Zhang Jia-Shu

Predicting Hyper-Chaotic Time Series Using Adaptive Higher-Order Nonlinear Filter

A newly proposed method, i.e. the adaptive higher-order nonlinear finite impulse response (HONFIR) filter based on higher-order sparse Volterra series expansions, is introduced to predict hyper-chaotic time series. The effectiveness of using the adaptive HONFIR filter for making one-step and multi-step predictions is tested based on very few data points by computer-generated hyper-chaotic time series including the Mackey-Glass equation and four-dimensional nonlinear dynamical system. A comparison is made with some neural networks for predicting the Mackey-Glass hyper-chaotic time series. Numerical simulation results show that the adaptive HONFIR filter proposed here is a very powerful tool for making prediction of hyper-chaotic time series.

FAST EVOLVING MULTI-LAYER PERCEPTRONS FOR NOISY CHAOTIC TIME SERIES MODELING AND PREDICTIONS

A fast evolutionary programming (FEP) is proposed to train multi-layer perceptrons (MLP) for noisy chaotic time series modeling and predictions. This FEP, which uses a Cauchy mutation operator that results in a significantly faster convergence to the optimal solution, can help MLP to escape from local minima. A comparison against back-propagation-trained networks was performed. Numerical experimental results show that the FEP can help MLP better capturing dynamics from noisy chaotic time series than the back-propagation algorithm and produce a more consistently modeling and prediction.

Adaptive nonlinear feedback control of chaotic systems based on reduced parameter quadratic predictors

An adaptive nonlinear feedback-control method is proposed to control continuous-time chaotic dynamical systems, where the adaptive nonlinear controller acts on only one-dimensional error signals between the desired state and the observed chaotic state of a system. The reduced parameter adaptive quadratic predictor used in adaptive feedback cancellation of the nonlinear terms can control the system at any desired state. Computer simulation results on the Lorenz system are shown to demonstrate the effectiveness of this feedback-control method.

Multistage adaptive higher-order nonlinear finite impulse response filters for chaotic time series predictions

A multistage adaptive higher-order nonlinear finite impulse response (MAHONFIR) filter is proposed to predict chaotic time series. Using this approach, we may readily derive the decoupled parallel algorithm for the adaptation of the coefficients of the MAHONFIR filter, to guarantee a more rapid convergence of the adaptive weights to their optimal values. Numerical simulation results show that the MAHONFIR filters proposed here illustrate a very good performance for making an adaptive prediction of chaotic time series.

Adaptive higher-order nonlinear FIR filter prediction of spatiotemporal chaotic time series

Based on the Volterra expansion of nonlinear dynamical system functions and the deterministic and nonlinear characterization of the chaotic signals, an adaptive higher-order nonlinear FIR (HONFIR) filter is proposed to perform prediction of spatiotemporal chaotic time series. The TDO algorithm is used to update the filters coefficients. A higher-order nonlinear adaptive filtering scheme is suggested in order to track the current chaotic trajectory by using the preceding predictive error for adjusting filter parameters rather than approximating the global or local map of the chaotic series. Experimental results show that this adaptive HONFIR filter can be successfully used to predict spatiotemporal chaotic time series generated by a globally coupled map (GCM), a two-way coupled map (TCM) and a single-way coupled map (SCM).