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Researches On Synchronization Of Fractional-order Chaotic Systems

Posted on:2013-08-11Degree:DoctorType:Dissertation
Country:ChinaCandidate:N SunFull Text:PDF
GTID:1220330467482730Subject:Control theory and control engineering
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Chaos is ubiquitous in nature and social sciences. Since the early20th Century, chaos theory, with its inner high randomicity and hyper sensitivity to initial con-ditions, has attracted the attention of lots of scholars. Since1990, the application of chaos control and synchronization have been especially found use in secure com-munications, signal progressing, image progressing areas, and have been spreading to other fields. Controlling and synchronizing chaos has become one of the focus in the nonlinear science research, and lots of remarkable results about integer order chaos synchronization have been constructed recently. As a tool of long history, the fractional calculus can describe the complex phenomena in the real world more accurately and efficiently. Therefore, many researchers start to study the control and synchronization of factional-order chaotic systems.So far, the stability theory of the fractional-order systems is still imperfect, and synchronization of fractional-order chaotic systems is a new challenge. In this dissertation, several problems about synchronizing fractional-order chaotic systems are studied, such as the complete synchronization, symmetric synchronization, pro-jective synchronization, chaotic synchronization with uncertain parameters, the stability criterion of nonlinear fractional-order systems and the circuit realization of synchronization of fractional-order hyperchaotic systems. The main contributions of this dissertation are as follows:1. Chaos is first found in one fractional-order four-dimensional energy resources system. The new synchronization controller for fractional order chaotic sys-tems is designed by activation feedback method. After that, for the prob-lems in synchronization control of a class of autonomous/non-autonomous fractional-order chaotic systems, a new controller design method is proposed. The nonlinear terms of the error systems are divided into stability-related part and stability-unrelated part, only the stability-related nonlinear terms are ab-sorbed by the designed controller. Therefore, the structure of the controller will become simplified. At last, how to utilize the symmetries of the chaotic systems to generate different synchronization patterns without altering the controllers’structure is studied. The definition of the symmetric synchroniza- tion and the necessary and sufficient condition of symmetric synchronization are derived.2. A new fractional-order hyper chaotic system is practised in a circuit simulation by using the tech of time-frequency regions. Generalized synchronization of fractional order chaotic systems based on nonlinear observer theory is realized. A state observer is designed on the bases of pole assignment and the stability theory of linear fractional-order system to realize the generalized synchroniza-tion between the arbitrary linear nonsingular transformation of the observer’s state and the state of the fractional-order hyper chaotic system. Thus the conventional modes of synchronization, e.g., the complete synchronization, anti-synchronization and projective synchronization are all available. Numer-ical simulation and circuit simulation realization verified the effectiveness of the method proposed,3. For the projective synchronization problem of a class of non-autonomous fractional-ordr chaotic systems with uncertain parameters and external distur-bance, a new sliding mode controller design method and a new synchronous criterion are proposed. Then, for the projective synchronization problem of a class of autonomous fractional-order hyper chaotic systems with external dis-turbance, new active sliding mode variable structure controller combined with fractional-order integral surface and the exponential reaching law is proposed. The chattering of sliding mode control is reduced by the design of boundary layer, and the controller can achieve synchronization with error bound. Based on the sliding mode control, some new synchronous criteria are proposed. The simulation results show the effectiveness of the controller and keep the system with strong robustness.4. Synchronization of fractional interval chaotic systems is investigated by de-signing a novel nonlinear active feedback controller. Two novel sufficient sta-bilization criteria for fractional-order interval chaotic systems are proposed in terms of the stability theory of interval fractional order linear time-invariant systems and linear matrix inequality technique. The numerical simulation results verify the effectiveness of the proposed schemes.5. To the stability analysis problem of nonlinear fractional-order systems, a sim-pler method is proposed. The definition of the generalized Caputo fractional derivative is proposed, and then the scalar comparison principle and the vec-tor comparison principle are constructed, respectively. After that, a Lya-punov theorem for analyzing the stability of nonlinear fractional-order sys-tems is achieved. At last, a discussion on using this theorem in stabilization is provided. Three examples are presented to illustrate how to stabilize and synchronize the chaotic fractional-order systems with that method in simpler way.
Keywords/Search Tags:fractional chaotic system, chaotic synchronization, active control, symmetric synchronization, fractional-order integral sliding surface, generalized Ca-puto fractional derivative, comparative principle, stability of nonlinear fractional-order systems
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