A Study on Predictive Control Using a Short-Term Prediction Method Based on Chaos Theory. Extension of a Short-Term Prediction Method Based on Chaos Theory and its Application to a Predictive Control Method for a System with Unknown Output.

Abstract

The main objective of this study is an application of a short-term prediction method of time series based on chaos theory to vibration control for mechanical systems. In this paper, a short-term prediction method based on the Takens's theorem was simply developed. Then the method was extended to apply to the wider range. Finally by utilizing the extended prediction method, two predictive control methods were developed for dynamic systems. It was shown by the numerical example using the Henon map that there are the optimal range of the number of data to be used in prediction. Through the numerical examples of control problems, it is seen that the performance of the proposed control method was improved in comparison with conventional feedback control methods and also seen that the introduction of the predictive control observed in the motions of human being became very effective.