SearcharxivSearch

arXiv · chao-dyn/9810029

Improved control of delayed measured systems

Abstract

In this paper we address the question how the control of delayed measured chaotic systems can be improved. Both unmodified OGY control and difference control can be successfully applied only for a certain range of Lyapunov numbers depending on the delay time. We show that this limitation can be overcome by at least two classes of methods, by rhythmic control and by the memory methods linear predictive logging control (LPLC) and memory difference control (MDC).

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jens Christian Claussen, Heinz Georg Schuster. 2004-07-30. Improved control of delayed measured systems. https://doi.org/10.1103/physreve.70.056225

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

The Bogdanov Map: Bifurcations, Mode Locking, and Chaos in a Dissipative System

We investigate the bifurcations and basins of attraction in the Bogdanov map, a planar quadratic map which is conjugate to the Hénon area-preserving map in its conservative limit. It undergoes a Hopf bifurcation as dissipation is added, and exhibits the panoply of mode locking, Arnold tongues, and chaos as an invariant circle grows out, finally to be destroyed in the homoclinic tangency of the manifolds of a remote saddle point. The Bogdanov map is the Euler map of a two-dimensional system of ordinary differential equations first considered by Bogdanov and Arnold in their study of the versal unfolding of the double-zero-eigenvalue singularity, and equivalently of a vector field invariant under rotation of the plane by an angle $2π$. It is a useful system in which to observe the effect of dissipative perturbations on Hamiltonian structure. In addition, we argue that the Bogdanov map provides a good approximation to the dynamics of the Poincaré maps of periodically forced oscillators.

chao-dyn

Passive Scalars and Three-Dimensional Liouvillian Maps

Global aspects of the motion of passive scalars in time-dependent incompressible fluid flows are well described by volume-preserving (Liouvillian) three-dimensional maps. In this paper the possible invariant structures in Liouvillian maps and the two most interesting nearly-integrable cases are investigated. In addition, the fundamental role of invariant lines in organizing the dynamics of this type of system is exposed. Bifurcations involving the destruction of some invariant lines and tubes and the creation of new ones are described in detail.

chao-dyn