Research On Chaos Control

This thesis is concerned with problems of chaos control.This world is full of chaos because of non-linear. It is usually deleterious when there appears chaos in the systems owing to chaos uncertainty, therefore, it is necessary to control chaos if chaos exists; On the other hand, chaos contains much information, but the trajectory of chaos attractor is almost unstable, rapidly variational and hard to hold on. The saved information is easy to alternate, so it is unuseful unless chaos is under controlled.Chaos control has attracted a great deal of attention from non-linear and this problem is also a complex problem of nonlinear. In this thesis, two control methods are proposed by analyzing the limitation of former control methods.Neural network is well capable of learning non-linear model. In this thesis, RBF neural network, which has rapid convergence property, is used to control chaos. RBF neural network learns the chaos system without analytic model by input and output data of the system, then controller is designed based on Lyapunov method. In this thesis, the proof is proposed that the control precision could besatisfied if the RBF NN model has enough precision. Simulation results show chaos control method based on RBF neural network can control chaos without analysis model. The method is still effective when there exists parameter perturbation and measurement noise.Because the state and the control value in the control process are limited in practice, the chaos control method based on the least energy is proposed in this thesis. The two-level algorithm that is used to solve large non-linear systems is amended. In the first level, the nonlinear system becomes linear system by estimating some variables and the linear optimize is easy to obtain by dynamic programming. In the second level, those variables are revised and estimated again. The optimizing ends until those variables estimated don't change. This method consumes least energy. Simulation results with Logistic mapping and Henon attractor show that this method is effective.