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Predictive Control And Synchronization Of Fractional-Order Chaotic Systems

Posted on:2017-04-18Degree:MasterType:Thesis
Country:ChinaCandidate:Z L JiFull Text:PDF
GTID:2180330488494338Subject:Control engineering
Abstract/Summary:PDF Full Text Request
Chaotic systems have extremely complex singularities, and thus its effective control is the key step in the study of chaos theory. Control and Synchronization of integer order chaotic systems has been relatively more mature, but it’s just an ideal treatment for complex problems. With the rapid development of modern computer technology and the theory of fractional order calculus to be increasingly mature, the research of the control and synchronization of the integer order chaotic systems has also gradually extended to fractional order. However, many experts and scholars found the control and synchronization of fractional order chaotic systems can objectively reflect the real problem. Particularly, the fractional order chaotic systems reflects the huge advantages and potential application value in image encryption, physics, chemistry, mathematics, biology and other field of engineering. At present, most research on the fractional order chaotic systems focus on these several fields:the research on synchronization control of fractional order chaotic system, image encryption of fractional order chaotic systems, synchronization of fractional order chaotic systems and its application in secure communication, the research on fractional order hyper chaotic systems and so on. In this paper, we propose a new method for the control and synchronization of fractional order chaotic systems, combining theoretical proof and numerical simulation, we do some theoretical study and simulation on the problem of the control and synchronization of fractional order chaotic systems.We mainly achieved the following results:1. Stabilizing an unstable equilibrium point in a fractional-order chaotic system is studied using prediction-based feedback method in this paper. Sufficient conditions for stabilization of equilibrium points are explicitly given and rigorously proven. The proposed approach is easy to be used, even if a prior information of the system itself and any externally generated control signal are unavailable. Numerical simulations show the effectiveness of the method.2. Fuzzy predictive feedback control method are proposed to realize the synchronization of fractional order chaotic systems. Based on the Lyapunov stability theory of fractional-order chaotic system, Sufficient conditions for the global asymptotic synchronization of fractional order chaotic systems are explicitly given and rigorously proved. Numerical simulations show the effectiveness of the proposed method.3. the local stability of the fractional order chaotic systems at various equilibrium points is analyzed using the stability theory of fractional order linear systems. Feedback control is designed to realize chaos control of the fractional order chaotic system according to fractional order Routh-Hurwitz criterion, and provide the sufficient conditions suppressing chaos to a unstable equilibrium point. Combining inverse synchronization with lag synchronization, a novel fractional order inverse lag synchronization method is proposed.A corresponding nonlinear controller is designed to reach the inverse lag synchronization of fractional order Chen system. Numerical simulation shows effective and feasibility of the proposed method.
Keywords/Search Tags:Fractional-order calculus, Stability theory, of fractional order system, Predictive control and synchronization, T-S fuzzy model, Routh-Hurwitz criterion
PDF Full Text Request
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