Reconstruction of piecewise chaotic dynamic using a genetic algorithm multiple model approach

Reconstruction of chaotic dynamics from its time-series measurement is an important problem for many engineering applications. In this paper, we propose using a novel multiple model (MM) predictor based on a genetic algorithm (GA) to reconstruct piecewise chaotic dynamics. The motivation relies on the observation that conventional single model is usually unable to reconstruct the piecewise dynamics properly because a piecewise map is nonsmooth. In our approach, multiple radial basis function (RBF) neural predictors are used to model the piecewise dynamic in different partition intervals. Switching between different intervals could be estimated by a nonlinear gate model. In particular, a GA is employed here to train the MM and to obtain the optimal RBF parameters. Compared to conventional chaos dynamic reconstruction techniques, the proposed GA-MM method is shown to greatly improve the reconstruction performance for piecewise chaotic dynamics. The superiority is further verified by applying the GA-MM method to model the real-life radar sea-clutter signal obtained from Nova Scotia (NS), Canada, and to predict the electric power pool price time series from Alberta (AB), Canada. Both kinds of real data show that the GA-MM is effective in building a dynamical model. The proposed GA-MM method is also applied to the channel equalization problem of chaos communication systems. Based on the minimum nonlinear prediction error equalization method, it is shown that the GA-MM method has a satisfactory equalization performance even under strong channel effects.