Time-delayed feedback control in astrodynamics

Abstract

In this paper we present time-delayed feedback control for the purpose of autonomously driving trajectories of nonlinear systems onto periodic orbits. As the generation of periodic orbits is a major component of many problems in astrodynamics, 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. First, time-delayed feedback control is applied to control the chaotic attitude motion of an asymmetric satellite in an elliptical orbit. Second, we apply timedelayed feedback control to the problem of maintaining a spacecraft in a periodic orbit about a body with large ellipticity (such as an asteroid). Third, we apply time-delayed feedback control to eliminate the drift between two satellites in low Earth orbits to ensure that their relative motion is bounded