11,206 research outputs found
Controlling Chaos Faster
Predictive Feedback Control is an easy-to-implement method to stabilize
unknown unstable periodic orbits in chaotic dynamical systems. Predictive
Feedback Control is severely limited because asymptotic convergence speed
decreases with stronger instabilities which in turn are typical for larger
target periods, rendering it harder to effectively stabilize periodic orbits of
large period. Here, we study stalled chaos control, where the application of
control is stalled to make use of the chaotic, uncontrolled dynamics, and
introduce an adaptation paradigm to overcome this limitation and speed up
convergence. This modified control scheme is not only capable of stabilizing
more periodic orbits than the original Predictive Feedback Control but also
speeds up convergence for typical chaotic maps, as illustrated in both theory
and application. The proposed adaptation scheme provides a way to tune
parameters online, yielding a broadly applicable, fast chaos control that
converges reliably, even for periodic orbits of large period
Time-delayed feedback control in astrodynamics
In this paper we present time-delayed feedback control (TDFC) for the purpose of autonomously driving trajectories of nonlinear systems into periodic orbits. As the generation of periodic orbits is a major component of many problems in astodynamics we propose this method as a useful tool in such applications. To motivate the use of this method we apply it to a number of well known problems in the astrodynamics literature. Firstly, TDFC is applied to control in the chaotic attitude motion of an asymmetric satellite in an elliptical orbit. Secondly, we apply TDFC to the problem of maintaining a spacecraft in a periodic orbit about a body with large ellipticity (such as an asteroid) and finally, we apply TDFC to eliminate the drift between two satellites in low Earth orbits to ensure their relative motion is bounded
Adapting Predictive Feedback Chaos Control for Optimal Convergence Speed
Stabilizing unstable periodic orbits in a chaotic invariant set not only
reveals information about its structure but also leads to various interesting
applications. For the successful application of a chaos control scheme,
convergence speed is of crucial importance. Here we present a predictive
feedback chaos control method that adapts a control parameter online to yield
optimal asymptotic convergence speed. We study the adaptive control map both
analytically and numerically and prove that it converges at least linearly to a
value determined by the spectral radius of the control map at the periodic
orbit to be stabilized. The method is easy to implement algorithmically and may
find applications for adaptive online control of biological and engineering
systems.Comment: 21 pages, 6 figure
Controlling spatiotemporal dynamics with time-delay feedback
We suggest a spatially local feedback mechanism for stabilizing periodic
orbits in spatially extended systems. Our method, which is based on a
comparison between present and past states of the system, does not require the
external generation of an ideal reference state and can suppress both absolute
and convective instabilities. As an example, we analyze the complex
Ginzburg-Landau equation in one dimension, showing how the time-delay feedback
enlarges the stability domain for travelling waves.Comment: 4 pages REVTeX + postscript file with 3 figure
Non-abelian plane waves and stochastic regimes for (2+1)-dimensional gauge field models with Chern-Simons term
An exact time-dependent solution of field equations for the 3-d gauge field
model with a Chern-Simons (CS) topological mass is found. Limiting cases of
constant solution and solution with vanishing topological mass are considered.
After Lorentz boost, the found solution describes a massive nonlinear
non-abelian plane wave. For the more complicate case of gauge fields with CS
mass interacting with a Higgs field, the stochastic character of motion is
demonstrated.Comment: LaTeX 2.09, 13 pages, 11 eps figure
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