A multi-objective genetic programming/NARMAX approach to chaotic systems identification

A chaotic system identification approach based on genetic programming (GP) and multi-objective optimization is introduced. NARMAX (Nonlinear Auto Regressive Moving Average with exogenous inputs) model representation is used for the basis of the hierarchical tree encoding in GP. Criteria related to the complexity, performance and chaotic invariants obtained by chaotic time series analysis of the models are considered in the fitness evaluation, which is achieved using the concept of the non-dominated solutions. So the solution set provides a trade-off between the complexity and the performance of the models, and derived model were able to capture the dynamic characteristics of the system and reproduce the chaotic motion. The simulation results show that the proposed technique provides an efficient method to get the optimum NARMAX difference equation model of chaotic systems.