Chaotic Nonlinear Systems, Intelligent Control Method

Based on the understanding of characters about the chaotic nonlinear dynamical systems, intelligent control methods for chaotic nonlinear systems are presented.Firstly, the artificial neural networks of BP and its improved algorithms which are both simple, direct in structure and algorithm, and also full-grown in the research and apply field is employed. The controlling algorithm used for training the network is based on the chaos control scheme developed by Ott,Grebogi and Yorke. According to the linear and nonlinear functions, the networks is trained to generate small disturbance time series signals necessary for suppression nonlinear chaotic motion as chaos controller. The two-dimensional Henon chaotic nonlinear map is effectively controlled by the proposed approach.Secondly, because of the distinguished advantages, such as rapid convergency and strong approachability, the RBF networks is trained as chaotic controller by OGY scheme, then successful of controlling the Henon chaotic map. In view of chaotic systems composed of a sum of a linear and nonlinear part, a compensative control method using radial basis function networks is proposed, the RBF networks trained can eliminate the nonlinear part of the chaotic system, the resulting system is dominated by the linear part. Then, a linear state-feedback controller designed is used to suppress the system to a desirable position. The simulations on the Lorenz equation and Duffing oscillator show the effectiveness of the proposed method.Thirdly, based on input-output data obtained from the underlying dynamical system, modeling and its control for an uncertain chaotic system are studied. Using Gaussian fuzzy membership functions in conjunction with the least-squares principle, a novel approach is developed for intelligent fuzzy modeling and adaptive control strategy of uncertain chaotic system. The theoretical analyses and simulation results show that while modeling the forecasting error is minimal with the proposed methodology, the controlled system is of rapid response and robustness.At last, a novel hybrid neural fuzzy inference system is presented. Only based on the desired input-output data pairs, both knowledge acquisition and initial fuzzy rule sets are available. Then employing neural networks learning techniques, fuzzy logic rules, input-output fuzzy membership functions and weights in networks can be easily tuned. So rule matching is reduced,inference process is accelerated, adaptability of the system is greatly improved. To illustrate the performance of the proposed neuro-fuzzy hybrid model, Simulations on chaotic Mackey-Glass time series prediction are performed. Combined either off-line or on-line learning with the proposed hybrid model, the results show the chaotic Mackey-Glass time series are accurately predicted, also demonstrate the effectiveness of the method proposed.