發(fā)布時(shí)間：2018-06-29 02:09

  本文選題：分?jǐn)?shù)階混沌系統(tǒng) + 變結(jié)構(gòu)控制�。� 參考：《東北石油大學(xué)》2017年碩士論文

【摘要】：在實(shí)際工程應(yīng)用與現(xiàn)實(shí)生活中,廣泛的存在非線性現(xiàn)象,而在近年來(lái),分?jǐn)?shù)階混沌系統(tǒng)已經(jīng)成為非線性科學(xué)中的熱點(diǎn)問(wèn)題。對(duì)于分?jǐn)?shù)階混沌系統(tǒng)的同步控制是一種特殊的控制問(wèn)題,在生物工程和信號(hào)安全等領(lǐng)域內(nèi)具有潛在應(yīng)用價(jià)值�；煦缋碚撛谠S多高精尖的領(lǐng)域中都有運(yùn)用。分?jǐn)?shù)階混沌系統(tǒng)同時(shí)兼具混沌系統(tǒng)和分?jǐn)?shù)階動(dòng)力學(xué)系統(tǒng)的特性,這個(gè)巨大的優(yōu)勢(shì)使得分?jǐn)?shù)階混沌系統(tǒng)在混沌保密通信領(lǐng)域中占有一席之地。因此十分有必要對(duì)分?jǐn)?shù)階混沌動(dòng)態(tài)系統(tǒng)的同步與控制展開(kāi)理論和應(yīng)用方面的研究。本文結(jié)合分?jǐn)?shù)階微積分理論,利用分?jǐn)?shù)階穩(wěn)定性和Lyapunov穩(wěn)定性理論與性質(zhì),對(duì)于分?jǐn)?shù)階混沌系統(tǒng)進(jìn)行穩(wěn)定性分析,控制與同步研究,主要研究?jī)?nèi)容如下:1.研究混沌系統(tǒng),分?jǐn)?shù)階微積分的概念以及分?jǐn)?shù)階混沌系統(tǒng)的基本概念,研究滑模變結(jié)構(gòu)控制的基本概念,并應(yīng)用傳統(tǒng)滑模變結(jié)構(gòu)控制方法及分?jǐn)?shù)階微分方程的穩(wěn)定性理論,設(shè)計(jì)滑�？刂破鱽�(lái)達(dá)成分?jǐn)?shù)階Liu系統(tǒng)的同步。然后進(jìn)行數(shù)值模擬,證明控制器的有效性。2.在分?jǐn)?shù)階混沌系統(tǒng)和滑模變結(jié)構(gòu)控制理論的基礎(chǔ)上,基于終端滑�？刂评碚�,設(shè)計(jì)了一種分?jǐn)?shù)階非奇異終端滑模面,針對(duì)系統(tǒng)中存在未知邊界的擾動(dòng)與不確定性設(shè)計(jì)了自適應(yīng)控制器,使誤差系統(tǒng)在有限時(shí)間內(nèi)到達(dá)平衡點(diǎn),并應(yīng)用Lyapunov穩(wěn)定性理論證明其穩(wěn)定性。運(yùn)用Matlab-simulink對(duì)于三維分?jǐn)?shù)階Chen混沌系統(tǒng)進(jìn)行數(shù)值仿真;在不消除非線性項(xiàng)的情況下,設(shè)計(jì)了一種自適應(yīng)滑�？刂破�,并證明了其穩(wěn)定性。最后對(duì)于四維分?jǐn)?shù)階Lorenz系統(tǒng)進(jìn)行數(shù)值仿真,證實(shí)了控制器的可行性。3.對(duì)分?jǐn)?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(gòu)建模型,對(duì)線性部分進(jìn)行動(dòng)態(tài)柔性變結(jié)構(gòu)控制器的設(shè)計(jì),而對(duì)于非線性部分則進(jìn)行自適應(yīng)滑�？刂破鞯脑O(shè)計(jì),并運(yùn)用分?jǐn)?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(duì)與三維分?jǐn)?shù)階Chen系統(tǒng)進(jìn)行仿真,證實(shí)了柔性變結(jié)構(gòu)同步控制器的優(yōu)勢(shì)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(xué)位授予單位】：東北石油大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O415.5;TP273
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本文編號(hào)：2080359