| Chaos, as a dynamic phenomen only in nonlinear dynamical systems, is widely exist invarious fields such as biology, mathematics, physics, mechanics, chemistry, electronics,information science and so on. Chaos has attracted attentions of many scholars in all fields and alot of achievements are made in the chaos research.With the fast development of computer andcommunication networks, we have entered the information age. Information security has becomeincreasingly important, especially in the military field. Chaos signal is especially suitable forsecure communications because of the dynamic properties of it such as ergodicity, highrandomicity, continuous broadband spectrum, noise-like characteristics and highly sensitivity toinitial conditions. So chaos control and synchronization has become a very hot topic in chaosscience due to its potential application in secure communication. Fractional calculus is theextension of integer order calculus to arbitrary order calculus. Because of the dynamicbehaviours are closely related to the system order and the historical memory effect for fractionaloperator, the dynamic behaviours has a better reaction to engineering phyics.The mian contents in this paper are as follows:Firstly, the paper introduced basic concepts for chaos, the characteristics of chaos and themethods in chaos control and chaos synchronization. And the definition, character, stability andnumerical algorithms of the fractional system are given. By using the time-domain solution basedon the MATLAB simulation platform, the bifurcations and chaotic behaviors of Lorenz systemwere analyzed and discussed numerically by means of phase portraits, bifurcation diagrams.Then fractional calculus theory is introduced to the chaos linear feedback control of Lorenzsystem. And the controlled system's stability is analyzed. Numerical simulation results show thatthe method can effectively guide the chaotic system to a stable equilibrium point. The controlmethods of fractional linear feedback is more flexible then the integer linear feedback.Secondly, by studying the characteristics of fractional-order exponential curves, thefractional calculus is introduced in the classical integer-order exponential sliding mode controllaw. This paper take Lorenz system as object. On the basis of variable structure control theory, byusing the fractional-order exponential approach law technology, a sliding mode synchronouscontroller is designed based on P-C synchronous theory. It realizes the system gradualsynchronization of chaos with the same structure. By adjusting the order and coefficientk1,k2of the fractional-order approach law, the performance of chaotic synchronization control can beimproved. The control method is also more flexibility and effectiveness. Simulation results showthat the control offers shorter synchronous time comparing with traditional sliding mode controland the overshoot of system is smaller. Moreover, the text propose that a new control methodwhich can switch on the coefficient when the system is in the process of control. The control method relieve the sliding mode chattering phenomenon in the discontinuous switch controller toa certain extent and improve the control precision.Finally, according to the three different methods, we design the Lorenz chaotic analogcircuit, construct the corresponding circuit and simulate with Multisim10, The systemparameters correspond with the circuit element parameters. By regulating the variable resistor inthe circuit, dynamic behaviors of the simplified Lorenz chaotic circuits, including limit cycle,pitchfork bifurcation, period-doubling bifurcation, chaos, and the route to chaos byperiod-doubling bifurcation, were observed in the oscilloscope. Then through the dSPACEcontrol experimental platform, we achieve the fractional-order chaos control of the simplifiedLorenz chaotic circuits. |
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