| Many chaos control techniques have been developed over the last decade. In particular, there has been some significant progress in the studies of identification, control, and utilization of chaos by artificial intelligence methods such as neural networks and fuzzy logic. In this research, we propose a new predictive fuzzy control method using only time-series data. A one-pass predictive fuzzy control scheme is developed for controlling an unknown chaotic system. The parameters of the membership functions in the fuzzy modeling and predictive control algorithm are automatically determined according to the designed adaptive mechanism for the purpose of controlling the unknown system states to desired targets. The main features and advantages of this predictive fuzzy control strategy include the following: (1) It guarantees the estimates be bounded by the limit of the observed samples. (2) The coefficients in the fuzzy model are determined in one pass through the data set (no iterative calculation is needed), and is a highly parallel structure leading to efficient numerical computations. (3) It reduces a complex problem to a simple least-squares estimation of only a small number of constant parameters. (4) It can reduce the modeling sensitivity to noise. (5) It is particularly suitable for sparse data in a real-time environment, because the predicting surface is instantly defined everywhere, even with only a few available samples. As an application, this method is applied to chaos prediction and control of an unknown system with satisfactory results. This work also discusses the stability issue of predictive fuzzy control systems. Finally, an integrated approach of predictive fuzzy control for uncertain chaotic systems is developed, where the controller is designed based on Lyapunov stability theory. Simulation results show that this control system works very effectively. |
