Chaotic Neural Network Control Method Based On Genetic Algorithm Optimization

There are great theoretic and practical values in researching chaos and chaos controlling. A new kind of methods is presented for controlling chaotic dynamical systems using Radial Basis Function (RBF) neural networks based on Genetic Algorithms (GA's), called GANN learning method. With the general-purpose stochastic search capability, GA's optimize the neural network's structure parameters, and with the strong nonlinear approaching character, the neural network can learn to produce a series of small perturbations to convert chaotic oscillations of a dynamical system into a periodic orbit. An entirely unsupervised learning strategy is adopted directly so that the system knowledge is not need to be realized in advance. In some real-world physical chaotic systems, it is difficult to determine the key parameters, so the proposed method can be applied to more practical situations. The algorithm convergence performance has been analyzed carefully and the proofs have been given. Computer simulations have been also conducted to control two chaotic systems, i.e., the Henon map and the logistic map. The results indicated that this method is effective.The main contents of this thesis are as follows:(1) The main concepts of chaos and the key methods of controlling chaos are discussed. The new research about this advanced research area is also summarized based on the demand of our tasks.(2) Applying GA, which has general-purpose optimization trait, to the neural networks' learning, a new method for controlling chaotic system called GANN controlling method is proposed.(3) The convergence of the GANN controlling system is analyzed and proved so as to determine the feasibility of this new method theoretically.(4) A new kind of modified adaptive GA is presented. In this algorithm, a new operator called simplification is applied.(5) Applying this modified GA to multimodal function optimization, the simulation results indicates that this method is feasible, and the modified algorithms are applied to GANN controlling system.(6) The multilayer feedforward networks are applied to GANN method so as to construct MFF-GANN controlling system. Its theories and learning algorithms arediscussed, and the simulation experiments for two kinds of typical chaotic systems have been done and the experiment results are analyzed.(7) Applying RBF neural networks to GANN method so as to construct RBF-GANN controlling system, we discuss its theories and learning algorithms, do the simulation experiments for two kinds of typical chaotic system and analyze the experiment results. The two kinds of GANN controlling methods, i.e., MFF-GANN method and RBF-GANN method, are summarized.