A delayed feedback based practical chaos control method: Tail aperture feedback

Abstract

Control of chaotic systems has been one of the central issues in the field of chaotic dynamics since early 1990s. A particularly simple and practical method is the Delayed Feedback Control (DFC) introduced by Kestutis Pyragas, to stabilize chaotic systems at an Unstable Periodic Orbit (UPO). The basic idea of the DFC method is to apply an additive control input that is proportional to the difference between the current state and the state of the system delayed by the period of the target UPO. Since the DFC method only requires the knowledge of the period of the UPO, it has attracted great interest and has been applied to many systems. To render the method even more feasible and applicable various modifications and extensions of the original DFC have been presented in the literature. In this thesis, a practical variant of the DFC, namely the Tail Aperture Feedback (TAF) method has been proposed that combines the basic approach of the DFC with some ideas borrowed from the OGY type chaos control. A practical procedure has been introduced for selecting the relevant parameters and applying the TAF method. More over, an original sparsification method has been presented which reduces the stored data. The performances of basic DFC method and the TAF method have been com pared and the improvement provided by the sparsification method has been demon strated on basis of simulation results.