Control of chaotic systems with time delayed feedback control

Abstract

Delayed Feedback Control (DFC) method proposed by Pyragas is a simple and efficient method to control chaotic systems by stabilizing the Unstable Periodic Orbits (UPOs) of these systems. Assuming that a UPO with period T has been chosen as the target, the basic idea of DFC method is to apply a control input proportional to the difference between the current state and the state one period (T) ago. This idea is improved by using the information from many previous states by Extended Delayed Feedback Control (EDFC) method. The drawbacks of DFC and EDFC methods are eliminated by Unstable Extended Delayed Feedback Control (UEDFC) method by introducing an unstable degree of freedom into the feedback loop. In this M.S. Thesis, the theory of time delayed feedback control and its derivatives are investigated in detail. Additional to applications of DFC and UEDFC methods to various chaotic maps and chaotic flows, some contributions have been made by introducing algorithms that adjust some parameters (like threshold, multiplier) which are usually selected by trial and error by the user. While applying DFC and UEDFC methods to chaotic flows, delayed feedback control is applied to only one of the output variables, which is the observer of the chaotic system, whereas additive feedback control is applied to all states of the system while applying DFC method to chaotic maps. It has been observed that successful stabilization of chaotic systems is achieved in both of the cases.