Nonlinear Adaptive Prediction Technologies Of Chaotic Signals And Its Applications

The real time or quasi-real time predictions of chaotic signals, nonlinear adaptive filtering technologies and their applications are studied in this paper. Main contents studied include: (1) Study on neural networks modeling of (noisy) chaotic time series and their applications; (2) Nonlinear adaptive predictions of chaotic signals, and the nonlinear adaptive prediction performance of chaotic signals; (3) Some new nonlinear adaptive (predictive) filters and nonlinear NLMS algorithms; (4) Nonlinear adaptive predicting control and synchronization methods of chaotic systems; (5) Study on new prediction methods for frequency series prediction of frequency agile radar. Several valuable and important results which bring forth new ideas are achieved and listed as following: 1. Neural networks modeling and prediction of (noisy) chaotic time series: (1) To account for performing inconsistently for reconstructing strange attractor by MLP BP-trained, a fast evolutionary programming (FEP) is proposed to train MLP for noisy chaotic time series modeling and predictions. Simulation results show that the FEP can help MLP better capture dynamics from noisy chaotic time series than the BP algorithm and produce more consistently modeling and attractor predictions. (2) RLS algorithm and the simplified RNN are proposed to make the multi-step prediction for chaotic signals based on few data, numerical results show that the proposed R.NN is a very powerful tool for making multi-step prediction for chaotic signals. (3) A neural network based method is proposed to design chaotic signal generator that can be synchronized by the nonlinear feedback methods. This chaos generator can produce many kinds of chaotic signals by means of switching different synapse weights of neural networks. (4) A new chaotic secure communication scheme is proposed based on parameter modulation and chaotic-map-switching, the neural network chaos generators and an extended chaotic map 醝e used to implement this secure scheme. Simulation results show that this secure communication scheme can better recover information signals while SNR> 10 dB, and has better security than that based on single chaotic map or system. 2. Nonlinear adaptive prediction of chaotic signals, which is a new concept that is clearly different from the chaotic prediction theory based on phase space, is proposed. (1) Nonlinear adaptive prediction scheme can make real-time or quasi-real-time prediction of chaotic time series and meet the engineering demands with adaptively updating nonlinear predictor抯 coefficients. The adaptive algorithms enable the predictor to track current chaotic trajectory by using current predictive error for adjusting filter parameters rather than approximating global or local map of chaotic series. Nonlinear adaptive prediction technologies demand less datum and shorter time to train predictors than global prediction methods, and are of better prediction performance. (2) The input dimension of nonlinear adaptive predictor is not limited by die Takens? embedding dimension. The proposed nonlinear adaptive prediction methods can effectively predict chaotic signals under ill-embedding condition. (3) Nonlinear adaptive predictions of hyper-chaotic and spatio-temporal time series are studied first time. The nonlinear adaptive prediction performance of hyper-chaotic and spatio-temporal time series is only determined by the nonlinear approximation of predictors and its adaptive algorithm. Due to diversity of chaotic c...