Feedback Control Method Based on Predicted Future States for Controlling Chaos

Abstract

A chaos control method is proposed on the basis of a combination of the prediction-based feedback control [13, 14] and the method of analogues [17] which is one of the nonlinear time series analysis for the prediction of chaotic time series. Control inputs for the prediction-based feedback control are based on the exact future states in a system without control inputs. Generally, it is quite difficult to know the exact future states in a chaotic dynamical system without the perfect model. In order to avoid the difficulty, we introduce control inputs based on the predicted future states with the method of analogues in stead of the exact future states. One of the advantages of our control method is that we need not the exact future states in a system but only time series data in the system without control inputs. Thus, the method can be widely applied to real-world systems, if we obtain time series data of the systems. In this chapter, the method is applied to simple chaotic systems, i.e. the logistic map and the Hénon map, in order to verify the method.