Identifying chaotic systems using a fuzzy model coupled with a linear plant

In this paper, a model for identifying chaotic systems is derived from the theory of a feed-forward neural network with three layers. One part of the derived model has the form of a fuzzy logic-based intelligent mechanism; the other part is a linear difference equation, similar to the Wiener-type cascade structure. Three dynamical systems are presented to demonstrate the effectiveness of the proposed model: a one-dimensional logistic map, two-dimensional Hénon map and the continuous-time pendulum system. For both discrete-time and continuous-time chaotic systems, the proposed model always takes the form of a difference equation. Numerical simulations show that the proposed model can well identify the dynamical systems. Time series and time-delayed pseudo-phase plane plots are drawn for both the dynamical systems and the proposed model.