fractional Chen system prove the advantages and effectiveness of the flexible variable structure synchronization controller.
【學位授予單位】：東北石油大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O415.5;TP273
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本文編號：2080359