Control Research Of Synchronization Of Chaotic Systems

Research on chaos is one of the important achievements in nonlinear science. Chaotic motion is a complex motion, whose equation is certain but the trajectory of the orbits is stochastic. There are lots of chaotic phenomena in real world. For oddities of chaos, uncontrolled chaos will not be applied, so chaos control is the first step of chaos application. Chaos control and chaos application have already become hot field in nonlinear science.In this paper, we present some techniques for the control and synchronization of chaotic continuous system from the viewpoint of classical control theory.(1)Based on the Tagaki-Sugeno (TS) fuzzy model representations of chaotic systems, a simple but effective control method of the generalized projective synchronization problem of chaotic systems is proposed in this paper. The advantage of the proposed approach is that it allows to express the generalized projective synchronization problem as a fuzzy logic observer design in terms of linear matrix inequalities (LMI), which can be solved numerically using readily available matlab software packages. The effectiveness of the proposed generalized projective synchronization method is illustrated through numerical simulations of the Lorenz system.(2)This paper is concerned with the generalized projective synchronization problem of discrete chaotic systems. Based on Takagi-Sugeno (TS) fuzzy dynamical models and the Lyapunov stability theory, a sufficient condition is derived for the generalized projective synchronization of discrete chaotic systems. By using some matrix operation techniques, this criterion is then transformed into linear matrix inequalities (LMI) form, which can be solved numerically using readily available Matlab software packages.(3)This paper presents hybrid projective synchronization between two different chaotic, when the parameters of the drive and response systems are unknown or uncertain. Based on the Lyapunov stability theory , hybrid projective synchronization of two different chaotic systems is realized using an adaptive control method. The proposed technique is applied to achieve hybrid projective synchronization for the Lüand Lorenz dynamical systems, Numerical simulations are presented to verify the effectiveness of the proposed scheme.(4)In this work, a new control method based on dynamical neural network for modeling unknown nonlinear chaos systems is presented. In the chaos modelling phase, a neural network is trained on the unknown chaos system. Then, a control mechanism has been implemented with the neural network to direct the chaos states towards desired target. Also, rigorous mathematical proof is given to analyze the stability properties of the system.