Title :
Tracking unstable periodic orbits in chaotic systems via time delayed feedback control
Author :
Yu, Xinghuo ; Chen, Guanrong
Author_Institution :
Central Queensland Univ., Rockhampton, Qld., Australia
Abstract :
A time-delayed feedback control (TDFC) system is by nature a rather special version of the familiar autoregressive moving-average (ARMA) control, or the canonical state-space control systems. Despite some of its inherent limitations, TDFC can be quite successful in many chaos control applications. To understand to what extent the TDFC method is useful, some analytic (sufficient) conditions for chaos control from the TDFC approach are derived in this paper, for both stabilization and tracking problems. A gradient descent based search algorithm is incorporated with the TDFC to estimate the time delay constant for tracking unstable periodic orbits. The established theoretical results and estimation method are further clarified via a case study of the typical chaotic Rossler system with computer simulations
Keywords :
autoregressive moving average processes; chaos; delays; feedback; gradient methods; periodic control; search problems; stability; state-space methods; tracking; ARMA control; TDFC; autoregressive moving-average control; canonical state-space control systems; chaos control applications; chaotic Rossler system; chaotic systems; gradient descent based search algorithm; time delayed feedback control; unstable periodic orbit tracking; Centralized control; Chaos; Chaotic communication; Control systems; Delay effects; Delay systems; Feedback control; Force control; Orbits; Target tracking;
Conference_Titel :
Decision and Control, 1998. Proceedings of the 37th IEEE Conference on
Conference_Location :
Tampa, FL
Print_ISBN :
0-7803-4394-8
DOI :
10.1109/CDC.1998.758603
