Using add-order method to translate the problem of generalized synchronization of different orders of chaotic systems into the synchronization of systems of identical order. Based on Lyapunov stability theory and adaptive control method, we give the expression of adaptive controller and the updating rule of parameters, then achieve generalized synchronization of different order of chaotic systems with unknown parameters and enable the estimation of the parameters of the drive and the response systems. This method has been applied to solve the generalized synchronization problem of hyperchaotic Lü system, Lorenz system, generalized Lorenz system, and Liu system with unknown parameters. It is proved theoretically that this method is feasible. Numerical simulations show the effectiveness of the adaptive control technique.
This paper presents a method of controlling gyro system based on bounded damping feedback. Firstly,using LaSalle invariable theorem,a stability analysis is given theoretically. Then by introducing a two order Butterworth lowpass filter,a feedback controller is proposed on the basis of measured signals. The chaotic gyro system can be stabilized to different periodic obits or fixed points in the numerical simulation. Furthermore,the effects of control parameter and noise are investigated. The results show that the implementation of this control method is simple and easy. In addition,the controller has strong robustness against weak external noise.
In this paper, the problem of lag synchronization for a class of chaotic systems with unknown parameters is proposed. Based on Lyapunov stability theory, lag controller and update law of parameters are obtained. This method is simple and systemic. A new chaotic system is taken as an example to illustrate the effectiveness of this proposed method. Numerical simulation illustrates the feasibility of this technique. To demonstrate the robustness against the effective of bounded noise of the proposed control strategy, it is applied to the new system and perfect simulation results are obtained.
The Euler's dynamical equation which describes the attitude motion of a perturbed rigid spacecraft is studied. A series of chaos systems is found from Euler's dynamical equation by selecting different parameter matrixes of perturbed torque. Based on the Lyapunov function, adaptive controller is designed such that the chaos control of unknown parameters of this system is accomplished, the state variables go to any appointed equilibrium points, and the unknown parameters are estimated simultaneously. Finally, the Newton-Leipnik system as an example is considered here to demonstrate the proposing technique. Simulation results show the feasibility and efficiency of this method.
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